end_seminars_2019/HW/HW1_solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars/sem_2/yYGiBqtirSM.jpg\" height=\"300\" width=\"300\"> \n",
    "\n",
    "# <center> R для тервера и матстата. <br>  <br> Домашка номер раз! </center>\n",
    "\n",
    "Данный ноутбук является домашкой по курсу «R для теории вероятностей и математической статистики» (РАНХиГС, 2019). Автор ноутбука - [вот этот парень по имени Филипп.](https://vk.com/ppilif) Если у вас для него есть деньги, слава или женщины, он от этого всего не откажется. Ноутбук распространяется на условиях лицензии [Creative Commons Attribution-Share Alike 4.0.](https://creativecommons.org/licenses/by-sa/4.0/) При использовании обязательно упоминание автора курса и аффилиации. При наличии технической возможности необходимо также указать активную гиперссылку на [страницу курса.](https://fulyankin.github.io/r_probability/) На ней можно найти другие материалы. Фрагменты кода, включенные в этот notebook, публикуются как [общественное достояние.](https://creativecommons.org/publicdomain/zero/1.0/)\n",
    "\n",
    "----------------------\n",
    "\n",
    "Приветствую вас внутри первой домашки. У каждой домашки должны быть свои герои (но это не точно). Моими героями являетесь вы! Вы - герои не потому, что я хочу кого-то простебать или обидеть, а потому что, когда любишь, хочется увековечить. Кто-то называет именами любимых людей вновь открытые звёзды и острова, кто-то созданную для нира папку на рабочем столе, а кто-то делает их героями своих историй. Будем искренне верить и надеяться, что я не Джордж Мартин, и в моих историях никто не погибнет. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Краткий брифинг:__\n",
    "\n",
    "\n",
    "* __Дедлайн:__ __12.05.19__\n",
    "* Первая домашка затрагивает то, что мы смотрели на первых двух парах.\n",
    "* Тетрадка делится на две части: __рыбёшки (60 баллов) и кит (40 баллов).__\n",
    "* Часть задач нужно решить не только с помощью симуляций, но и вручную.\n",
    "* Ваша команда пытается решить как можно больше задач и присылает их мне.\n",
    "-------------\n",
    "\n",
    "Ближе к делу. С чего начинается любой скрипт? Правильно! С подгрузки пакетов :) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(\"ggplot2\")  # Пакет для красивых графиков \n",
    "library(\"grid\")     # Пакет для субплотов\n",
    "\n",
    "# Отрегулируем размер картинок, которые будут выдаваться в нашей тетрадке\n",
    "library('repr')\n",
    "options(repr.plot.width=4, repr.plot.height=3)\n",
    "\n",
    "# Внимание! Если вы делаете дз в Rstudio, то вам не нужны пакеты grid, repr и т.п.\n",
    "# Вам нужен только пакет ggplot2! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Полезные функции:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 2\n",
       "3. 2\n",
       "4. 2\n",
       "5. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 2 2 2 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rep(2, 5)  # повторяет число 2 целых 5 раз"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>0.2</li>\n",
       "\t<li>0.4</li>\n",
       "\t<li>0.6</li>\n",
       "\t<li>0.8</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 0.2\n",
       "\\item 0.4\n",
       "\\item 0.6\n",
       "\\item 0.8\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 0.2\n",
       "3. 0.4\n",
       "4. 0.6\n",
       "5. 0.8\n",
       "6. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.0 0.2 0.4 0.6 0.8 1.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seq(0, 1, 0.2)  # выдаёт все числа от 0 до 1 с шагом 0.2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>-1</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item -1\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. -1\n",
       "3. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  1 -1  2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- c(1, 2, 3)\n",
    "y <- c(2, -1, 4)\n",
    "z <- c(3, 5, 2)\n",
    "\n",
    "pmin(x, y, z)   # находит поэлементные минимумы во всех векторах"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3"
      ],
      "text/latex": [
       "3"
      ],
      "text/markdown": [
       "3"
      ],
      "text/plain": [
       "[1] 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "which.max(x) # выдаёт позицию максимума"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>6</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 2 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cumprod(x)  # кумулятивное (накапливающееся) произведение\n",
    "# 1, 1*2, 1*2*3 и тд"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "\t<li>6</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 3\n",
       "3. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 3 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cumsum(x)  # кумулятивная сумма\n",
    "# 1, 1 + 2, 1 + 2 + 3 и тд "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 25\n",
      "[1] 5929\n",
      "[1] 9\n"
     ]
    }
   ],
   "source": [
    "# В R можно писать вот такие пафосные циклы:\n",
    "# item будет по очереди принимать все значения из списка c(5,77,3)\n",
    "# это питоновский стиль написания циклов, привыкайте :)\n",
    "\n",
    "for(item in c(5,77,3)){\n",
    "    print(item^2)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Мелкие рыбёшки\n",
    "\n",
    "В этом разделе вас ждёт много довольно простых задачек. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2]  Задачка 1 (скучная) \n",
    "\n",
    "В R [куча встроенных наборов данных.](https://vincentarelbundock.github.io/Rdatasets/datasets.html) Например, в наборе данных `women` лежит немного данных про рост и вес американских женщин. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>height</th><th scope=col>weight</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>58 </td><td>115</td></tr>\n",
       "\t<tr><td>59 </td><td>117</td></tr>\n",
       "\t<tr><td>60 </td><td>120</td></tr>\n",
       "\t<tr><td>61 </td><td>123</td></tr>\n",
       "\t<tr><td>62 </td><td>126</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " height & weight\\\\\n",
       "\\hline\n",
       "\t 58  & 115\\\\\n",
       "\t 59  & 117\\\\\n",
       "\t 60  & 120\\\\\n",
       "\t 61  & 123\\\\\n",
       "\t 62  & 126\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| height | weight |\n",
       "|---|---|\n",
       "| 58  | 115 |\n",
       "| 59  | 117 |\n",
       "| 60  | 120 |\n",
       "| 61  | 123 |\n",
       "| 62  | 126 |\n",
       "\n"
      ],
      "text/plain": [
       "  height weight\n",
       "1 58     115   \n",
       "2 59     117   \n",
       "3 60     120   \n",
       "4 61     123   \n",
       "5 62     126   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(women,5)  # команда head позволяет посмотреть на\n",
    "               # первые пять строк таблички "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Постройте гистограмму с распределением веса женщин\n",
    "* Постройте эмпирическую функцию распределения для веса женщин\n",
    "* Постройте scatterplot веса и роста\n",
    "\n",
    "Найдите базовые характеристики распределения:\n",
    "\n",
    "* средний вес женщины\n",
    "* медианный вес женщины\n",
    "* дисперсию веса женщины\n",
    "* среднее квадратическое отклонения веса женщин\n",
    "* эмпирические квантили уровня 5%, 50% и 95%. \n",
    "* правда ли, что 50% квантиль совпал с медианой? А почему?\n",
    "* почему я выбрал для этого задания именно этот датасет?  **(За правильный ответ на этот вопрос плюс 4 балла)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = women$weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(x, bins=7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nRK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(women, aes(x = weight)) + stat_ecdf( )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nJEACMUiAAjgGK41ZJgESIAESiH0C/w+bYB1AJ0GwagAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(women$weight, women$height)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "136.733333333333"
      ],
      "text/latex": [
       "136.733333333333"
      ],
      "text/markdown": [
       "136.733333333333"
      ],
      "text/plain": [
       "[1] 136.7333"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "135"
      ],
      "text/latex": [
       "135"
      ],
      "text/markdown": [
       "135"
      ],
      "text/plain": [
       "[1] 135"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(x)\n",
    "median(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "240.209523809524"
      ],
      "text/latex": [
       "240.209523809524"
      ],
      "text/markdown": [
       "240.209523809524"
      ],
      "text/plain": [
       "[1] 240.2095"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "15.4986942614378"
      ],
      "text/latex": [
       "15.4986942614378"
      ],
      "text/markdown": [
       "15.4986942614378"
      ],
      "text/plain": [
       "[1] 15.49869"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var(x)\n",
    "sd(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>5%</dt>\n",
       "\t\t<dd>116.4</dd>\n",
       "\t<dt>50%</dt>\n",
       "\t\t<dd>135</dd>\n",
       "\t<dt>95%</dt>\n",
       "\t\t<dd>160.5</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[5\\textbackslash{}\\%] 116.4\n",
       "\\item[50\\textbackslash{}\\%] 135\n",
       "\\item[95\\textbackslash{}\\%] 160.5\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "5%\n",
       ":   116.450%\n",
       ":   13595%\n",
       ":   160.5\n",
       "\n"
      ],
      "text/plain": [
       "   5%   50%   95% \n",
       "116.4 135.0 160.5 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quantile(x,c(0.05, 0.5, 0.95))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# да правда, она и есть 50% квантиль "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# не буду тут это писать, спросите лично"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2]  Задачка 2 \n",
    "Случайная величина $X$ имеет распределение Пуассона с $\\lambda = 2$. Иногда пишут, что $X \\sim Pois(2)$. С помощью симуляций оцените $P(X > 10)$, $P(X > 10 \\mid X > 5)$, $P(X > 5 \\cap X < 7)$, а также $E(X^7)$ и $E(X \\mid X > 5)$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Решение:__ Всегда, когда генерируете какую-то случайную величину, стаьте `seed` для воспроизводимости. Мало ли я перезапущу ваш код, а там сгенерируется совсем другое... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.999915"
      ],
      "text/latex": [
       "1.999915"
      ],
      "text/markdown": [
       "1.999915"
      ],
      "text/plain": [
       "[1] 1.999915"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(42) # ставьте всегда како\n",
    "\n",
    "n_obs = 10^6 \n",
    "x <- rpois(n_obs, lambda = 2) # сгенерировали выборку\n",
    "\n",
    "mean(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ещё имеет смысл проверить правда ли оценка $\\lambda$ после генерации равна $2$. Если отличается, не очень хорошо. Всегда, когда делаете генерации, чётко следите за тем, что в вашей выборке предпосылки $\\pm$ выполнены."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.2e-05"
      ],
      "text/latex": [
       "1.2e-05"
      ],
      "text/markdown": [
       "1.2e-05"
      ],
      "text/plain": [
       "[1] 1.2e-05"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "8.30822436848067e-06"
      ],
      "text/latex": [
       "8.30822436848067e-06"
      ],
      "text/markdown": [
       "8.30822436848067e-06"
      ],
      "text/plain": [
       "[1] 8.308224e-06"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# P(X > 10)\n",
    "mean(x > 10)\n",
    "# либо \n",
    "1 - ppois(10, lambda = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.000732019764533642"
      ],
      "text/latex": [
       "0.000732019764533642"
      ],
      "text/markdown": [
       "0.000732019764533642"
      ],
      "text/plain": [
       "[1] 0.0007320198"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# P(X > 10 | X > 5)\n",
    "mean(x[x > 5] > 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.012013"
      ],
      "text/latex": [
       "0.012013"
      ],
      "text/markdown": [
       "0.012013"
      ],
      "text/plain": [
       "[1] 0.012013"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# P(X > 5 & X < 7)\n",
    "mean((x > 5) & (x < 7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "13939.332037"
      ],
      "text/latex": [
       "13939.332037"
      ],
      "text/markdown": [
       "13939.332037"
      ],
      "text/plain": [
       "[1] 13939.33"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# E(X^7)\n",
    "mean(x**7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6.34545232721283"
      ],
      "text/latex": [
       "6.34545232721283"
      ],
      "text/markdown": [
       "6.34545232721283"
      ],
      "text/plain": [
       "[1] 6.345452"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#E(X | X > 5)\n",
    "mean(x[x > 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [1] Задачка 3 \n",
    "\n",
    "Предположим, что вы получаете в среднем три спам-письма в день. Какова доля дней, в которые вы получаете пять или больше спам-писем?\n",
    "\n",
    "__Решение:__ Нам дана свобода мыслить, как мы хотим. Предполался примерно такой ход мыслей: спам-письма это случайная величниа - счётчик. Наверное, её логично моделировать распределением Пуассона.\n",
    "\n",
    "Можно было найти вероятность либо через функцию распределения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.184736755476228"
      ],
      "text/latex": [
       "0.184736755476228"
      ],
      "text/markdown": [
       "0.184736755476228"
      ],
      "text/plain": [
       "[1] 0.1847368"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 - P(X <= 4) = 1 - F(4)\n",
    "1 - ppois(4, lambda=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "либо напрямую через вероятности:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.184736755476228"
      ],
      "text/latex": [
       "0.184736755476228"
      ],
      "text/markdown": [
       "0.184736755476228"
      ],
      "text/plain": [
       "[1] 0.1847368"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1 - [P(X = 0) + P(X = 1) + ... + P(X = 4)]\n",
    "1 - (dpois(0, lambda=3) + dpois(1, lambda=3) + dpois(2, lambda=3) + dpois(3, lambda=3) +  dpois(4, lambda=3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [4] Задачка 4\n",
    "\n",
    "Куратор Вова случайным образом с возможностью повторов выбирает $5$ натуральных чисел от $1$ до $100$. После выбора он раздаёт эти числа $5$ второкурсникам. Каждый второкурсник берёт экспоненциальное распределение $Exp(\\lambda_i)$, где $\\lambda_i$ - число, выданное Вовой, и выбрасывает из него случайное число. Получаются случайные величины $X_1, X_2, X_3, X_4$ и $X_5$. \n",
    "\n",
    "После этого Вова собирает все выпавшие числа назад и вычисляет \n",
    "\n",
    "$$ Y_1 = \\min(X_1, \\ldots, X_5), \\qquad Y_2 = \\max(X_1, \\ldots, X_5),$$\n",
    "\n",
    "а также \n",
    "\n",
    "$$ Z = \\frac{Y_1}{Y_1 + Y_2}.$$\n",
    "\n",
    "С помощью симуляций оцените: \n",
    "\n",
    "a) $P(Y_2 > 3 Y_1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_obs <- 10^6\n",
    "\n",
    "x1 <- rep(0, n_obs)\n",
    "y1 <- rep(0, n_obs)\n",
    "y2 <- rep(0, n_obs)\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    x = sample(size=5, x=1:100, replace = TRUE)\n",
    "\n",
    "    cur = rep(0, 5)\n",
    "    \n",
    "    for(j in 1:5){\n",
    "        # важно! вектор иксов - один, их не два! \n",
    "        cur[j] = rexp(1, rate = x[j])\n",
    "    }\n",
    "    \n",
    "    x1[i] = cur[1]\n",
    "    y1[i] = min(cur)\n",
    "    y2[i] = max(cur)\n",
    "}\n",
    "\n",
    "z = y1/(y1 + y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.981148"
      ],
      "text/latex": [
       "0.981148"
      ],
      "text/markdown": [
       "0.981148"
      ],
      "text/plain": [
       "[1] 0.981148"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(y2 > 3*y1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "б) $E(Z)$ и $Var(Z)$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0554776679585527"
      ],
      "text/latex": [
       "0.0554776679585527"
      ],
      "text/markdown": [
       "0.0554776679585527"
      ],
      "text/plain": [
       "[1] 0.05547767"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.00398833853194114"
      ],
      "text/latex": [
       "0.00398833853194114"
      ],
      "text/markdown": [
       "0.00398833853194114"
      ],
      "text/plain": [
       "[1] 0.003988339"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(z)\n",
    "var(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "в) $P(Y_2 > 3 \\cdot Y_1 \\mid Z > 0.5)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0"
      ],
      "text/latex": [
       "0"
      ],
      "text/markdown": [
       "0"
      ],
      "text/plain": [
       "[1] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "usl = z > 0.5\n",
    "sum(usl) # =( "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Неудачно я этот пункт сформулировал :("
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "г) $E(Z \\mid X_1 > 80)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "NaN"
      ],
      "text/latex": [
       "NaN"
      ],
      "text/markdown": [
       "NaN"
      ],
      "text/plain": [
       "[1] NaN"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(z[x1 > 80])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "д) $Corr(Z, Y_1)$, $Corr(Z, Y_2)$, $Corr(Y_1, Y_2)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.537229544680625"
      ],
      "text/latex": [
       "0.537229544680625"
      ],
      "text/markdown": [
       "0.537229544680625"
      ],
      "text/plain": [
       "[1] 0.5372295"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "-0.273661584283053"
      ],
      "text/latex": [
       "-0.273661584283053"
      ],
      "text/markdown": [
       "-0.273661584283053"
      ],
      "text/plain": [
       "[1] -0.2736616"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.0890106998263416"
      ],
      "text/latex": [
       "0.0890106998263416"
      ],
      "text/markdown": [
       "0.0890106998263416"
      ],
      "text/plain": [
       "[1] 0.0890107"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Тут надо было спросить у вас про интуицию, и только потом просить генерить\n",
    "cor(z, y1)\n",
    "cor(z, y2)\n",
    "cor(y1, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "е) постройте гистограмму для случайной величины $Z$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(z, bins=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2] Задачка 5\n",
    "\n",
    "Юра завёл себе две нейросетки и два сервера и начал их обучать. Две нейросети обучаются независимо на двух серверах. Время их обучения $T_1$ и $T_2$ равномерно распределено на отрезке $[1;3]$ (обучение измеряется в минутах). В процессе обучения сервер может упасть. Момент падения сервера $T$ распределён экспоненциально с параметром $\\lambda = 0.3$. Момент падаения сервера не зависит от времени обучения нейросеток. Известно, что одна из нейросетей успела обучиться, а вторая не успела. Какова вероятность того, что $T \\le 1.5$?\n",
    "\n",
    "**Hint:** при решении задачи помните о том, что у вас две нейросетки!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "T1 <- runif(n_obs, min = 1, max = 3)\n",
    "T2 <- 3*runif(n_obs) + 1  # то же самое можно сгенеить вот так\n",
    "\n",
    "T <- rexp(n_obs, rate = 0.3) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Тут генерация на формулу Байеса, но для непрерывных случайных велчин. У нас есть бсесконечное число гипотез, нас интересует отрезок $T \\le 1.5$ для пересчёта :) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.1424"
      ],
      "text/latex": [
       "0.1424"
      ],
      "text/markdown": [
       "0.1424"
      ],
      "text/plain": [
       "[1] 0.1424"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "usl1 = (T1 >= T)&(T2 < T) # Первая не смогла обучиться, вторая смогла \n",
    "usl2 = (T1 < T)&(T2 >= T) # Наоборот \n",
    "\n",
    "# оценка для полной вероятности (кстати говоря, так то она не нужна) \n",
    "mean(usl1 | usl2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.127977528089888"
      ],
      "text/latex": [
       "0.127977528089888"
      ],
      "text/markdown": [
       "0.127977528089888"
      ],
      "text/plain": [
       "[1] 0.1279775"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Находим нужную вероятность \n",
    "mean(T[usl1 | usl2] <= 1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in eval(expr, envir, enclos): объект 'usl1' не найден\n",
     "output_type": "error",
     "traceback": [
      "Error in eval(expr, envir, enclos): объект 'usl1' не найден\nTraceback:\n"
     ]
    }
   ],
   "source": [
    "length(T[usl1 | usl2]) # проверка достаточно ли событий для оценки"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Важно!__ Если вы оцениваете вероятность, как сумму делить на сумму, то тут нужно делить не на `n_obs`, а на `sum(usl1 | usl2)`, так как известно, что одна из нейросетей упала."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.127977528089888"
      ],
      "text/latex": [
       "0.127977528089888"
      ],
      "text/markdown": [
       "0.127977528089888"
      ],
      "text/plain": [
       "[1] 0.1279775"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(T[usl1 | usl2] <= 1.5)/sum(usl1 | usl2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [4] Задачка 6\n",
    "\n",
    "Каждый день Света съедает случайное количество булочек, которое распределено по Пуассону с параметром $10$. Логарифм затрат в рублях на каждую булочку распределён нормально $N(2,1)$. Ксюша каждый день съедает биномиальное количество булочек $Bin(8, 0.5)$. Затраты Ксюши на каждую булочку распределены равномерно на отрезке $[2;20]$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Решение:__ можно прочесть задачу двояко. Первый вариант: цена на все булочки в рамках одного дня одинаковая. Второй вариант: цена на каждую булочку в течение дня случайная. Я имел в виду первый вариант. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__а)__ Сколько в среднем Света тратит на булочки за день? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "121.741593750172"
      ],
      "text/latex": [
       "121.741593750172"
      ],
      "text/markdown": [
       "121.741593750172"
      ],
      "text/plain": [
       "[1] 121.7416"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6\n",
    "x1 = rpois(n_obs, lambda = 10)   # спрос светы на булочки\n",
    "p1 = rnorm(n_obs, mean=2, sd=1)  # цена булочек \n",
    "\n",
    "costs1 = exp(p1)*x1  # расхрды Светы \n",
    "mean(costs1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__б)__ Чему равна дисперсия дневных расходов Светы? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "29358.9234046683"
      ],
      "text/latex": [
       "29358.9234046683"
      ],
      "text/markdown": [
       "29358.9234046683"
      ],
      "text/plain": [
       "[1] 29358.92"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var(costs1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__в)__ Какова вероятность того, что за один день Света потратит больше денег, чем Ксюша? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "44.0062487864432"
      ],
      "text/latex": [
       "44.0062487864432"
      ],
      "text/markdown": [
       "44.0062487864432"
      ],
      "text/plain": [
       "[1] 44.00625"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Осторожнее! В rbinom аргумент n - число генераций, size - число испытаний!\n",
    "# rbinom(n, size, prob)\n",
    "# https://www.tutorialspoint.com/r/r_binomial_distribution.htm\n",
    "\n",
    "x2 = rbinom(n_obs, size = 8, prob = 0.5)  # спрос светы на булочки\n",
    "p2 = runif(n_obs, min=2, max=20)          # цена булочек \n",
    "\n",
    "costs2 = p2*x2  # расходы Ксюши\n",
    "mean(costs2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.699902"
      ],
      "text/latex": [
       "0.699902"
      ],
      "text/markdown": [
       "0.699902"
      ],
      "text/plain": [
       "[1] 0.699902"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# нужная вероятность\n",
    "mean(costs1 > costs2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__г)__ Какова условная вероятность того, что Света за день съела больше булочек, чем Ксюша, если известно, что Ксюша потратила больше денег? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.898173263400622"
      ],
      "text/latex": [
       "0.898173263400622"
      ],
      "text/markdown": [
       "0.898173263400622"
      ],
      "text/plain": [
       "[1] 0.8981733"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "usl <- costs1 < costs2\n",
    "mean(x1[usl] > x2[usl])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "300098"
      ],
      "text/latex": [
       "300098"
      ],
      "text/markdown": [
       "300098"
      ],
      "text/plain": [
       "[1] 300098"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(usl) # много ли у нас примеров для оценивания"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [3] Задачка 7\n",
    "\n",
    "Удав Анатолий любит французские багеты. Длина французского багета равна $1$ метру. За один заглот Удав Анатолий заглатывает кусок случайной длины, равномерно распределённый на отрезке $[0;1]$. Для того, чтобы съесть весь багет удаву потребуется случайное количество $N$ заглотов. \n",
    "\n",
    "Найдите $E(N)$ и $Var(N)$. Как поменяются ответы, если багет имеет длину $2$ метра? \n",
    "\n",
    "Кстати говоря, эту задачку можно решить руками с помощью метода первого шага. Его мы разберём на второй паре. Правда для этого придётся выписать систему из двух уравниний с интегралами. В сборнике сложных задач по терверу, [культурном коде,](https://github.com/bdemeshev/probability_dna/raw/master/probability_dna.pdf) можно найти три разных решения этой задачки. Она там находится под номером $46$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3"
      ],
      "text/latex": [
       "3"
      ],
      "text/markdown": [
       "3"
      ],
      "text/plain": [
       "[1] 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Багеты! Давайте начнём с одной итерации эксперемента\n",
    "\n",
    "l = 1 # длина багета\n",
    "m = 0 # число заглотов\n",
    "\n",
    "# пока длина багета больше 0 \n",
    "while(l > 0){\n",
    "    # делай заглоты \n",
    "    l = l - runif(1)\n",
    "    m = m + 1 # на один заглот стало больше\n",
    "}\n",
    "\n",
    "m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В принципе это всё. Теперь нужно сделать этот эксперимент с заглотами много-много раз. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_obs <- 10^6\n",
    "N <- rep(0, n_obs)\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    l = 1 # длина багета\n",
    "    m = 0 # число заглотов\n",
    "\n",
    "    # пока длина багета больше 0 \n",
    "    while(l > 0){\n",
    "        # делай заглоты \n",
    "        l = l - runif(1)\n",
    "        m = m + 1 # на один заглот стало больше\n",
    "    }\n",
    "    N[i] = m # сохранили текущее число заглотов\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.718797"
      ],
      "text/latex": [
       "2.718797"
      ],
      "text/markdown": [
       "2.718797"
      ],
      "text/plain": [
       "[1] 2.718797"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.767348640139645"
      ],
      "text/latex": [
       "0.767348640139645"
      ],
      "text/markdown": [
       "0.767348640139645"
      ],
      "text/plain": [
       "[1] 0.7673486"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(N)\n",
    "var(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2] Задачка 8\n",
    "\n",
    "На шнуре длиной $1$ м случайным образом делают два разреза. С какой вероятностью хотя бы один из получившихся кусков будет длиннее $0.5 м$?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.750117"
      ],
      "text/latex": [
       "0.750117"
      ],
      "text/markdown": [
       "0.750117"
      ],
      "text/plain": [
       "[1] 0.750117"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6\n",
    "\n",
    "x1 = runif(n_obs) # первый надрез \n",
    "x2 = runif(n_obs) # второй надрез \n",
    "\n",
    "usl_1 = (x1 < x2)&(x1 > 0.5 | x2 - x1 > 0.5 | 1 - x2 > 0.5)  # первый вариант \n",
    "usl_2 = (x1 >= x2)&(1 - x1 > 0.5 | x1 - x2 > 0.5 | x2 > 0.5) # второй вариант \n",
    "\n",
    "mean(usl_1 | usl_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2] Задачка 9 \n",
    "\n",
    "Семён любит мешать не только джим бим с колой, но и распределения! И вот сейчас две трети её данных идут в смесь из экспоненциального распределения с параметром $\\lambda = 1$, а остальная треть из стандартного нормального. Как это часто бывает, Сёма сначала намешал, а потом чёт подумал-подумал и всё Диме отдал. И теперь у Димы проблема со свойствами намешанного распределения.\n",
    "\n",
    "Сгенерируйте выборку из распределения Семёна и помогите Диме оценить математическое ожидание и дисперсию случайной величины, постройте гистограмму. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.667544379124517"
      ],
      "text/latex": [
       "0.667544379124517"
      ],
      "text/markdown": [
       "0.667544379124517"
      ],
      "text/plain": [
       "[1] 0.6675444"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.21947903731006"
      ],
      "text/latex": [
       "1.21947903731006"
      ],
      "text/markdown": [
       "1.21947903731006"
      ],
      "text/plain": [
       "[1] 1.219479"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs <- 10^6\n",
    "\n",
    "# round, чтобы код не бросал ошибку\n",
    "X1 <- rexp(round(2/3*n_obs), rate = 1)\n",
    "X2 <- rnorm(round(1/3*n_obs))\n",
    "\n",
    "# объединили в одно целое \n",
    "Y <- c(X1,X2)\n",
    "\n",
    "mean(Y)\n",
    "var(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA\nOI2NVV1oHFUUPrtzZyMkzlNsNIV0qD8NJQ2TVjShtLp/3d02bpZJNtoi6GT27s6Yyc44M7v9\noU9FUHwx6psUxL+3gCAo9Q/bPrQvlQol2tQgKD60+INQ6Ium65k7M5lpurHeZe58853vnnvu\nuWfvBei5qliWkRQBFpquLRcy4nOHj4g9K5CEh6AXBqFXUR0rXalMAjZPC3e1W99Dwntf2dXd\n/p+tt0YdFSBxH2Kz5qgLiI8B8KdVy3YBevqRHz/qWh72Yui3MUDEL3q44WPXw3M+fo1pZuQs\n4tOIBVVTaoiXEI/MxfhGDPsxsNZfoE1q66ro5aJim3XdoLFw72H+n23BaIXzbcOnz5mfPoTv\nYVz7KzUl5+FRxEuqkp9G/Ajia219thzg25abkRE/BpDc3pqvphHvRFys2weqvp+krbWKIX7n\nhDbzLOItiM8358pTwdirqpPFnMF2xLc1WvLyOwTAibpbmvHHcvttU57y5+XqNZrLe3lE/Pq8\neUj2fXKfOe3pfOjzhJYtB/yll5SDFcSDiH+hRkH25+L+sdxKEAMZahrlSX8ukqMOWy/jXW2m\n6M9LDBc31B9LFuv6gVKg/0Szi3KAr1kGq1GMjU/aLbnq6/lRxc4XfJ98hTargX++DbMJBSiY\nMIe9Ck1YAxFkKEAG3xbYaKmDDgYyFK0UGYpfoWYXG+fAPPI6tJnNwb7ClP7IyF+D+bjOtCpk\nhz6CFrIa/I6sFtNl8auFXGMTP34sNwI/JhkgEtmDz14ySfaRcTIBInmKPE32kxyyE2Tv+thK\nbEVePDfW/byMM1Kmm0XdObS7oGD/MypMXFPXrCwOtoYjyyn7BV29/MZfsVzpLDdRtuIZnbpX\nzvlf+ev8MvYr/Gqk4H/kV/G3csdazLuyTMPsbFhzd1UabQbjFvDRmcWJxR3zcfHkVw9GfpbJ\nmeev9F08WW8uDkaslwX6avlWGU6NRKz0g/SHtCy9J30o/ca9zX3Kfc19zn3BXQKRO8ud477h\nLnAfc1/G9mrzGlrfexZ5GLdn6ZZrrEohI2wVHhZywjbhUWEy8icMCGNCUdiBlq3r+xafL549\nHQ5jH+an+1y+LlYBifuxAvRN/lVVVOlwlCkdVm9NOL5BE4wkQ2SMlDZU97hX86EilU/lUmkQ\nUztTE6mx1EEPh7OmdqBtAvv8HdWpbrJS6tJj3n0CWdM6busNzRV3S9KTYhqvNiqWmuroiKgY\nhshMjmhTh9ptWhsF7970j/SbMrsPE1suR5z7DMC+P/Hs+y7ijrQAlhyAgccjbhjPygfeBTjz\nhNqy28EdkUh8C+DU9+z2v/oyeH791OncxHOs5y2AtTc7nb/f73TWPkD/qwBnjX8BoJ98VVBg\n/m8AADxPSURBVHgB7Z0LjBXXece/ZRfYZWFheb8dsIJxSWKo64JxZNcNocTm4SLbstviFrAt\nGoqIHFWO69SBGBnJisHQ1LIrXIwQKThYbRMZRyWVKtvgBKn1k4eAgo0b3u/H8lrY+n+Sucy9\nu3vn3mVm75zd35F278x8Z74553fmzH/OY2bKGr4IRoAABCAAAQhAoFUJdGjVo3EwCEAAAhCA\nAAQcAQSYEwECEIAABCBQAgIIcAmgc0gIQAACEIAAAsw5AAEIQAACECgBAQS4BNA5JAQgAAEI\nQAAB5hyAAAQgAAEIlIAAAlwC6BwSAhCAAAQgUJEmBG+//bZ169bNxowZk5Wsq1ev2scff2wf\nfPCB9evXz+6++27r3LlzJs6mTZvs3LlzmXUt3HzzzTZkyJDMtn379tnmzZutZ8+eNn78eOva\ntWvGpoUo+5kzZ0zH0e/YsWNt6NChWfuzAgEIQAACECiGQFlaXsQhcf3Od75jjz32mP35n/95\nJg9Hjx61Rx991AnuLbfcYu+9954Tz1deecVqamrsypUrNnHiRCfcFRXX7icef/xxt12OVq9e\nbStWrLC77rrL9u/fbxcvXrTly5dbbW2tO06Ufe/evTZ79mwbPny4DRo0yAnxokWLbNy4cZl0\nNrdw+vRpu3DhQnNmt71jx45WXV1tdXV1dunSpbxx02wsLy+3ysrKRjdDaU5zU2nr0aOHO690\ns+Vz0M2s73moqqpydV/1SDfivoagwaBrj69B9VvnlPJw/vx5X7NhZWVlTkOSrBti1atXr0hG\n1xQrMmoyEerr651ASgQFJjesX7/eBg4caC+99JIzqeCnT59u69atc2L9+eefO9F69dVXm8yw\nWrYrV660ZcuW2ejRo03HmzNnjttfv1F2HXTx4sU2depUmz9/vkvjqlWrbOnSpbZ27dom0xzO\ngy4auknIFyTAnTp1cid1VNx8fkpt69Chg+nP5zyIocpD52JbyIfOP59fdqfzSXVDefC5PHQ+\n+Z6HoCwuX77sdVkoH2qspeF8KvkY8IYNG+zNN9+05557LqvLOBCTLl262COPPBKsmu6IR44c\n6Vqy2rhr1y7r3bt3k+Ir+5YtW5yAS3wVBH7SpEm2ceNGtx5lP3bsmG3fvt2mTZuWEdvJkye7\n42/bts354B8EIAABCECgWAIlbwHfcccdds899zhhDFq54UyExVfbjx8/bu+//77NnTvXRdu9\ne7frFlmyZInrGla3sva58847nf3AgQOu29it/O6fWtTq2lbrIMp+8OBBt5f2CYK6FnRXfvjw\nYRs1alSw2a2rJR4Of/RHf2Rf/epXw5saLQdd5+q+VdeFr0FpV+tR3VS+B90l+56PIA8+t4BV\nzxQ0RONzF7TqhYLP9Vvnk4LvdVy9EUHdcBlK4F+hda7kAlxIP3nAR+OjCxYssBtuuMHuu+8+\nt3nnzp1OlEeMGOEmV7311lv29NNP2/PPP2+33367SUA1VhwOurCqMp86dSrSLoHW+E0whhP4\nkY8TJ04Eq+5XNwevvfZa1rYvfelLLh1ZG5tZaeo4zURN9ebcCW6pTmwzidOFsi3kQ8LVFoJ6\nwtpCyL2O+Jgn3RQFN0Y+pj9Ic5L1u9C5PCUX4ABG1K8mYTz11FOmX42/BneUEmSJaTChShOj\n1CrWGLEEWPE07hsOwboqdUvs8qXxg9yLgm4MdNxw0IQetbbzBVVKCfrZs2cjJ2zl81Nqm1ry\nasUrHz4H3RSqfE+ePOlzNkznnm4yC70bT2NmdQOhYSfd7KZhzK6ljJQHlUPUhMyW+m+N/VS/\ndU5pHk7uUyetcfy4jqHWrxplSdZvtbILaVx6IcASMM2QVmX88Y9/bN27d8+URXg52Cjhfeed\nd9yqxoc//fTTwOR+JeISbAlfIXZVfM1QDguufAwYMCDLrypZMNYcGFTIUTMGg24pHUcTHHwO\nusj4ngfxbyv5UFn4LMBBt7NumoMbZx/rh1qMbeWcUpn4XMclwEmXRXBNjzpXSz4JKyqBhw4d\nsm9/+9tugpYeHcoV3CeffNI0UzocPvzwQzfxStuGDRtmO3bsyKq8W7duzYwLR9kHDx7sxqe1\nTxA0KUsnYXhcOLDxCwEIQAACECiEQOoF+IUXXnBdTw888IATUomr/vRsroJe2qFHmDQbWs+n\nvfHGGy7egw8+6OwTJkxwv2vWrHGiuWfPHtPM6xkzZhRkl+DrOWM9yhR0EeuZYs2k7tOnj/PB\nPwhAAAIQgECxBFLdBa2XZujFGwp6Bjcc9DaqH/3oR+7xoI8++shmzZrlJgaoW1mTsNQNraD1\nZ5991hYuXGgSYXUT6zlivQ2rELvi6Hlh7T9lyhTnTy8EmTdvntuffxCAAAQgAIGWEEjNm7Ba\nkvjwPpoUoDeb6FWVGgBvKqg7W63WYDp9bpwou8Z91bdfzMzSQsaANXFJY9KaMKOxZl+DJrSJ\nTZKTG1qDTf/+/d2QRdTkudZIy/UcQ+e68uDzGLAmy+icOnLkSNYw0vVwKcW+yoPKwff6rTkz\nutbqWuhr0PVfryROsn5LJ/r27RuJKNUt4MjUhyLoBNdfviBxzhei7LmPM+XzhQ0CEIAABCCQ\nj0Dqx4DzJR4bBCAAAQhAwFcCCLCvJUe6IQABCEDAawJtpgva61Ig8aklMHPmzEzaNBOeAAEI\nQCAuArSA4yKJHwhAAAIQgEARBBDgImARFQIQgAAEIBAXAQQ4LpL4gQAEIAABCBRBAAEuAhZR\nIQABCEAAAnERQIDjIokfCEAAAhCAQBEEEOAiYBEVAhCAAAQgEBcBBDgukviBAAQgAAEIFEEA\nAS4CFlEhAAEIQAACcRFAgOMiiR8IQAACEIBAEQQQ4CJgERUCEIAABCAQFwEEOC6S+IEABCAA\nAQgUQQABLgIWUSEAAQhAAAJxEUCA4yKJHwhAAAIQgEARBBDgImARFQIQgAAEIBAXAQQ4LpL4\ngQAEIAABCBRBAAEuAhZRIQABCEAAAnERqIjLEX6aJlBWVmYdO3Zs2vi7rRUVvy2G8vLyyLh5\nHZXYqHx06NDB6zwECJsqt6hyDPZN029wbqUpTcWkReeTgvKhMvE1qG43NDR4XTeCc8n3Oq7z\nqKn6Hee5Vei5igDHSb0JX6p4nTp1asJybZPiKChesHzN6s+STjpV0urqan8S3UxKdZHJzUfu\nejO7pmZzU3lITeIKTEhw01NVVeUErMDdUhdN9UIC7Hv9FliViW91IfeESLpuXLlyJfeQTa4j\nwE1iiW9jfX29nTlzJq/DyspKJ77nz5+3urq6vHHTbAwq5smTJ9OczMi09e/f31SBcvORux7p\nqMQR+vTpY6dOnfJauGpqatxNneqQ6pKvQYIlAfa9futadfHiRTt9+rSvReF66Xr27NmofseZ\nId1ode3aNdIlY8CRiIgAAQhAAAIQiJ8AAhw/UzxCAAIQgAAEIgkgwJGIiAABCEAAAhCInwAC\nHD9TPEIAAhCAAAQiCSDAkYiIAAEIQAACEIifAAIcP1M8QgACEIAABCIJIMCRiIgAAQhAAAIQ\niJ8AAhw/UzxCAAIQgAAEIgkgwJGIiAABCEAAAhCInwACHD9TPEIAAhCAAAQiCSDAkYiIAAEI\nQAACEIifAAIcP1M8QgACEIAABCIJIMCRiIgAAQhAAAIQiJ8AAhw/UzxCAAIQgAAEIgkgwJGI\niAABCEAAAhCInwACHD9TPEIAAhCAAAQiCVRExiACBCDgCMycOTOLxMqVK7PWWYEABCBQDAFa\nwMXQIi4EIAABCEAgJgIIcEwgcQMBCEAAAhAohgACXAwt4kIAAhCAAARiIoAAxwQSNxCAAAQg\nAIFiCKRqEtbbb79t3bp1szFjxmTl4cqVK/bBBx/Ytm3bbOTIkXbbbbcVZVfkffv22ebNm61n\nz542fvx469q1a5aPKPuZM2ds06ZNpt+xY8fa0KFDs/ZnBQIQgAAEIFAMgdS0gCWwzzzzjBPZ\ncAYkvnPmzLEf/OAH9pvf/MZ++MMf2pIlSzJRouyKuHr1apsxY4bz/frrr9tf//Vf24kTJzI+\noux79+61adOm2fr16+2TTz6xWbNm2a9+9avM/ixAAAIQgAAEiiVQ8hZwfX29E0iJYFlZWaP0\nSzDPnj1r69ats+rqavvss8+cmN5777120003WZRdLVs9LrJs2TIbPXq06XgSdPnTb5RdCVq8\neLFNnTrV5s+f79K4atUqW7p0qa1du7bJNDfKBBsgAAEIQAACOQRK3gLesGGDvfnmm/bcc8/Z\nkCFDcpJn9u6779o3v/lNJ74y3nDDDfaVr3zFNm7c6OJG2bds2WIDBw504qsdKioqbNKkSZn9\no+zHjh2z7du3uxZwcIMwefJk279/f6PWuksQ/yAAAQhAAAIFECh5C/iOO+6we+65xwnjSy+9\n1CjJBw4ccAIaNkhQDx8+7DYVYh80aFB4d+fv6NGjdvXqVdP++ewHDx50++qYQejVq5d16tTJ\npWHUqFHBZtc6/+53v5tZ14K6qydMmJC1LXelQ4ff3gephV9VVZVr9mZdNyjl5eUmPr6HQvKR\n9nwqD5rz4HNQHhR69OhhDQ0N3mZF+VD6fa/fKoDKykrr2LGjt2XRGtcpDY0WEkouwPkuYuou\nllDW1NRk5UXrO3fudN3J+ezaSQKau78mekl8T506FWmXQHfu3Nn9hRMhH+FxZNkuXLjgxojD\n8U6fPl3wyapKGlxwwj58W/a5cgasVUmj8hFlD3yV8teHNBbCRz1XbSG0hfqtBkPQaPC5TNJQ\nN1J9VutkVUFLiMNB62otRtm1jyA3tb9sXbp0aZFd++oOR/uHg8akd+zYEd5kJ0+edCKftTFn\nRXeUtbW1JrGuq6vLsfqzKtYqF+XZ59C/f//MzV2+fAS9I/nilNLWp08fdwPrc8tRN886p3Sj\nnVuPS8m22GMrDyoH3+t37969XR50rfI1SFPUM6RzKqkgberbt2+k+5KPAedLoVohAqVHf8JB\nha+LZJRd++iEaWp/CZ5atoXYJba5FUdpGDBgQDhZLEMAAhCAAAQKJpBqAVYuhg8fblu3bs3K\nkJ4HDsZto+zDhg1zrdLw3bP8BftH2QcPHuzGp8Np0KQsdWGHx4WzEsgKBCAAAQhAIIJA6gX4\n/vvvt1/+8pduxrG6cN544w27dOmSm7ilvEXZgwlQa9ascaK5Z88e08xrPResEGXv3r27TZw4\n0T3KpMehNM67YsUKN5NaXXwECEAAAhCAQEsIpHoMWBkaN26cPfTQQzZ37lw3XquW6/e///3M\nm6yi7OpmfvbZZ23hwoUmEdYsxOnTp7u3Ycl/lF1x9Lyw9p8yZYqLf8stt9i8efNkIkAAAhCA\nAARaRKDsi1alF3P71erVuKvGbJsKUXbtc+jQIVOrtbkZfFF2HV+D65pQUWjQhKTz58/njR5M\nwtKs7Nyx5rw7pszYFidh5X4DOIw87d8DbkuTsI4cOcIkrPDJV4Jl1W9df8+dO+euxSVIQiyH\nTNMkrNS3gAPieu62OfFVnCi74vTr108/zYYoe+7jTM06wgABCEAAAhCIIJD6MeCI9GOGAAQg\nAAEIeEkAAfay2Eg0BCAAAQj4TgAB9r0EST8EIAABCHhJAAH2sthINAQgAAEI+E4AAfa9BEk/\nBCAAAQh4SQAB9rLYSDQEIAABCPhOAAH2vQRJPwQgAAEIeEkAAfay2Eg0BCAAAQj4TgAB9r0E\nST8EIAABCHhJAAH2sthINAQgAAEI+E4AAfa9BEk/BCAAAQh4SQAB9rLYSDQEIAABCPhOAAH2\nvQRJPwQgAAEIeEkAAfay2Eg0BCAAAQj4TgAB9r0EST8EIAABCHhJAAH2sthINAQgAAEI+E6g\nwvcMkH4IlIrAzJkzM4deuXJlZpkFCEAAAoUQoAVcCCXiQAACEIAABGImgADHDBR3EIAABCAA\ngUII0AVdCKXriNOhQwerrq7O66Gi4rfF0KlTJysrK8sbN83G8vJyU16i8pvmPARpK6Tcgrj6\nTWOedS516dIlnEzvljt27OjSXFVVZVevXvUu/UGCVbcbGhq8r9/Kj+91XPWi2PodlGOhvyrr\nQgICXAil64xTaGHoMMXEvc5kxb57kPbgN/YDtLLDYvJRTNzWzEZa01UogyD9+g2WC903TfGC\ntAe/aUpboWkJpz28XOj+aYuXhjwgwAmfFbprP3/+fN6jVFZWupbKpUuXrK6uLm/cNBvVWlEr\n2Oc8iG9NTY1rbRWTj2LitlYZqlWucy8NF5qW5lmtrc6dO9uFCxesvr6+pW5Kvp9aXSqHNJ4n\nhcJR/e7atasrB5/zodavelSSzIOug4UExoALoUQcCEAAAhCAQMwEEOCYgeIOAhCAAAQgUAgB\nBLgQSsSBAAQgAAEIxEwAAY4ZKO4gAAEIQAAChRBAgAuhRBwIQAACEIBAzAQQ4JiB4g4CEIAA\nBCBQCAEEuBBKxIEABCAAAQjETAABjhko7iAAAQhAAAKFEECAC6FEHAhAAAIQgEDMBBDgmIHi\nDgIQgAAEIFAIAQS4EErEgQAEIAABCMRMAAGOGSjuIAABCEAAAoUQQIALoUQcCEAAAhCAQMwE\nEOCYgeIOAhCAAAQgUAgBBLgQSsSBAAQgAAEIxEwAAY4ZKO4gAAEIQAAChRCoKCQScSDQXgjM\nnDmzvWSVfEIAAiUmQAu4xAXA4SEAAQhAoH0SQIDbZ7mTawhAAAIQKDEBBLjEBcDhIQABCECg\nfRJAgNtnuZNrCEAAAhAoMYHUT8LauHGjXb16tRGmrl272h133OG2b9q0yc6dO5cV5+abb7Yh\nQ4Zktu3bt882b95sPXv2tPHjx5v2D4co+5kzZ0zH0e/YsWNt6NCh4d1ZhgAEIAABCBRFIPUC\nvHLlSrt06VJWpo4ePWo33XSTE+ArV67YM888Y926dbOKimvZefzxxzMCvHr1aluxYoXddddd\ntn//ftP68uXLrba21vmNsu/du9dmz55tw4cPt0GDBtkrr7xiixYtsnHjxmWlixUIQAACEIBA\noQSuKVahe7RyvJ/85CdZR/yf//kfe+KJJ2zu3Llu++eff+4E+tVXX7VevXplxdWKWrYS8WXL\nltno0aOtvr7e5syZY+vWrXO/UXb5WLx4sU2dOtXmz59vZWVltmrVKlu6dKmtXbvWrSsOoX0T\nyH18SeccAQIQgEA+Al6NAdfV1Tkx/LM/+zP72te+5vK1a9cu6927d5PiqwhbtmyxgQMHOvHV\nulrJkyZNMnVtK0TZjx07Ztu3b7dp06ZlxHby5MmuJb1t2zbnI/xPAh/+a2hoCJtZhgAEIAAB\nCDgCqW8Bh8vp5Zdfts6dO9usWbMym3fv3u26n5csWeLGaNWt/Mgjj9idd97p4hw4cMB1G2d2\n+GJBgqxubI0tR9kPHjzodtU+QVBLu1OnTnb48GEbNWpUsNl27NjhhDqz4YuFBQsW2MMPPxze\n1Oxy9+7dTX++h6qqKt+zcN3pHzBgwHX7iMNB//7943BTch99+vQpeRriSEBbqN/V1dWmP99D\nknU0d9i0OVbeCLAmP7355ps2b968rLHenTt32vHjx23EiBFuctVbb71lTz/9tD3//PN2++23\nmwS0pqYmK/8aL5b4njp1KtIugZbo6y8c5OPEiRPhTe6kvPXWW7O2adJXVGF06NDB5Ukt56Ym\nnGU5TPGKuueVF43Lt/cQVeatwadjx452+fLl1jhUYscoLy83/SkfPvcmqV4o+F6/dU6pfvte\nx9UTquttUkG+1UiLCt4I8H/8x384kZo4cWJWntTC1EkdTKjSxCi1ijXGKwHWCZMLOljv0qVL\ni+xKgE5A7R8OmnWdO2Z98uRJUzd2vlBZWenSr5nc6mb3NYi17oyV5/Yeosq8Nfio1aibU5+F\nSzfPwTkV1NvWYBf3MZQHlYPv9VvDfRcuXLDTp0/HjajV/OlmSA2jJOuobhpz9aGpDHozBvzz\nn//cvvWtbzXKlLp0AvENMijhVctVQSeMWs/hoJNH+6hVW4hdYptbceQjyS6McHpZhgAEIACB\ntkfACwHWncr//u//useIcovgySeftPXr12dt/vDDD904rzYOGzbMjc2G7563bt2aGReOsg8e\nPNi1vLVPEDQpS63u8LhwYOMXAhCAAAQgUAgBLwT4008/dXmRWOaGMWPGuOd6NRv64sWL9sYb\nbzjBffDBB13UCRMmuN81a9Y40dyzZ49t2LDBZsyYUZBdLWx1e+uxkrNnz7ruFz1TrJnUbWVi\nSC5T1iEAAQhAIHkCXowBS4DVZdyjR49GRPR40EcffeRmRmvQW93KmoSlbmgFrT/77LO2cOFC\nkwhrhu706dPdhK1C7Iqj54a1/5QpU5y/W265xU0Gk40AAQhAAAIQaAmBsi8mBrSJB1U1gUlj\nvf369cs8r5sL5NChQ67VGsxILNaucV8NrhczBV8Tks6fP597qKz1YBKWZmXnjjVnRUz5SluY\nhJX7Qo2WIk/DizjUQ6PH7Xyu4sEkrCNHjjSaTNnSsinFfm1pEpautW1hEpbqRlJBOtG3b99I\n9160gCNz8UUEneBRwihxzhei7LmPM+XzhQ0CEIAABCCQj4AXY8D5MoANAhCAAAQg4CMBBNjH\nUiPNEIAABCDgPQEE2PsiJAMQgAAEIOAjAQTYx1IjzRCAAAQg4D0BBNj7IiQDEIAABCDgIwEE\n2MdSI80QgAAEIOA9AQTY+yIkAxCAAAQg4CMBBNjHUiPNEIAABCDgPQEE2PsiJAMQgAAEIOAj\nAQTYx1IjzRCAAAQg4D0BBNj7IiQDEIAABCDgIwEE2MdSI80QgAAEIOA9AQTY+yIkAxCAAAQg\n4CMBBNjHUiPNEIAABCDgPQEE2PsiJAMQgAAEIOAjAQTYx1IjzRCAAAQg4D2BCu9zQAYgkEIC\nM2fOzKRq5cqVmWUWIAABCAQEaAEHJPiFAAQgAAEItCIBBLgVYXMoCEAAAhCAQECALuiAREK/\nFRUVVltbm9d7hw6/vQ/q0qWLde7cOW/cNBvLysqskPymOQ9JpC2q/JM4pnzqvOrRo0dS7lvF\nr84nhZqaGmtoaGiVYyZxkPLycufW9/qtTCgPpTqn4yoblUeSebhy5UpBSUWAC8LU8kgqiAsX\nLuR1oBO6U6dOdvHixci4eR2V2KiLZVVVlZ09e7bEKUnX4UvFQ+JbqmPHVQLV1dXupq6urs4K\nvajFdew4/ahe6AYi6loQ5zHj9qX6rWvV5cuX7dy5c3G7bzV/QUMhybqhY+jcjQoIcBSh67Sr\n0umEzReCu2NdYKLi5vOTBtvVq1e9z0PcHEtZpvX19V63HHU+KSgf+vM16Aa7kGuBD/nzvY6r\nZyjpsgiu6VHlyRhwFCHsEIAABCAAgQQIIMAJQMUlBCAAAQhAIIoAAhxFCDsEIAABCEAgAQII\ncAJQcQkBCEAAAhCIIoAARxHCDgEIQAACEEiAAAKcAFRcQgACEIAABKIIIMBRhLBDAAIQgAAE\nEiCAACcAFZcQgAAEIACBKAIIcBQh7BCAAAQgAIEECCDACUDFJQQgAAEIQCCKAAIcRQg7BCAA\nAQhAIAECCHACUHEJAQhAAAIQiCKAAEcRwg4BCEAAAhBIgAACnABUXEIAAhCAAASiCCDAUYSw\nQwACEIAABBIggAAnABWXEIAABCAAgSgCCHAUIewQgAAEIACBBAhUJOATlxCAQIjAzJkzQ2tm\nK1euzFpnBQIQaJ8EaAG3z3In1xCAAAQgUGICCHCJC4DDQwACEIBA+yTgRRf0pk2b7Ny5c1kl\ndPPNN9uQIUPctitXrtgHH3xg27Zts5EjR9ptt92WFVcr+/bts82bN1vPnj1t/Pjx1rVr16w4\nUfYzZ86Y0qHfsWPH2tChQ7P2ZwUCEIAABCBQDIHUC7DE9ZlnnrFu3bpZRcW15D7++ONOgGWf\nM2eOHThwwL7+9a/b66+/bnfffbc98cQTGQ6rV6+2FStW2F133WX79+83rS9fvtxqa2tdnCj7\n3r17bfbs2TZ8+HAbNGiQvfLKK7Zo0SIbN25c5hgsQAACEIAABIohcE3RitmrFeN+/vnndunS\nJXv11VetV69ejY4swT179qytW7fOqqur7bPPPrMZM2bYvffeazfddJNr+WrSy7Jly2z06NFW\nX1/vBFvxJdxq+eaz64CLFy+2qVOn2vz5862srMxWrVplS5cutbVr17r1RoliAwQgAAEIQCCC\nQOrHgHft2mW9e/duUnyVt3fffde++c1vOvHV+g033GBf+cpXbOPGjVq1LVu22MCBA534al2t\n6EmTJhVsP3bsmG3fvt2mTZuWEdvJkye7lrS6vAkQgAAEIACBlhBIfQt49+7drvt5yZIlbgxW\n3caPPPKI3XnnnS6/6nqWwIaD1g8fPpyxq9s4HGQ/evSoXb161XVd57MfPHjQ7Ro+hlrinTp1\ncscYNWpUxnVdXZ198sknmXUt6Oahe/fuWdtyV4Ku9fLycuc31+7LutLfoUMHr/PQGqx17rRW\n6NixY2sdKpHj6JxSUD50bvkalI+Ghgav60ZwnfK9jqsXU39J1kP5LySkXoB37txpx48ftxEj\nRrjJU2+99ZY9/fTT9vzzz7vJVhLSmpqarLxqXfspSEBz7RpPlvieOnUq0i6B79y5s/sLH0Q+\nTpw4Ed7kurPV/R0OCxYssIcffji8qdllTQzLnRzWbOQUG8SL0DyBpoZSmo99fZbWPNb1pTT/\n3j169MgfwRNrW6jfVVVVpj/fQ5J1Q8OmhYTUC7AETGIZTJjSxCe1ijWGq2XdjWlcNxy0rvFg\nBd05N2WXrUuXLi2ya19N/tL+4aAC1eSwcLjxxhvdGHV4W+6y7iwrKyvt4sWLdvny5VyzN+sq\nC/FWPgjNE9CchdYIOj/VK+Nz0M2czinlQ9cBX4PyoBZw7rXIp/yofuuckrgUKjBpzJ9ap7re\nnj9/PrHk6VwtpIWdegFuqvv29ttvt3feecd1I+ixIj0aFA6nT5+2/v37u03qAv7000/DZpNd\ngq7KXYhdYqsLQFhw5WPAgAFZfvv06WPf/e53s7adPHmyUfqyInyxopNBfxcuXPD6gqmLjG58\ncssjN7/tfb21+Oicktjrwu9r0MVS55UeQ/RZvFQvVA4+3xCpHHQNVCOhtc7hJM7boAs9yTxo\nyCG357WpvKR+UOXJJ5+09evXZ6X9ww8/zIz76tGgrVu3Ztk1OSoY1x02bJjt2LEjq/IqfqH2\nwYMHu4lb4WNoUpbucMLjwlkJYAUCEIAABCAQQSD1AjxmzBj33K5mQ6tr84033nCC+uCDD7qs\n3X///fbLX/7SvYRDd5iyq3vknnvucfYJEya43zVr1jjR3LNnj23YsME9qiRDlF0t8IkTJ7pH\nldSaUCtVzxRrJrVavAQIQAACEIBASwikvgtaj/989NFHNmvWLNenrm5jTcJSN7SCxoEfeugh\nmzt3ruuqUsv2+9//fmYyk+I/++yztnDhQpMIa/LA9OnT3YQu7R9lVxw9L6z9p0yZ4uLfcsst\nNm/ePJkIEIAABCAAgRYRKPui1ejFAJHGgNRn369fv8zzuOEcq9WrcVmN6TYXDh065FqtGgNo\nKkTZ5V99+8EEr6Z85G7TGHDUYL/G6jQmrVnZvo8RiY3y7GvI/XJREvlora8hqYdGTwl4UsWb\nRK1xNJ1TR44cyRpGajJyije2lTFgXV91Lda10Neg67/mDqluJBWkE3379o10n/oWcJADncD6\nay5oxlk+8dV+Eu98IcpeyKB6Pv/YIAABCEAAAgGBppuCgZVfCEAAAhCAAAQSIYAAJ4IVpxCA\nAAQgAIH8BBDg/HywQgACEIAABBIh4M0YcCK5xykESkAgPNGrtSZklSCbHBICEIggQAs4AhBm\nCEAAAhCAQBIEEOAkqOITAhCAAAQgEEEAAY4AhBkCEIAABCCQBAEEOAmq+IQABCAAAQhEEECA\nIwBhhgAEIAABCCRBAAFOgio+IQABCEAAAhEEEOAIQJghAAEIQAACSRBAgJOgik8IQAACEIBA\nBAEEOAIQZghAAAIQgEASBBDgJKjiEwIQgAAEIBBBAAGOAIQZAhCAAAQgkAQBBDgJqviEAAQg\nAAEIRBBAgCMAYYYABCAAAQgkQQABToIqPiEAAQhAAAIRBBDgCECYIQABCEAAAkkQQICToIpP\nCEAAAhCAQASBigg75usk0LFjR+vWrVteL2VlZc6ueF27ds0bN+3GDh06WN++fdOezNSkL0lW\nKos+ffqkJq8tSUhQN3r27NmS3VOzT5AP3+u3gFZVVVllZWVq2LYkIUlfpy5fvlxQshDggjC1\nPJIK4vTp03kd6GSura21M2fOWF1dXd64aTbqZqO6utpOnjyZ5mSmKm333ntvJj0rV67MLMex\nIPE9evSoNTQ0xOGuJD5qamrcOXX8+HGrr68vSRriOKjqhcrB9/rdu3dvO3/+fOQ1LQ5mSfmQ\n+OqGTnUjqVBeXl7QTQpd0EmVAH4hAAEIQAACeQggwHngYIIABCAAAQgkRQABToosfiEAAQhA\nAAJ5CCDAeeBgggAEIAABCCRFAAFOiix+IQABCEAAAnkIIMB54GCCAAQgAAEIJEUAAU6KLH4h\nAAEIQAACeQggwHngYIIABCAAAQgkRQABToosfiEAAQhAAAJ5CCDAeeBgggAEIAABCCRFAAFO\niix+IQABCEAAAnkIIMB54GCCAAQgAAEIJEWAjzEkRRa/ECiSwMyZM7P2iPvjDFnOWYEABEpO\ngBZwyYuABEAAAhCAQHskgAC3x1InzxCAAAQgUHICCHDJi4AEQAACEIBAeySAALfHUifPEIAA\nBCBQcgIIcMmLgARAAAIQgEB7JIAAt8dSJ88QgAAEIFByAghwyYuABEAAAhCAQHskgAC3x1In\nzxCAAAQgUHICXryI4+rVq/bxxx/bBx98YP369bO7777bOnfunIG3adMmO3fuXGZdCzfffLMN\nGTIks23fvn22efNm69mzp40fP966du2asWkhyn7mzBnTcfQ7duxYGzp0aNb+rEAAAhCAAASK\nIZB6AT569Kg9+uijTnBvueUWW79+va1atcpeeeUVq6mpsStXrtgzzzxj3bp1s4qKa9l5/PHH\nMwK8evVqW7Fihd111122f/9+0/ry5cuttrbWsYqy792712bPnm3Dhw+3QYMGuWMvWrTIxo0b\nVwxr4kIAAhCAAAQyBK4pVmZTuhYkuAMHDrSXXnrJJez8+fM2ffp0W7dunT322GP2+eef26VL\nl+zVV1+1Xr16NUq8WrZ6pd+yZcts9OjRVl9fb3PmzHH76zfKLoeLFy+2qVOn2vz5862srMzd\nACxdutTWrl3r1hsdlA0QgAAEIACBCAKpHwPu0qWLPfLII5lsVFVV2ciRI11LVht37dplvXv3\nblJ8Zd+yZYsTcImvglrJkyZNso0bN7r1KPuxY8ds+/btNm3atIzYTp482R1/27Ztzgf/IAAB\nCEAAAsUSSH0LOCy+ytzx48ft/ffft7lz57q87t6923U/L1myxI3RqltZ+9x5553OfuDAAddt\n7FZ+908tanVta2w5yn7w4EG3l/YJglranTp1ssOHD9uoUaOCzSax/ulPf5pZ18Jtt91mX/7y\nl7O25a4EXefyqRa2r6G8vNzd4FRXV/uahVSl+3o56lySj4aGhlTlq5jEdOzY0UXXjbfqq69B\ndVvB9/qtPOh6db3npvyUKnTo0MH0l2QeCq1zqRfgcCGpq3nBggV2ww032H333edMO3fudKI8\nYsQIN7nqrbfesqefftqef/55u/32200CqrHicNB4sSrzqVOnIu0SaE34Ck/6ki/5OHHiRNit\nHTlyxNQ1HQ5K76233hre1OyyLjL68z0EF03f81Hq9D/44IOZJPziF7/ILBezoPO0LYTcSZO+\n5qmystLXpGfS3dT1MGP0aCFXF+JMurSqkOCNAJ8+fdqeeuop069ELrjIS+AkpsGEKk2MUqtY\nY8QSYMXTuG84BOvq3m6JXb40+Uv7h8PgwYPt5ZdfDm9yrW+12vMF3R3rAqOZ3BcvXswXNdU2\ntYB1gcmdkZ7qRHuSuKhzqKlsdO/e3dWXQu/Gm/JR6m2qYzqndLOsOudrUB5UDr7Xb51TFy5c\nsLq6Ol+LwvVC6MZUWpJk0BM3UcELAVZ38Xe+8x3XZfDjH//YdBIEIbwcbJPwvvPOO25V48Of\nfvppYHK/Ai/B1p1cIXZVfJ1wYcGVjwEDBmT5lYjqEalwOHnypGniWL4QdEvpxsDnCqqbGd1M\n+JyHfOVUSltLmAYXfJ8FOOh5UosiuHEuZTm09Njqtg3Ko6U+Sr1f0OjR9bAl52Op0x8cX93P\nSZeFGiOFhNRPwjp06JB9+9vfdo8U6dGhXMF98skn3aNJ4cx++OGHbuKVtg0bNsx27NiRVXm3\nbt2aGReOsqtVq8qjfYKgSVlqdYfHhQMbvxCAAAQgAIFCCKRegF944QXX9fTAAw84IZW46k/P\n5iqMGTPGPder2dC6K3vjjTdcvGD8bMKECS7emjVrnGju2bPHNmzYYDNmzHDbo+wS/IkTJ7pH\nmc6ePeu6X/RMsWZS9+nTx/ngHwQgAAEIQKBYAqnugtZLM9577z2XJz2DGw56G9WPfvQj93jQ\nRx99ZLNmzXLdn+qy0iQsdUMraP3ZZ5+1hQsXmkRYk5z0HLHehlWIXXH0vLD2nzJlivOnF4LM\nmzfP7c8/CEAAAhCAQEsIlH3RF+7vMwqhHGvij14TqVdVBmOqIbNbVHe2Wq0aA2gqRNk17qu+\n/WKmrxcyBqwJGhqT1kQTnyc3aIxIbJRnn8LMmTNTn1y9TKbYoHNd8yd8ruKaqapzSk8Y+DwG\nrDyoHHyv35ozo2tt0hOYij3Xi4mv678mSKluJBWkE3379o10n+oWcGTqQxF0gusvX5A45wtR\n9iSnredLF7Z4CfgguPHmGG8QgEAaCTTdFExjSkkTBCAAAQhAoA0RQIDbUGGSFQhAAAIQ8IdA\nm+mC9gc5KYVA8QRyu81bMiZc/FHZAwIQSJIAApwkXXynhkCugKUmYSQEAhBotwTogm63RU/G\nIQABCECglAQQ4FLS59gQgAAEINBuCSDA7bboyTgEIAABCJSSAAJcSvocGwIQgAAE2i0BJmG1\n26Jv2xln0lXbLl9yB4G2QIAWcFsoRfIAAQhAAALeEaAF7F2RkWAImIVb+DwTzBkBAT8J0AL2\ns9xINQQgAAEIeE4AAfa8AEk+BCAAAQj4SYAuaD/LjVQ3QSDcLduEmU0QgAAEUkWAFnCqioPE\nQAACEIBAeyGAALeXkiafEIAABCCQKgIIcKqKg8RAAAIQgEB7IcAYcHspafLZZgnkjn3zWFKb\nLWoy1sYIIMBtrEDbU3Zyhac95Z28QgAC/hNAgFuhDMvLy/MepUOH344E6Dcqbl5HJTYq/WVl\nZV7nocQIYzl8+BwKzq1YHJfASZD+tlA3GhoavK4bQVn4XseVfoVwPYn71A5YRflFgKMIXae9\noqLCqqqq8noJCquystI6deqUN26ajUHF7N69e5qT2ebTFvDXeRUs+5pp1R+Fbt26mQTM16CL\nvdLve/0Wf+XB9/NK5ZFkHq5cuVLQqYoAF4Sp5ZHq6+vtzJkzeR1IeGtra62urs795Y2cYmPH\njh2turraTp48meJUtv2kHT9+3GWyT58+duLECa+Fq6amxp1Tp06dMtUlX4PqhQRYddzXoPrd\nu3dvu3jxop0+fdrXbJhuTHv27GlBPUkiIxL4Ll26RLpmFnQkIiJAAAIQgAAE4idACzh+pniE\nQEkJhCenvfbaayVNCweHAASaJ4AAN88GSwoJhMUlhckjSRCAAAQKJkAXdMGoiAgBCEAAAhCI\njwACHB9LPEEAAhCAAAQKJoAAF4yKiBCAAAQgAIH4CDAGHB9LPEEgdQT+6q/+KitNvKYyCwcr\nECgpAQS4pPg5eBQBJl1FEcIOAQj4SoAuaF9LjnRDAAIQgIDXBGgBe118JB4CxREI9yjQHV0c\nO2JDIG4CtIDjJoo/CEAAAhCAQAEEaAEXAIkorUsg3Epr3SNzNAhAAAKtRwABbj3WHAkCqSKQ\ne6NDl3SqiofEtAMCdEG3g0ImixCAAAQgkD4CCHD6yoQUQQACEIBAOyBAF3Q7KOS0ZzG3KzTt\n6W2r6QuXA93RbbWUyVeaCNACTlNpkBYIQAACEGg3BGgBt5uiJqMQKJxAuDWsvWgRF86OmBAo\nlAACXCgp4sVKIPcCH6tznMVOIFxeiHHseHHYTgnQBd1OC55sQwACEIBAaQnQAi4t/3Zz9HAL\nqt1kuo1mNF9Z0jpuo4VOthIhgAAXiPXMmTO2adMm0+/YsWNt6NChBe5JNAhAAAIQgEBjAghw\nYyaNtuzdu9dmz55tw4cPt0GDBtkrr7xiixYtsnHjxjWKy4ZrBPK1lK7FYqktEchX5rSO21JJ\nk5c4CCDABVBcvHixTZ061ebPn29lZWW2atUqW7p0qa1du9atF+CCKBBo9wQQ53Z/CgAghwAC\nnAMkd/XYsWO2fft2e+qppzJiO3nyZFuxYoVt27bNRo0albtLu13/i7/4i3abdzJ+fQTyifMv\nfvGL63PO3hBIKQEEOKJgDh486GIMHDgwE7NXr17WqVMnO3z4cJYA/9///Z8tXLgwE08LDz30\nkN1xxx1Z23JXOnT47WT0Ll26WOfOnXPNketXr15tNs6VK1cytvr6+syyFs6ePZtZV17C4eTJ\nk5nVX//615llLbz99ttZ66xAIEkCkyZNum73d955Z5aPqqqqzHr//v0zy1qoqanJrFdWVmaW\ntaB6H4QePXoEi+43XL/CPmQMbKqr6kULh4qKa5fhjh07hk0Wrr/V1dVZtvPnz2fWc68bwTUl\nE+F3C7nbw9eOXFtDQ0Nmd6VZf0qP0ltbW5uxhX1oY66fTMSULCgf5eXlWXmIO2nhcsvn+1rJ\n54vVjm0HDhxwoph7gnfr1s1OnDiRRUaClitOf/zHf2y5lThrp9CKKl9uBQyZY18MV6IhQ4Y0\n6/8b3/hGlu3v/u7vstZZgQAEWp+ArkGlCBKvthAKvS63JK+XLl0qaDcEOAKTBDG4ew1H1R2O\nWqzh8OUvf9lyW4uXL1+2oBUdjhte1omgu+nTp09bXV1d2OTVsliJyalTp7xKd25i+/Xr58pc\nww8+h969e5vyEG7J+JYftSR1Th09erTJeuhLfoJrhe/1W71/586dc0+D+MI+N51qoavxkWT9\n1k1Knz59cg/daB0BboQke4MuYhJbVZygEimGxHLAgAFZkQU9t1tKXblNCXh4x+ACqd9gOWz3\nZTlIe/DrS7qbS2dbyIfy4HM+grT7ng+dY77nISiLIC/N1Zu0bw/yEfwmkd5CffMmrAj6gwcP\ndmMeW7duzcTUpCyNe4THhTNGFiAAAQhAAAIFEECAIyB1797dJk6c6F5GrzHeCxcuuBnQmhhS\nSBdDhHvMEIAABCDQTgkgwAUU/Jw5c9zsxylTpth9993nWsTz5s0rYE+iQAACEIAABJomwBhw\n01yytmrA/sUXX3TjvhrnzX0cICsyKxCAAAQgAIECCCDABUAKouQ+2xds5xcCEIAABCBQLAG6\noIslRnwIQAACEIBADAQQ4Bgg4gICEIAABCBQLAEEuFhixIcABCAAAQjEQAABjgEiLiAAAQhA\nAALFEkCAiyVGfAhAAAIQgEAMBMq+eGXWtU9exOAQF9kE9N7UqBdz60tEeruW3iXt89u1gq+M\nRL16M5tQ+tb0QQ09anbrrbemL3FFpEhf7ok694pwV5Kou3btsv3799sf/MEfeP34X/ABg0K/\nklMS2BEH1et333//fdPbAW+88caI2Ok26731ek9/UkHvm9ZLnKICAhxFqBXsP/vZz+xv//Zv\n7e///u+Nb+q2AvCIQ+gbzyNGjLB//dd/jYiJOWkCzzzzjK1bt87+/d//3UaOHJn04fCfh8CH\nH35oDz74oP3lX/6l8UW0PKCKMNEFXQQsokIAAhCAAATiIoAAx0USPxCAAAQgAIEiCCDARcAi\nKgQgAAEIQCAuAowBx0XyOvwcP37cPvvsMxsyZIjp+8OE0hLQWFdlZaXddNNNpU0IR7fPP//c\njh496sZ/q6qqIFJCAppQunPnTuvbt68NGjSohClpO4dGgNtOWZITCEAAAhDwiABd0B4VFkmF\nAAQgAIG2QwABbjtlSU4gAAEIQMAjAnyOMCWFtXv3btuzZ09Wanr27OleQJC1kZVECezbt882\nb95sYj9+/Hjr2rVrosfDedMEzpw5Y++9914j49133216iQKhdQj85je/cfXhgQceaHRA6koj\nJEVvQICLRpbMDv/yL/9i7777rnXr1i1zgK9+9asIcIZG8gurV6+2FStW2F133eXevqT15cuX\nW21tbfIH5whZBDQR7rnnnms0KfH2229HgLNIJbdy9uxZ+973vmedO3e2XAGmrsTDHQGOh+N1\ne9Hswscee8zuv//+6/aFg+IJ6G5+5cqVtmzZMhs9erTpdZpz5sxxb2HSL6F1CegVlHoj2T/+\n4z+27oE5miPw61//2p5//nk7efKkDRs2LIsKdSULx3WtMAZ8Xfji2fnixYumk5rHXuLh2RIv\nW7Zsce/hlvgqVFRU2KRJk2zjxo0tccc+10lAAkx9uE6ILdxd3f961eS3vvUte/jhhxt5oa40\nQtLiDbSAW4wuvh337t1rV69etV/96lf24osvmrp+NNY1c+ZM1/0T35Hw1ByBAwcONHq2UR/G\n0DOoKhu9XJ3QegQkwOr6VBfojh077Oabb7a/+Zu/aVRGrZei9nMkPW/9+uuvW69evey1115r\nlHHqSiMkLd7AVaXF6OLbURcbBbWE586da9/4xjfcy+dfeOGF+A6Cp7wEDh48aDU1NVlxNB4v\n8T116lTWdlaSJaAWmMpDNz9Tp061Rx991HTRV93QzSkhWQLq/ZH4NheoK82RKX47LeDimV3X\nHppcok8PBkGfvJs4caKbbDVgwAC3+fd///dNny/T3afu+nOFIdiX3/gIaGZt7mcUg/UuXbrE\ndyA8RRLQzPOf/vSnbia6Pqmo8Hu/93vuKzz/+Z//adOmTYv0QYTkCFBX4mOLAMfHsiBP27Zt\ns5///OeZuJphq+8AB+IbGMaNG+cEuKm7zSAOv/ER0CtAP/300yyH+v6pykddoYTWI6DvSvfv\n3z/rgMOHD7c+ffq4lnCWgZVWJ0BdiQ85XdDxsSzIkyY1/OQnP8n8/cmf/ImtX7/ennzyyaz9\n1VLWhShXmLMisRIbAc301Fhj0OqV461btzLmGBvhwh3pRkjfnNV7oIOgLugjR45QHgGQEv5S\nV+KDjwDHx7LFnvTCB03710fHJQD//d//7ZY1Czf8XHCLD8COkQQmTJjg4qxZs8aN++qlKBs2\nbLAZM2ZE7kuEeAl86Utfch/DePnll+3EiROu1fvSSy+53gjNjyCUlgB1JT7+fIwhPpbX5Ulj\nXv/0T//kLv5XrlwxtYyfeOIJuj+vi2pxO7///vu2cOFCq6urM80E1VjjrFmzinNC7FgIqDfi\nhz/8oXshihyqC3rBggU2dOjQWPzjpDACmoeiFwTpBTXhQF0J02j5MgLccnax76nW7+HDh93b\nf4LJJ7EfBIeRBA4dOuTGG3n0KBJV4hE0E1qTfrp37574sThA8QSoK8UzC++BAIdpsAwBCEAA\nAhBoJQKMAbcSaA4DAQhAAAIQCBNAgMM0WIYABCAAAQi0EgEEuJVAcxgIQAACEIBAmAACHKbB\nMgQgAAEIQKCVCCDArQSaw0AAAhCAAATCBBDgMA2WIQABCEAAAq1EgHdBtxJoDgOBtkpAXyg6\nduyYe3lJ3759m82mviqlD7zr4yJ6xzYBAu2dAC3g9n4GkH8IXCcBfT5wzJgxduONN9pnn33W\npLdLly7Z17/+dRsxYkTWO56bjMxGCLQTAghwOylosgmBpAjogyHLly933+p9/PHHmzzMokWL\n7JNPPjH9fu1rX2syDhsh0N4I8Cas9lbi5BcCCRHQu7N/9rOf2T//8z/bzJkzM0fRl71uu+02\n0yc2/+u//st4xWcGDQvtnAAC3M5PALIPgbgI6NvVo0aNch8U0Xev1TLW+83/8A//0Hbv3m0S\nYn3KjgABCPyWAF3QnAkQgEAsBPr372//8A//4CZa6UteCi+++KLpyzn6RXxjwYyTNkSAFnAb\nKkyyAoE0EPjTP/1T+7d/+zfTp+zmzp1r+n6s1gkQgEA2AQQ4mwdrEIDAdRLQJ+rUFa1Hk/RY\n0scff+x+r9Mtu0OgzRGgC7rNFSkZgkBpCfTr18++973vuUT84Ac/QHxLWxwcPcUEEOAUFw5J\ng4CvBIIXbQS/vuaDdEMgSQIIcJJ08Q0BCEAAAhBohgAC3AwYNkMAAhCAAASSJIAAJ0kX3xCA\nAAQgAIFmCCDAzYBhMwQgAAEIQCBJAjyGlCRdfEMAAhCAAASaIUALuBkwbIYABCAAAQgkSQAB\nTpIuviEAAQhAAALNEECAmwHDZghAAAIQgECSBBDgJOniGwIQgAAEINAMAQS4GTBshgAEIAAB\nCCRJAAFOki6+IQABCEAAAs0QQICbAcNmCEAAAhCAQJIEEOAk6eIbAhCAAAQg0AwBBLgZMGyG\nAAQgAAEIJEkAAU6SLr4hAAEIQAACzRBAgJsBw2YIQAACEIBAkgQQ4CTp4hsCEIAABCDQDIH/\nB2eVfA97bOUuAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(Y, bins=100) # обратите внимание на то, что правый хвост очень длинный "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [3] Задачка 10\n",
    "\n",
    "Помните? Мы всё это изучаем, чтобы решать реальные проблемы! С помощью генераций в R мы можем оценить любое математическое ожидание и любые вероятности. Нам позволяет сделать это великий и могучий фундаментальный ЗБЧ!\n",
    "\n",
    "Давайте попробуем проверить несколько свойств математических ожиданий и дисперсий, которые вы доказали на лекциях по теории вероятностей в прошлом семестре. Выберите конкретные случайные величины (любые) и проверьте для них утверждения, перечисленные ниже. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Хочу экспоненциальную и равномерную, нанизанную на экспоненциальную!\n",
    "# Так зависимсоть между величинами будет\n",
    "\n",
    "n_obs = 10^6\n",
    "\n",
    "x = rexp(n_obs, rate = 2)\n",
    "y = x + runif(n_obs, min = 2, max = 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__a)__ Верно ли, что $E(X + Y) = E(X) + E(Y)$? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "4.49762629550675"
      ],
      "text/latex": [
       "4.49762629550675"
      ],
      "text/markdown": [
       "4.49762629550675"
      ],
      "text/plain": [
       "[1] 4.497626"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "4.49762629550675"
      ],
      "text/latex": [
       "4.49762629550675"
      ],
      "text/markdown": [
       "4.49762629550675"
      ],
      "text/plain": [
       "[1] 4.497626"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a) Из курс тервера мы знаем, что это правда всегда \n",
    "mean(x + y)\n",
    "mean(x) + mean(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__b)__ Верно ли, что $E(X \\cdot Y) = E(X) \\cdot E(Y)$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.2457471458471"
      ],
      "text/latex": [
       "2.2457471458471"
      ],
      "text/markdown": [
       "2.2457471458471"
      ],
      "text/plain": [
       "[1] 2.245747"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.99674044240762"
      ],
      "text/latex": [
       "1.99674044240762"
      ],
      "text/markdown": [
       "1.99674044240762"
      ],
      "text/plain": [
       "[1] 1.99674"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# b) Ну тут явно чего-то не хватает...\n",
    "mean(x*y)\n",
    "mean(x)*mean(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.24574739485405"
      ],
      "text/latex": [
       "2.24574739485405"
      ],
      "text/markdown": [
       "2.24574739485405"
      ],
      "text/plain": [
       "[1] 2.245747"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Давайте посмотрим лекции по терверу и вспомним чего не хватает :) \n",
    "mean(x)*mean(y) + cov(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__c)__ Верно ли, что $Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X,Y)$? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.74573442929709"
      ],
      "text/latex": [
       "1.74573442929709"
      ],
      "text/markdown": [
       "1.74573442929709"
      ],
      "text/plain": [
       "[1] 1.745734"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.74573442929709"
      ],
      "text/latex": [
       "1.74573442929709"
      ],
      "text/markdown": [
       "1.74573442929709"
      ],
      "text/plain": [
       "[1] 1.745734"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#c) Это чистая правда! В лекциях даже доказательство есть!\n",
    "var(x + y)\n",
    "var(x) + var(y) + 2*cov(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__d)__ Верно ли, что $Var(X \\cdot Y) = Var(X) \\cdot Var(Y)$? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "8.13094557321404"
      ],
      "text/latex": [
       "8.13094557321404"
      ],
      "text/markdown": [
       "8.13094557321404"
      ],
      "text/plain": [
       "[1] 8.130946"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.248504812890086"
      ],
      "text/latex": [
       "0.248504812890086"
      ],
      "text/markdown": [
       "0.248504812890086"
      ],
      "text/plain": [
       "[1] 0.2485048"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#d) Ложь! Очередная! А слабо найти правильную формулу? Она довольно неочевидна :)\n",
    "var(x*y)\n",
    "var(x)*var(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__e)__ Верно ли, что если $Cov(X, Y) = 0$, то две случайные величины независимы? Удастся ли проверить это с помощью генераций? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Это наглая ложь! Простейший пример. Пусть случайная величина $X$ равновероятно принимает три значения:\n",
    "\n",
    "|$X$|$-1$|$0$|$1$| \n",
    "|---|----|---|---|\n",
    "| $P$  |1/3 |1/3|1/3|\n",
    "\n",
    "Пусть $Z = |X|$.\n",
    "\n",
    "|$Z$|$0$|$1$| \n",
    "|---|---|---|\n",
    "| $P$  |1/3|2/3|\n",
    "\n",
    "Тогда эти две виличины явно зависимы. Одна выражается через другую. Но при этом \n",
    "\n",
    "$$\n",
    "Cov(X,Z) = E(X \\cdot Z) - E(X) \\cdot E(Z) = 0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "8.11881531881533e-05"
      ],
      "text/latex": [
       "8.11881531881533e-05"
      ],
      "text/markdown": [
       "8.11881531881533e-05"
      ],
      "text/plain": [
       "[1] 8.118815e-05"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = sample(c(-1,0,1), size = n_obs, replace = TRUE)\n",
    "z = abs(x)  # задаём зависимость между z и x  \n",
    "cov(x,z)    # получаем близкое к нулю число"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [4] Задачка 11\n",
    "\n",
    "Филя и Никита решили попытать счастье и попасть на стажировку в ЦБ. В качестве вступительного испытания, они получили листочки с задачками по терверу и случайным процессам. Одна из задач из листочка выглядела следующим образом:\n",
    "\n",
    "Пусть $X \\sim N(0, \\sigma^2)$. Пусть $\\Phi(x)$ — функция распределения для $N(0,1)$. Нужно найти математическое ожидание для случайной величины $\\Phi(X)$. \n",
    "\n",
    "Собеседователи, дав Филе и Никите задание, сказали, что у них 2 часа, и куда-то ушли. Пользоваться можно чем угодно (но это не точно). В голове у парней есть какое-то решение. Правда они в нём не уверены. Зато у них с собой есть ноутбуки. Помогите Филе и Никите оценить $E(\\Phi(X))$ с помощью симуляций. Постройте для случайной величины $\\Phi(X)$ гистограмму. Возьмите $\\sigma = 1$, после $\\sigma = 3$, после $\\sigma = 100$. Как ведут себя математическое ожидание и распределение при росте дисперсии?\n",
    "\n",
    "__P.S.__ На стажировку в ЦБ парни конечно же не попали."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.499877838749967"
      ],
      "text/latex": [
       "0.499877838749967"
      ],
      "text/markdown": [
       "0.499877838749967"
      ],
      "text/plain": [
       "[1] 0.4998778"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# В этом пункте всё логично,  в соответствии с квантильным преобразованием \n",
    "# (на него мы посмотрим на третьей паре) мы получили равномерное распределение\n",
    "\n",
    "n_obs = 10^6\n",
    "x <- rnorm(n_obs, mean=0, sd=1)\n",
    "y <- pnorm(x)\n",
    "mean(y)\n",
    "qplot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.499912532389991"
      ],
      "text/latex": [
       "0.499912532389991"
      ],
      "text/markdown": [
       "0.499912532389991"
      ],
      "text/plain": [
       "[1] 0.4999125"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nL/D/AYAtDTZvEWFCAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Тут уже результат будет поинтереснее и непредсказумее! \n",
    "# распределение начало разъезжаться в разные стороны\n",
    "\n",
    "n_obs = 10^6\n",
    "x <- rnorm(n_obs, mean=0, sd=3)\n",
    "y <- pnorm(x)\n",
    "mean(y)\n",
    "qplot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.500219422095731"
      ],
      "text/latex": [
       "0.500219422095731"
      ],
      "text/markdown": [
       "0.500219422095731"
      ],
      "text/plain": [
       "[1] 0.5002194"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nSwhAAAIQgAACTBuAAAQgAAEI5IDA/wcS5uq9IGWTiwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# При огромной дисперсии оно совсем-совсем разъехалось и \n",
    "# в пределе получится дискретная случайная величина! \n",
    "\n",
    "n_obs = 10^6\n",
    "x <- rnorm(n_obs, mean=0, sd=100)\n",
    "y <- pnorm(x)\n",
    "mean(y)\n",
    "qplot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Давайте попробуем повыяснять почему такое происходит. Для этого решим по-честному теоретическую задачку и найдём предел для функции распределения нашей новоиспечённой случайной величины. $\\Phi(x)$ - функция распределения, значит принимает значения на отрезке от $0$ до $1$. Найдём функцию распределения случайной величины $Y = \\Phi(X)$. Будем делать это по определению: \n",
    "\n",
    "$$\n",
    "F(y) = P(Y \\le y) = \\begin{cases}0, \\text{ если } y \\le 0 \\\\ 1, \\text{ если } y > 1 \\\\ P(\\Phi(X) \\le y), \\text{ если } y \\in (0; 1].    \\end{cases}\n",
    "$$\n",
    "\n",
    "Самая интересная тут последняя строчка. Немного поработаем с ней.\n",
    "\n",
    "$$\n",
    "P(\\Phi(X) \\le y) = P(X \\le \\Phi^{-1}(y)) = P \\left( \\frac{X}{\\sigma} \\le \\frac{ \\Phi^{-1}(y)}{\\sigma} \\right) = \\Phi \\left( \\frac{ \\Phi^{-1}(y)}{\\sigma} \\right).\n",
    "$$\n",
    "\n",
    "Дело осталось за малым, найти придел для функции распределения случайной величины $Y$. При $\\sigma \\to \\infty$ выражение $\\frac{ \\Phi^{-1}(y)}{\\sigma}$ сходится к нулю. Нормальное распределения симметрично относительно нуля. Значит $\\Phi(0) = \\frac{1}{2}$.  В пределе получаем функцию \n",
    "\n",
    "$$\n",
    "F(y) = P(Y \\le y) = \\begin{cases}0, \\text{ если } y \\le 0 \\\\ 1, \\text{ если } y > 1 \\\\ \\frac{1}{2}, \\text{ если } y \\in (0; 1].    \\end{cases}\n",
    "$$\n",
    "\n",
    "Как мы помним из лекций, функция распределения всегда задаёт какую-то одну конкретную случайную величину. В данном случае мы получили функцию распределения для случайной величины, принмающей либо значение $1$ либо $0$ с вероятностями $0.5$. Ровно этот резулььаь выше у нас получился на графике. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [6] Задачка 12\n",
    "\n",
    "__За генерацию можно получить только 1 балл. Она, блин, делается в две строчки. Остальное ставится за ручное решение.__\n",
    "\n",
    "Чтобы получить на посвяте стакан Уколовки, разлитый лично Димой Генераловым, нужно решить задачку по терверу. Случайные величины $X$, $Y$ и $Z$ равномерны на отрезке $[0;1]$ и независимы. Диму интересует случайная величина $(XY)^Z$. Ему очень интересно было бы узнать её распределение. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6\n",
    "X <- runif(n_obs)\n",
    "Y <- runif(n_obs)\n",
    "Z <- runif(n_obs)\n",
    "\n",
    "M = (X*Y)**Z\n",
    "qplot(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tOne-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  M\n",
       "D = 0.00078834, p-value = 0.5632\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Понравилось у парней, что они проверили что распределение равномерное тестом Колмогорова.\n",
    "# Про это мы будем говорить в будущем, поэтому это забегание вперёд паровоза, но забегание правильное.\n",
    "ks.test(M, \"punif\", 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Это было довольно просто, не так ли? Давайте займёмся кое-чем более интересным, попробуем найти плотность распределения случайной величины $(XY)^Z$ вручную. Это не особо сложно. Перед нами просто-напросто возникнет несколько интегралов, которые придётся взять. Задача, как и Удав Анатолий из [культурного кода.](https://github.com/bdemeshev/probability_dna/raw/master/probability_dna.pdf) Но её решения там нет.\n",
    "\n",
    "__a)__ Какое распределение имеет случайная величина $- \\ln X$?\n",
    "\n",
    "__Решение:__\n",
    "\n",
    "$X, Y, Z$ распределены равномерно на $[0; 1]$. Для них $F(x) = x$. Давайте найдём плотность случайной величины $X_1 = -\\ln X$. План будет таким: из определения найдём функцию распределения, а потом возьмём от неё производную. Погнали: \n",
    "\n",
    "$$\n",
    "F(x_1) = P(X_1 \\le x_1) = P(- \\ln X \\le x_1) = P(\\ln X \\ge -x_1) = 1 - P(\\ln X \\le -x_1) = 1 - P(X \\le e^{-x_1}) = 1 - e^{-x_1}\n",
    "$$\n",
    "\n",
    "Берём производную, получаем плотность распределения:\n",
    "\n",
    "$$\n",
    "f(x_1) = F'(x_1) = -e^{x_1}\n",
    "$$\n",
    "\n",
    "Не забываем про область определения случайной величины. Если $x \\in [0; 1]$, тогда $-\\ln x \\in [0; + \\infty)$. Выходит, что $X_1$ имеет экспоненциальное распределение, $Exp(1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__б)__ Какое распределение у случайной величины $-(\\ln X + \\ln Y)$\n",
    "\n",
    "__Решение:__ \n",
    "\n",
    "Нам надо понять как распределена сумма $X_1 + Y_1$, то есть сумма двух независимых экспоненциальных случайных величин. Можно пойти в семинары, вспомнить формулу свёртки и воспользоваться ей. Вспомните как она выводится, ибо в следующем пункте нам надо будет самостоятельно вывести свёртку для произведения. Итак, $U = X_1 + Y_1$. Формула свёртки выглядит как-то так: \n",
    "\n",
    "$$\n",
    "f(u) = \\int_{-\\infty}^{+\\infty} -e^{-x_1} \\cdot - e^{-(u - x_1)} dx_1\n",
    "$$\n",
    "\n",
    "Немного поразбираемся в том, как ведут себя наши случайные величины. Обе принимают значение от $0$ до $+\\infty$. У первой экспоненты в степени всё хорошо всегда, $x_1$ модет ползать по всему отреку. Для второй экспоненты, в степени находится $x_2 = u - x_1$. Мы знаем, $x_2$ должен принимать значения от $0$ до $+\\infty$. Но если $x_1 > u$, тогда наступает беда и степень становится отрицательной. Когда $x_2$ отрицательный, плотность принимает нулевое значение. \n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/HW/images/exp_sum.png\" width=\"500\"> \n",
    "\n",
    "\n",
    "Получается, что на отрезке $[0; u]$ наша плотность будет ненулевой. В диапазоне между ~~отчаянием и надеждой~~ $(-\\infty; 0)$ и $(u; +\\infty)$. Случайная величина зануляется. \n",
    "\n",
    "$$\n",
    "f(u) = \\int_{0}^{u} -e^{-x_1} \\cdot - e^{-(u - x_1)} dx_1 = e^{-u} \\int_0^u d x_1 = u \\cdot e^{-u}.\n",
    "$$\n",
    "\n",
    "На $u$ никих дополнительных ограничений не накладывалось. Она бегает от $[0; + \\infty)$, как ей и положено. \n",
    "\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__в)__ Найдите функцию распределения для случайной величины $-Z (\\ln X + \\ln Y)$\n",
    "\n",
    "__Решение:__ \n",
    "\n",
    "Нам нужно вывести аналог формулы свёртки для произведения, а после найти как распределена случайная величина $T = U \\cdot Z$. Посмним, что $U$ бегает от $0$ до $+\\infty$, а $Z$ от $0$ до $1$. Выведем для $T$ функцию распределения: \n",
    "\n",
    "$$\n",
    "F_T(t) = P(T \\le t) = P(Z \\cdot U \\le t)\n",
    "$$\n",
    "\n",
    "Нам нужно найти эту вероятность. Случайные величины взаимосвязаны между собой формулой  $t = x_1 \\cdot x_2$.  Нарисуем картиночку. \n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/HW/images/prod.png\" width=\"400\"> \n",
    "\n",
    "Нас интересует область, где $x_1 \\cdot x_2 \\le t$, то есть $x_2 \\le \\frac{t}{x_1}$. То есть область под синей кривой. Будем держать в голове, что по оси $x_2$ мы можем поднятся наверх только до $1$. Эта ось отвечает за случайную величину $Z$. \n",
    "\n",
    "Выходит, что вероятность того, что при произвольном $t$ выполнится $x_1 \\cdot x_2 \\le t$ равна площади под синей кривой. То есть \n",
    "\n",
    "$$\n",
    "F_T(t) = P(T \\le t) = P(Z \\cdot U \\le t) = \\int_0^1 \\int_0^{\\frac{t}{x_2}} f(x_1) \\cdot f(x_2) dx_1 dx_2.\n",
    "$$\n",
    "\n",
    "Взяв этот двойной интеграл, получаем функцию распределения: \n",
    "\n",
    "$$\n",
    "= \\int_0^1 \\int_0^{\\frac{t}{x_2}} x_1 \\cdot e^{-x_1} \\cdot 1 \\cdot  dx_1 dx_2  = 1-e^{-t}.\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Для полноты картины выведем формулу свёртки для произведения случайных величин (так скучно написал эту фразу, аж самому тошно).__ Интерал выше - это функция распределения. Чтобы получить из неё плотность, нужно взять производную по $t$. Сделаем это. Не будем забывать, что $x_1 = \\frac{t}{x_2}$. \n",
    "\n",
    "$$\n",
    "f_T(t) = \\int_0^1 \\frac{1}{x_2} \\cdot f(\\frac{t}{x_2}) \\cdot f(x_2) d x_2 \n",
    "$$\n",
    "\n",
    "Если воспользоваться этой формулой, можно получить \n",
    "\n",
    "$$\n",
    "f_T(t) = e^{-t}.\n",
    "$$\n",
    "\n",
    "Обратите внимание, что здесь мы играли только в положительной области ($x > 0, y>0$). Если бы игра шла на всей числовой прямой, формула была бы немного другой. Пример выведения формулы для частного случайных величин можно глянуть в [Гнеденко](https://yadi.sk/i/O4hwgm4Xxz05yQ) на странице 143. Там же, кстати говоря, можно найти выведение плотностей для $\\chi^2_n$, Cтьюдента и Фишира. Мало ли вас всегда интересовало почему они именно такие."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__г)__ Наконец вы готовы ответить на главный вопрос: какое распределение у $(XY)^Z$.\n",
    "\n",
    "__Решение:__ \n",
    "\n",
    "Мы получили, что $T = -Z (\\ln X + \\ln Y) = -\\ln(XY)^{Z} \\sim Exp(1)$. Интересующая нас $W = (XY)^Z = e^{-T}$. \n",
    "\n",
    "$$\n",
    "F(w) = P(W \\le w) = P(e^{-T} \\le w) = P(-T \\le \\ln w) = 1 - P(T \\le - \\ln w)  = 1 - (1 - e^{-\\ln w}) = w\n",
    "$$\n",
    "\n",
    "Посмотрим на область определения. $T$ распределена от $0$ до $+\\infty$. Значит $e^{-T}$ от $0$ до $1$. Получаем на выходе, что $W \\sim U[0;1]$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2] Задачка 13\n",
    "\n",
    "Пока все однокурсники Самира занимались одномерными случайными величинами, он увлёкся матрицами. И вот теперь он хочет пропихнуть свои увлечения в теорию вероятностей. Самир собирается сгенерировать случайную квадратную матрицу $A$, где каждый элемент матрицы взят из равномерного на $[0;1]$ распределения. \n",
    "\n",
    "Пусть случайная величина $X$ — это определитель случайной матрицы. Помогите Самиру найти $E(X)$. Чему равна вероятность того, что матрица $A$ вырождена? Постройте для этой случайной величины гистограмму. \n",
    "\n",
    "Пусть случайная величина $Y$ — это самое большое собственное значение этой матрицы. Помогите Самиру найти $E(Y)$. Постройте гистограмму. \n",
    "\n",
    "Перед тем как решать задачу, выскажите свои априорные представления относительно этих распределений, опираясь на свою интуицию и знание линала. Подтвердились ли они? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_obs = 10^5\n",
    "\n",
    "# размерность матрицы можно было зафиксировать, можно было выбирать \n",
    "# на каждом шаге рандомно (почему бы и нет, в условии ничего ж не прописано)\n",
    "# в решении поступлю вторым способом\n",
    "\n",
    "x <- rep(0, n_obs)\n",
    "y <- rep(0, n_obs)\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    n = sample(2:10, size = 1) # выберем какуюнибудь размерность \n",
    "    A = matrix(runif(n^2), nrow=n, ncol=n, byrow=T)\n",
    "    x[i] <- det(A)\n",
    "                \n",
    "    # иногда собственные числа бывают комплексными, будем брать модуль от них\n",
    "    # (почему нет? в условии это не запрещалось)\n",
    "    y[i] <- max(abs(eigen(A)$values))\n",
    "}              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nJujuhd9vkN4AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(x, bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-0.000420316964109884"
      ],
      "text/latex": [
       "-0.000420316964109884"
      ],
      "text/markdown": [
       "-0.000420316964109884"
      ],
      "text/plain": [
       "[1] -0.000420317"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(x) # билзко к нулю, с чего бы этого... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(y, bins=100) # классная же гистограмма! просто огненная! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.99619518389641"
      ],
      "text/latex": [
       "2.99619518389641"
      ],
      "text/markdown": [
       "2.99619518389641"
      ],
      "text/plain": [
       "[1] 2.996195"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [4] Задачка 14\n",
    "\n",
    "Закон больших чисел — это теорема, которая позволяет людям зарабатывать деньги! В 1600-х годах люди научились составлять актуарные таблицы. Это такие таблицы, где указана ожидаемая продолжительность жизни для данного возраста и пола. Люди начали собирать данные о смертности и оценивать вероятность дожития человека до определённого возраста. На этом строились тарифы на страхование. \n",
    "\n",
    "Появление подобных таблиц обязано зарождению в течение 1600-х годов теории вероятности, которая впервые объяснила людям как случайные вещи при достаточно больших масштабах сглаживаются и становятся очень даже предсказуемыми. Надо признать, что у страхования было довольно трудное детство — как раз потому, что люди плоховато понимали концепцию вероятности. В голове довольно трудно удержать её. Многие люди и по сей день ошибочно думают, что могут влиять на случайность каким-то образом. Например, некоторые думают, что чаще других выбрасывают на кубике шестёрки. Более того, люди довольно плохо понимают условные вероятности. \n",
    "\n",
    "Несмотря на всё это недопонимание, страховые компании в наше время на диверсификации рисков делают кэш. Давайте представим, что мы в их шкуре и замутим простенький бизнес, связанный со страховками. Конечно же бизнес мы будем делать в России. Для того, чтобы как следует сделать его, мы нашли [актуарные таблицы для России 2009 года выпуска.](https://yadi.sk/i/-k-9kB263Uv8uH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>X</th><th scope=col>Мужчины.и.женщины.город</th><th scope=col>Мужчины.город</th><th scope=col>Женщины.город</th><th scope=col>Мужчины.и.женщины.село</th><th scope=col>Мужчины.село</th><th scope=col>Женщины.село</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0 лет   </td><td>0.992525</td><td>0.991658</td><td>0.993442</td><td>0.990321</td><td>0.989209</td><td>0.991496</td></tr>\n",
       "\t<tr><td>1 год   </td><td>0.999307</td><td>0.999221</td><td>0.999397</td><td>0.998812</td><td>0.998709</td><td>0.998921</td></tr>\n",
       "\t<tr><td>2 года  </td><td>0.999558</td><td>0.999517</td><td>0.999601</td><td>0.999358</td><td>0.999298</td><td>0.999420</td></tr>\n",
       "\t<tr><td>3 года  </td><td>0.999668</td><td>0.999609</td><td>0.999730</td><td>0.999441</td><td>0.999288</td><td>0.999601</td></tr>\n",
       "\t<tr><td>4 года  </td><td>0.999700</td><td>0.999671</td><td>0.999731</td><td>0.999524</td><td>0.999445</td><td>0.999607</td></tr>\n",
       "\t<tr><td>5 лет   </td><td>0.999695</td><td>0.999636</td><td>0.999757</td><td>0.999515</td><td>0.999444</td><td>0.999589</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllll}\n",
       " X & Мужчины.и.женщины.город & Мужчины.город & Женщины.город & Мужчины.и.женщины.село & Мужчины.село & Женщины.село\\\\\n",
       "\\hline\n",
       "\t 0 лет    & 0.992525 & 0.991658 & 0.993442 & 0.990321 & 0.989209 & 0.991496\\\\\n",
       "\t 1 год    & 0.999307 & 0.999221 & 0.999397 & 0.998812 & 0.998709 & 0.998921\\\\\n",
       "\t 2 года   & 0.999558 & 0.999517 & 0.999601 & 0.999358 & 0.999298 & 0.999420\\\\\n",
       "\t 3 года   & 0.999668 & 0.999609 & 0.999730 & 0.999441 & 0.999288 & 0.999601\\\\\n",
       "\t 4 года   & 0.999700 & 0.999671 & 0.999731 & 0.999524 & 0.999445 & 0.999607\\\\\n",
       "\t 5 лет    & 0.999695 & 0.999636 & 0.999757 & 0.999515 & 0.999444 & 0.999589\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| X | Мужчины.и.женщины.город | Мужчины.город | Женщины.город | Мужчины.и.женщины.село | Мужчины.село | Женщины.село |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 0 лет    | 0.992525 | 0.991658 | 0.993442 | 0.990321 | 0.989209 | 0.991496 |\n",
       "| 1 год    | 0.999307 | 0.999221 | 0.999397 | 0.998812 | 0.998709 | 0.998921 |\n",
       "| 2 года   | 0.999558 | 0.999517 | 0.999601 | 0.999358 | 0.999298 | 0.999420 |\n",
       "| 3 года   | 0.999668 | 0.999609 | 0.999730 | 0.999441 | 0.999288 | 0.999601 |\n",
       "| 4 года   | 0.999700 | 0.999671 | 0.999731 | 0.999524 | 0.999445 | 0.999607 |\n",
       "| 5 лет    | 0.999695 | 0.999636 | 0.999757 | 0.999515 | 0.999444 | 0.999589 |\n",
       "\n"
      ],
      "text/plain": [
       "  X      Мужчины.и.женщины.город Мужчины.город Женщины.город\n",
       "1 0 лет  0.992525                0.991658      0.993442     \n",
       "2 1 год  0.999307                0.999221      0.999397     \n",
       "3 2 года 0.999558                0.999517      0.999601     \n",
       "4 3 года 0.999668                0.999609      0.999730     \n",
       "5 4 года 0.999700                0.999671      0.999731     \n",
       "6 5 лет  0.999695                0.999636      0.999757     \n",
       "  Мужчины.и.женщины.село Мужчины.село Женщины.село\n",
       "1 0.990321               0.989209     0.991496    \n",
       "2 0.998812               0.998709     0.998921    \n",
       "3 0.999358               0.999298     0.999420    \n",
       "4 0.999441               0.999288     0.999601    \n",
       "5 0.999524               0.999445     0.999607    \n",
       "6 0.999515               0.999444     0.999589    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = read.csv('/Users/fulyankin/Yandex.Disk.localized/R/R_prob_data/aktuar2009.csv', sep=';', dec=',')\n",
    "head(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В табличке находится вероятность того, что человек проживёт конкретный год. В первой строке вероятность дожить до года, во второй до 2 лет, если человек уже дожил до года и так далее. Значит, если мы хотим узнать, какова вероятность того, что человек проживёт два года, мы должны умножить вероятность прожить первый год на вероятность прожить второй год. Из части __полезные функции,__ которая была в самом начале, можно узнать, что посчитать такую вероятность, помогает функция `cumprod`. Давайте посмотрим каково в России живётся женщинам и мужчинам. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nEvgPNzvcmOa4aVsAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df['age'] = 0:100\n",
    "df['man_prob'] = cumprod(df[,3])   # вероятность дожить до какого-то возраста\n",
    "df['woman_prob'] = cumprod(df[,4])\n",
    "\n",
    "ggplot(df, aes(age))+\n",
    "    geom_line(aes(y=man_prob, colour = \"man\"))+\n",
    "    geom_line(aes(y=woman_prob, colour = \"woman\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Что мы видим? А ничего хорошего. Рыжая кривая — вероятность того, что мужчина доживёт до конкретного возраста. Голубая - женщина. Женщины намного живучее, чем мужчины. Страховать их от несчастий намного выгоднее. Было бы интересно узнать насколько это выгоднее. Будем смотреть на женщин и мужчин, которые живут в городах. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Пусть мы продаём страховки только 25-летним городским дамам. Сколько нужно клиентов, чтобы с вероятностью 99% прибыль оказалась положительной.\n",
    "\n",
    "- Пусть мы продаём страховки только 60-летним городским дамам по той же цене. Сколько нужно клиентов, чтобы с вероятностью 99% прибыль оказалась положительной. \n",
    "\n",
    "Для простоты будем предполагать, что выплата в случае смерти составляет $10^6$ рублей."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.999013"
      ],
      "text/latex": [
       "0.999013"
      ],
      "text/markdown": [
       "0.999013"
      ],
      "text/plain": [
       "[1] 0.999013"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_small = df[c('X','Женщины.город')]\n",
    "p_wom = as.numeric(df_small[df_small['X'] == '25 лет'][2])\n",
    "p_wom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Давайте начнём с теории (всё то, что я буду писать ниже, было у вас в лекциях в первом семестре после формулы Лапласа, переосмыслите их). Прикинем исходя из ЦПТ сколько нам нужно людей для положительной прибыли. Мы помним, что если $X_i$ — прибыль с одной страховки и $L$ - её цена, а $M$ - выплаты, тогда\n",
    "\n",
    "  $X_i$     | $L$  | $L - M$\n",
    " ---------- | ------ | -------------\n",
    "$P(\\ldots)$ | $p$  | $1 - p$\n",
    "\n",
    "Средняя прибыль компании составит $\\frac{1}{n} \\sum X_i$. По закону больших чисел:\n",
    "\n",
    "$$\n",
    "\\frac{1}{n} \\sum_{i=1}^n X_i \\overset{p}{\\to} E(X_i) \n",
    "$$\n",
    "\n",
    "У нас число $n$ может быть конечным, поэтому нас интересует число $n$ такое, что \n",
    "\n",
    "$$\n",
    "P \\left( \\frac{1}{n} \\sum X_i > 0 \\right) > 0.99 \n",
    "$$\n",
    "\n",
    "Найдём математическое ожидание и дисперсию случайной величины $X_i$: \n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{aligned} \n",
    "E(X_i) = L - (1 - p) \\cdot M \\\\\n",
    "Var(X_i) = M^2 \\cdot p \\cdot (1-p)\n",
    "\\end{aligned} \n",
    "\\end{equation}\n",
    "\n",
    "По ЦПТ \n",
    "\n",
    "$$\n",
    "\\bar x \\sim N \\left( E(X_i), \\frac{Var(X_i)}{n} \\right),\n",
    "$$\n",
    "\n",
    "Знание этого факта позволяет нам найти в явном виде формулу для $n$. Давайте сделаем это. Мы хотим, чтобы \n",
    "\n",
    "$$\n",
    "P(\\bar x > 0) > 0.99.\n",
    "$$\n",
    "\n",
    "Найдём вероятность того, что среднее больше нуля. \n",
    "\n",
    "$$\n",
    "P \\left( \\bar x > 0 \\right) = P \\left( \\frac{\\bar x - E(X_i)}{\\sqrt{\\frac{Var(X_i)}{n}}} > \\frac{- E(X_i)}{\\sqrt{\\frac{Var(X_i)}{n}}} \\right) = 1 - \\Phi \\left(\\frac{- E(X_i)}{\\sqrt{\\frac{Var(X_i)}{n}}} \\right) =  \\Phi \\left(\\frac{E(X_i)}{\\sqrt{\\frac{Var(X_i)}{n}}} \\right) > 0.99\n",
    "$$\n",
    "\n",
    "Получается, что \n",
    "\n",
    "$$\n",
    "\\frac{E(X_i)}{\\sqrt{\\frac{Var(X_i)}{n}}} > u_{0.99}.\n",
    "$$\n",
    "\n",
    "Отсюда находим, что требуемое число клиентов должно быть таким: \n",
    "\n",
    "$$\n",
    "n > \\left(\\frac{u_{0.99}}{E(X_i)}\\right)^2 \\cdot Var(X_i)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для начала просто вобьём формулку. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "теоретический средний доход: 9013 \n",
      "теоретическая дисперсия: 986025831 \n",
      "Вероятность дожить: 0.999013 \n",
      "Число клиентов: 65.68994 \n"
     ]
    }
   ],
   "source": [
    "L = 10000  # цена страховки\n",
    "M = 10^6   # выплата, при наступлении страхового случая \n",
    "\n",
    "mu = L - (1 - p_wom)*M\n",
    "cat('теоретический средний доход:', mu,'\\n')\n",
    "\n",
    "s2 = M^2*p_wom*(1 - p_wom)\n",
    "cat('теоретическая дисперсия:', s2, '\\n')\n",
    "\n",
    "p_wom = as.numeric(df_small[df_small['X'] == '25 лет'][2])\n",
    "cat('Вероятность дожить:', p_wom,'\\n')\n",
    "\n",
    "n = s2*(qnorm(0.99)/mu)**2\n",
    "cat('Число клиентов:', n,'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Обратите внимание на тот факт, что из-за большой дисперсии, даже при высоком теоретическом доходе, нам необходимо довольно большое число клиентов. Давайте убедимся в том, что мы правильно вывели формулу, и попробуем посимулировать это добро для разных взносов и разных $n,$ начиная с которых мы получаем положительную прибыль. \n",
    "\n",
    "Просто меняйте $L$ и $M$, запускайте код выше, смотрите на оптимальное $n$. После запускайте ячейку ниже и убеждайтесь в том, что вероятность того, что средняя прибыли окажется больше нуля и правда выше $0.99$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.99011"
      ],
      "text/latex": [
       "0.99011"
      ],
      "text/markdown": [
       "0.99011"
      ],
      "text/plain": [
       "[1] 0.99011"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 0\n",
    "for(i in 1:10^6){\n",
    "    x <- rnorm(n+1, mean=mu, sd=sqrt(s2))\n",
    "    if(mean(x) > 0){\n",
    "        k = k + 1\n",
    "    }\n",
    "}\n",
    "\n",
    "k/10^6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Поосторожнее с ценой, в окрестности которой ожидаемая прибыль равна нулю. На самом деле во всей этой ситуации вполне осмысленен вопрос: а какого чёрта, мы решили взять и апроксимировать поведение среднего нормальным распределением? Если мы попробуем сделать большое количество генераций и посмотреть что происхиодит с распределением, мы увидим, что даже при больших $n$ у нас есть проблемы. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nIJAoARJwopqLYBFAAAEE0iLw/xIg+d2hvBORAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 10000  # цена страховки\n",
    "M = 10^6   # выплата, при наступлении страхового случая \n",
    "\n",
    "mns = rep(0,10^6)\n",
    "for(i in 1:10^6){\n",
    "    mns[i] = mean(sample(c(L, L - M), size=1000, prob = c(p_wom, 1 - p_wom),replace=TRUE))\n",
    "}\n",
    "\n",
    "qplot(mns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "При этом, если бы вероятность дожить до конца года у женщин была бы поменьше, мы бы могли увидеть привычный нам купол. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 10000  # цена страховки\n",
    "M = 10^6   # выплата, при наступлении страхового случая \n",
    "\n",
    "mns = rep(0,10^6)\n",
    "for(i in 1:10^6){\n",
    "    mns[i] = mean(sample(c(L, L - M), size=1000, prob = c(0.8, 1 - 0.8),replace=TRUE))\n",
    "}\n",
    "\n",
    "qplot(mns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Дело в том, что при маленьком $p$ сходимость к нормальному распределению идёт очень-очень медленно, и нам необходимо сделать на порядок больше симуляций, чтобы получить купол. \n",
    "\n",
    "В лекциях по терверу вы говорили, что кода $p$ или $(1-p)$ близко к нулю, мы имеем дело с редкими событиями. Для таких них лучше себя зарекомендовала апроксимация Пуассона. Давайте посмотрим, что нам про оптимальную численность скажет оно. Переведём $X_i$ в Бернуллиевскую случайную величину. \n",
    "\n",
    "  $X_i$     | $L$  | $L - M$\n",
    " ---------- | ------ | -------------\n",
    "$P(\\ldots)$ | $p$  | $1 - p$\n",
    "\n",
    "\n",
    "Если $Y_i = \\frac{X_i - L}{M} \\cdot (-1)$, тогда \n",
    "\n",
    "  $Y_i$     | $0$  | $1$\n",
    " ---------- | ------ | -------------\n",
    "$P(\\ldots)$ | $p$  | $1 - p$\n",
    "\n",
    "Вероятность $1-p$ - это вероятность успеха. Она очень близка к нулю. В прибилжении Пуассона именно это и требуется. Начинаем искать вероятность. \n",
    "\n",
    "$$\n",
    "P(\\bar X \\ge 0) = P \\left(\\sum X_i \\ge 0\\right) = P\\left(\\sum(L - M \\cdot Y_i  \\ge 0\\right) = P\\left(nL - M \\sum Y_i \\ge 0\\right) = P\\left(\\sum Y_i \\le n \\cdot \\frac{L}{M}\\right).\n",
    "$$\n",
    "\n",
    "Кажется, что формула готова. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9990135 \n",
      "0.9980279 \n",
      "0.9970434 \n",
      "0.9960598 \n",
      "0.9950772 \n",
      "0.9940955 \n",
      "0.9931148 \n",
      "0.9921351 \n",
      "0.9911563 \n",
      "0.9901785 \n"
     ]
    }
   ],
   "source": [
    "L = 10000\n",
    "for(n in 1:10){\n",
    "    cat(ppois(n*L/M, lambda = n*(1-p_wom)),'\\n')\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вот незадача! Уже при первом же человеке апроксимация выдаёт нам нужный результат. Дальше вероятность будет сначала убывать, потом увеличится и уйдёт к единице. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nl8D/A64UZU5yD5HQAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 10000\n",
    "\n",
    "prob = rep(0, 1000)\n",
    "\n",
    "for(n in 1:1000){\n",
    "    prob[n] = ppois(n*L/M, lambda = n*(1-p_wom))\n",
    "    }\n",
    "\n",
    "qplot(1:1000, prob, geom = 'line')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Если по-честному проделать симуляции, у вас в качестве ответа вывалится единица. Конечно же, чисто формально, это правильно, но мы же большая фирма и хотим много денег... Поэтому лучше взять более большое $n$. \n",
    "\n",
    "При генерациях для $p_{wom} = 0.98$ все получали адекатный результат, так как $10^6$ симуляций вполне хватало. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Выясните, начиная с какого возраста страховка для мужчин стоит дешевле, чем страховка для женщин. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "89"
      ],
      "text/latex": [
       "89"
      ],
      "text/markdown": [
       "89"
      ],
      "text/plain": [
       "[1] 89"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# где вероятность впервые окажется больше, тот возраст и подойдёт\n",
    "max(which(df$Женщины.город - df$Мужчины.город > 0)) + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [6]  Задачка 15 (Парадокс дней рождений)\n",
    "\n",
    "\n",
    "Вы когда-нибудь слышали про парадокс дней рождений? На википедии есть статья. Остановитесь, не нужно её гуглить. Давайте попробуем поразмышлять. Как думаете, какова вероятность того, что в комнате, в которой находится $23$ человека, хотя бы у двоих из них дни рождения совпадают (не у вас с кем-нибудь совпадёт, а у двоих произвольных людей)? \n",
    "\n",
    "__Внимание, ответ:__ вероятность этого $0.5$. Если в комнате $50$ человек, то вероятность этого возрастает до $0.97$. Получается, что если вы находитесь в большой аудитории, то вы смело можете ставить деньги на то, что в ней дни рождения у каких-нибудь двух произвольных людей совпадут. Делая такие ставки довольно часто, вы сможете обогатиться. Конечно же, иногда вы будете проигрывать, но математическое ожидание такой игры будет суперположительным. Например, если вы будете ставить $1000$ рублей, ваш ожидаемый выигрыш составит\n",
    "\n",
    "$$\n",
    "E(X) = 0.97\\cdot1000 - 0.03\\cdot1000.\n",
    "$$ \n",
    "\n",
    "Слабо найти вероятность того, что хотя бы у двоих людей из $n$ дни рождения совпадут? Если слабо, добро пожаловать на [википедию.](https://ru.wikipedia.org/wiki/Парадокс_дней_рождения)\n",
    "\n",
    "Почему нам трудно в это поверить? Ответ математический: степени трудно осознать. Как визирь в [древней задаче про шахматы и зёрнышки,](https://ru.wikipedia.org/wiki/Задача_о_зёрнах_на_шахматной_доске) мы плохо понимаем степенную функцию. Даже если мы подучились математике и статистике, это всё равно как-то непривычно. Вот пример неправильной логики: какова вероятность выпадения $10$ решек подряд?\n",
    "\n",
    "Нетренированный мозг может составить примерно такую цепочку мыслей: одна решка - $50%$, две решки - $25%$. Значит, десяток решек в $10$ раз труднее, ну то есть $5%$. Ну вот мы и облажались. Реальный шанс это $0.5^{10}$. Ошиблись немного. Примерно в $50$ раз.\n",
    "\n",
    "Итак, в произвольной группе из $50$ человек вероятность того, что хотя бы у двоих людей дни рождения совпадут, равна $0.97$. Но это всё только в теории. При решении задачи мы предполагаем, что рождения людей равномерно распределены в течение года. Однако на практике это может быть не так. В связи с этим реальная вероятность может отличаться от теоретической. \n",
    "\n",
    "В этой задачке вам предстоит проверить парадокс дней рождений на эмпирических данных. В табличке `vk_bdates.csv` лежит информация о $4589300$ пользователей из вконтакте. В табличке можно найти данные о имени пользователя `first_name`, его поле `sex`, его родном городе `home_town`, городе проживания `city`, дне `bdate`, месяце `bmonth` и годе `byear` рождения. Также там лежит информация о том удалена ли его страничка `deactivated`. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__[3] Простая часть (её решение можно найти во второй домашке прошлого года):__ \n",
    "\n",
    "Попробуйте на основе данных из этой таблички проверить парадокс дней рождений. Проверять его мы будем, конечно же в R. __Обратите внимание, что часто придётся прогонять один и тот же код. Не надо его копировать. Оформите его в виде функции.__ \n",
    "\n",
    "__Таблица тут: https://yadi.sk/d/hcysIe6d3Uv8rr__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4589300</li>\n",
       "\t<li>11</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4589300\n",
       "\\item 11\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4589300\n",
       "2. 11\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4589300      11"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>X</th><th scope=col>city</th><th scope=col>deactivated</th><th scope=col>first_name</th><th scope=col>home_town</th><th scope=col>id</th><th scope=col>last_name</th><th scope=col>sex</th><th scope=col>byear</th><th scope=col>bmonth</th><th scope=col>bday</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0              </td><td>Москва         </td><td>               </td><td>Илья           </td><td>               </td><td> 5             </td><td>Перекопский    </td><td>2              </td><td>  NA           </td><td>11             </td><td>18             </td></tr>\n",
       "\t<tr><td>1              </td><td>Санкт-Петербург</td><td>               </td><td>Николай        </td><td>               </td><td> 6             </td><td>Дуров          </td><td>2              </td><td>  NA           </td><td>NA             </td><td>NA             </td></tr>\n",
       "\t<tr><td>2              </td><td>Санкт-Петербург</td><td>               </td><td>Михаил         </td><td>Санкт-Петербург</td><td>11             </td><td>Петров         </td><td>2              </td><td>  NA           </td><td>12             </td><td>18             </td></tr>\n",
       "\t<tr><td>3              </td><td>Санкт-Петербург</td><td>               </td><td>Татьяна        </td><td>               </td><td>34             </td><td>Плуталова      </td><td>1              </td><td>  NA           </td><td>NA             </td><td>NA             </td></tr>\n",
       "\t<tr><td>4              </td><td>               </td><td>banned         </td><td>Габриел        </td><td>               </td><td>47             </td><td>Шалел          </td><td>2              </td><td>  NA           </td><td>NA             </td><td>NA             </td></tr>\n",
       "\t<tr><td>5              </td><td>               </td><td>               </td><td>Сергей         </td><td>               </td><td>57             </td><td>Владимиров     </td><td>2              </td><td>  NA           </td><td>NA             </td><td>NA             </td></tr>\n",
       "\t<tr><td>6              </td><td>Москва         </td><td>               </td><td>Людмила        </td><td>               </td><td>71             </td><td>Романченко     </td><td>1              </td><td>  NA           </td><td> 2             </td><td> 7             </td></tr>\n",
       "\t<tr><td>7              </td><td>Санкт-Петербург</td><td>               </td><td>Наташа         </td><td>               </td><td>74             </td><td>Филимонова     </td><td>1              </td><td>1988           </td><td> 7             </td><td>18             </td></tr>\n",
       "\t<tr><td>8              </td><td>               </td><td>banned         </td><td>Давид          </td><td>               </td><td>79             </td><td>Спектер        </td><td>2              </td><td>  NA           </td><td>NA             </td><td>NA             </td></tr>\n",
       "\t<tr><td>9              </td><td>Санкт-Петербург</td><td>               </td><td>Фёдор          </td><td>Санкт-Петербург</td><td>84             </td><td>Медведев       </td><td>2              </td><td>  NA           </td><td>NA             </td><td>NA             </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " X & city & deactivated & first\\_name & home\\_town & id & last\\_name & sex & byear & bmonth & bday\\\\\n",
       "\\hline\n",
       "\t 0               & Москва          &                 & Илья            &                 &  5              & Перекопский     & 2               &   NA            & 11              & 18             \\\\\n",
       "\t 1               & Санкт-Петербург &                 & Николай         &                 &  6              & Дуров           & 2               &   NA            & NA              & NA             \\\\\n",
       "\t 2               & Санкт-Петербург &                 & Михаил          & Санкт-Петербург & 11              & Петров          & 2               &   NA            & 12              & 18             \\\\\n",
       "\t 3               & Санкт-Петербург &                 & Татьяна         &                 & 34              & Плуталова       & 1               &   NA            & NA              & NA             \\\\\n",
       "\t 4               &                 & banned          & Габриел         &                 & 47              & Шалел           & 2               &   NA            & NA              & NA             \\\\\n",
       "\t 5               &                 &                 & Сергей          &                 & 57              & Владимиров      & 2               &   NA            & NA              & NA             \\\\\n",
       "\t 6               & Москва          &                 & Людмила         &                 & 71              & Романченко      & 1               &   NA            &  2              &  7             \\\\\n",
       "\t 7               & Санкт-Петербург &                 & Наташа          &                 & 74              & Филимонова      & 1               & 1988            &  7              & 18             \\\\\n",
       "\t 8               &                 & banned          & Давид           &                 & 79              & Спектер         & 2               &   NA            & NA              & NA             \\\\\n",
       "\t 9               & Санкт-Петербург &                 & Фёдор           & Санкт-Петербург & 84              & Медведев        & 2               &   NA            & NA              & NA             \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| X | city | deactivated | first_name | home_town | id | last_name | sex | byear | bmonth | bday |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0               | Москва          |                 | Илья            |                 |  5              | Перекопский     | 2               |   NA            | 11              | 18              |\n",
       "| 1               | Санкт-Петербург |                 | Николай         |                 |  6              | Дуров           | 2               |   NA            | NA              | NA              |\n",
       "| 2               | Санкт-Петербург |                 | Михаил          | Санкт-Петербург | 11              | Петров          | 2               |   NA            | 12              | 18              |\n",
       "| 3               | Санкт-Петербург |                 | Татьяна         |                 | 34              | Плуталова       | 1               |   NA            | NA              | NA              |\n",
       "| 4               |                 | banned          | Габриел         |                 | 47              | Шалел           | 2               |   NA            | NA              | NA              |\n",
       "| 5               |                 |                 | Сергей          |                 | 57              | Владимиров      | 2               |   NA            | NA              | NA              |\n",
       "| 6               | Москва          |                 | Людмила         |                 | 71              | Романченко      | 1               |   NA            |  2              |  7              |\n",
       "| 7               | Санкт-Петербург |                 | Наташа          |                 | 74              | Филимонова      | 1               | 1988            |  7              | 18              |\n",
       "| 8               |                 | banned          | Давид           |                 | 79              | Спектер         | 2               |   NA            | NA              | NA              |\n",
       "| 9               | Санкт-Петербург |                 | Фёдор           | Санкт-Петербург | 84              | Медведев        | 2               |   NA            | NA              | NA              |\n",
       "\n"
      ],
      "text/plain": [
       "   X city            deactivated first_name home_town       id last_name   sex\n",
       "1  0 Москва                      Илья                        5 Перекопский 2  \n",
       "2  1 Санкт-Петербург             Николай                     6 Дуров       2  \n",
       "3  2 Санкт-Петербург             Михаил     Санкт-Петербург 11 Петров      2  \n",
       "4  3 Санкт-Петербург             Татьяна                    34 Плуталова   1  \n",
       "5  4                 banned      Габриел                    47 Шалел       2  \n",
       "6  5                             Сергей                     57 Владимиров  2  \n",
       "7  6 Москва                      Людмила                    71 Романченко  1  \n",
       "8  7 Санкт-Петербург             Наташа                     74 Филимонова  1  \n",
       "9  8                 banned      Давид                      79 Спектер     2  \n",
       "10 9 Санкт-Петербург             Фёдор      Санкт-Петербург 84 Медведев    2  \n",
       "   byear bmonth bday\n",
       "1    NA  11     18  \n",
       "2    NA  NA     NA  \n",
       "3    NA  12     18  \n",
       "4    NA  NA     NA  \n",
       "5    NA  NA     NA  \n",
       "6    NA  NA     NA  \n",
       "7    NA   2      7  \n",
       "8  1988   7     18  \n",
       "9    NA  NA     NA  \n",
       "10   NA  NA     NA  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = read.csv('/Users/fulyankin/Yandex.Disk.localized/R/R_prob_data/vk_bdates.csv', sep='\\t', dec='.')\n",
    "\n",
    "dim(df)   # размер таблицы\n",
    "head(df,10)  # её шапочка "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFoCAYAAACPNyggAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Когда будете строить такой график, избавьтесь от колонки NA\n",
    "# Это позволяет сделать грамотное выполнение 1 и 2 пунктов инструкции :) \n",
    "ggplot(df, aes(x=factor(bmonth)))+\n",
    "  geom_bar(stat=\"count\", width=0.7, fill=\"steelblue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "От вас требуется: \n",
    "\n",
    "__1.__ Удалить из таблички всех людей, чьи страницы были забанены или удалены."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: ‘dplyr’\n",
      "\n",
      "The following objects are masked from ‘package:stats’:\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Будем работать с табличками в пакете dplyr, если он у вас не стоит, поставьте \n",
    "\n",
    "library('dplyr')\n",
    "options(repr.plot.width=8, repr.plot.height=3) # размер картинок"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>deactivated</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>       </td></tr>\n",
       "\t<tr><td>banned </td></tr>\n",
       "\t<tr><td>deleted</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|l}\n",
       " deactivated\\\\\n",
       "\\hline\n",
       "\t        \\\\\n",
       "\t banned \\\\\n",
       "\t deleted\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| deactivated |\n",
       "|---|\n",
       "|         |\n",
       "| banned  |\n",
       "| deleted |\n",
       "\n"
      ],
      "text/plain": [
       "  deactivated\n",
       "1            \n",
       "2 banned     \n",
       "3 deleted    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Посмотрим какие у нас в колонке deactivated бывают значения. \n",
    "# Можно сделать это напрямую\n",
    "# команда select вытащила столбец из таблицы, distinct оставила уникальные значения\n",
    "distinct(select(df, deactivated))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>deactivated</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>       </td></tr>\n",
       "\t<tr><td>banned </td></tr>\n",
       "\t<tr><td>deleted</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|l}\n",
       " deactivated\\\\\n",
       "\\hline\n",
       "\t        \\\\\n",
       "\t banned \\\\\n",
       "\t deleted\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| deactivated |\n",
       "|---|\n",
       "|         |\n",
       "| banned  |\n",
       "| deleted |\n",
       "\n"
      ],
      "text/plain": [
       "  deactivated\n",
       "1            \n",
       "2 banned     \n",
       "3 deleted    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# А можно сделать это через трубочку, которая будет последовательно применять \n",
    "# команды к тому, что стоит слева :)\n",
    "\n",
    "df %>% select(deactivated) %>% distinct()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Были забанены: 255167 \n",
      "Удалили свои страницы: 635954"
     ]
    }
   ],
   "source": [
    "# Посмотрим сколько у нас в таблице заблоченых и удалённых людей\n",
    "# cat это модный print\n",
    "\n",
    "cat('Были забанены:', sum(df$deactivated == 'banned'),'\\n')\n",
    "cat('Удалили свои страницы:', sum(df$deactivated == 'deleted'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>X</th><th scope=col>city</th><th scope=col>deactivated</th><th scope=col>first_name</th><th scope=col>home_town</th><th scope=col>id</th><th scope=col>last_name</th><th scope=col>sex</th><th scope=col>byear</th><th scope=col>bmonth</th><th scope=col>bday</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0              </td><td>Москва         </td><td>               </td><td>Илья           </td><td>               </td><td> 5             </td><td>Перекопский    </td><td>2              </td><td>NA             </td><td>11             </td><td>18             </td></tr>\n",
       "\t<tr><td>1              </td><td>Санкт-Петербург</td><td>               </td><td>Николай        </td><td>               </td><td> 6             </td><td>Дуров          </td><td>2              </td><td>NA             </td><td>NA             </td><td>NA             </td></tr>\n",
       "\t<tr><td>2              </td><td>Санкт-Петербург</td><td>               </td><td>Михаил         </td><td>Санкт-Петербург</td><td>11             </td><td>Петров         </td><td>2              </td><td>NA             </td><td>12             </td><td>18             </td></tr>\n",
       "\t<tr><td>3              </td><td>Санкт-Петербург</td><td>               </td><td>Татьяна        </td><td>               </td><td>34             </td><td>Плуталова      </td><td>1              </td><td>NA             </td><td>NA             </td><td>NA             </td></tr>\n",
       "\t<tr><td>5              </td><td>               </td><td>               </td><td>Сергей         </td><td>               </td><td>57             </td><td>Владимиров     </td><td>2              </td><td>NA             </td><td>NA             </td><td>NA             </td></tr>\n",
       "\t<tr><td>6              </td><td>Москва         </td><td>               </td><td>Людмила        </td><td>               </td><td>71             </td><td>Романченко     </td><td>1              </td><td>NA             </td><td> 2             </td><td> 7             </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " X & city & deactivated & first\\_name & home\\_town & id & last\\_name & sex & byear & bmonth & bday\\\\\n",
       "\\hline\n",
       "\t 0               & Москва          &                 & Илья            &                 &  5              & Перекопский     & 2               & NA              & 11              & 18             \\\\\n",
       "\t 1               & Санкт-Петербург &                 & Николай         &                 &  6              & Дуров           & 2               & NA              & NA              & NA             \\\\\n",
       "\t 2               & Санкт-Петербург &                 & Михаил          & Санкт-Петербург & 11              & Петров          & 2               & NA              & 12              & 18             \\\\\n",
       "\t 3               & Санкт-Петербург &                 & Татьяна         &                 & 34              & Плуталова       & 1               & NA              & NA              & NA             \\\\\n",
       "\t 5               &                 &                 & Сергей          &                 & 57              & Владимиров      & 2               & NA              & NA              & NA             \\\\\n",
       "\t 6               & Москва          &                 & Людмила         &                 & 71              & Романченко      & 1               & NA              &  2              &  7             \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| X | city | deactivated | first_name | home_town | id | last_name | sex | byear | bmonth | bday |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0               | Москва          |                 | Илья            |                 |  5              | Перекопский     | 2               | NA              | 11              | 18              |\n",
       "| 1               | Санкт-Петербург |                 | Николай         |                 |  6              | Дуров           | 2               | NA              | NA              | NA              |\n",
       "| 2               | Санкт-Петербург |                 | Михаил          | Санкт-Петербург | 11              | Петров          | 2               | NA              | 12              | 18              |\n",
       "| 3               | Санкт-Петербург |                 | Татьяна         |                 | 34              | Плуталова       | 1               | NA              | NA              | NA              |\n",
       "| 5               |                 |                 | Сергей          |                 | 57              | Владимиров      | 2               | NA              | NA              | NA              |\n",
       "| 6               | Москва          |                 | Людмила         |                 | 71              | Романченко      | 1               | NA              |  2              |  7              |\n",
       "\n"
      ],
      "text/plain": [
       "  X city            deactivated first_name home_town       id last_name   sex\n",
       "1 0 Москва                      Илья                        5 Перекопский 2  \n",
       "2 1 Санкт-Петербург             Николай                     6 Дуров       2  \n",
       "3 2 Санкт-Петербург             Михаил     Санкт-Петербург 11 Петров      2  \n",
       "4 3 Санкт-Петербург             Татьяна                    34 Плуталова   1  \n",
       "5 5                             Сергей                     57 Владимиров  2  \n",
       "6 6 Москва                      Людмила                    71 Романченко  1  \n",
       "  byear bmonth bday\n",
       "1 NA    11     18  \n",
       "2 NA    NA     NA  \n",
       "3 NA    12     18  \n",
       "4 NA    NA     NA  \n",
       "5 NA    NA     NA  \n",
       "6 NA     2      7  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. Чистим таблицу от удалённых и забаненых \n",
    "\n",
    "df_clean = df %>% filter(deactivated != 'banned', deactivated != 'deleted')\n",
    "head(df_clean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Срез df_clean = df[(df$deactivated != 'banned')&(df$deactivated != 'deleted'),]\n",
    "# дал бы на выход то же самое, но он бы отработал медленнее деплировской фильтрации.\n",
    "# Ниже все срезы мы будем делать командой filter()."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Удалить из таблички всех людей, для которых недоступны день и месяц рождения."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2570799</li>\n",
       "\t<li>11</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2570799\n",
       "\\item 11\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2570799\n",
       "2. 11\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2570799      11"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>X</th><th scope=col>city</th><th scope=col>deactivated</th><th scope=col>first_name</th><th scope=col>home_town</th><th scope=col>id</th><th scope=col>last_name</th><th scope=col>sex</th><th scope=col>byear</th><th scope=col>bmonth</th><th scope=col>bday</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 0             </td><td>Москва         </td><td>               </td><td>Илья           </td><td>               </td><td>  5            </td><td>Перекопский    </td><td>2              </td><td>  NA           </td><td>11             </td><td>18             </td></tr>\n",
       "\t<tr><td> 2             </td><td>Санкт-Петербург</td><td>               </td><td>Михаил         </td><td>Санкт-Петербург</td><td> 11            </td><td>Петров         </td><td>2              </td><td>  NA           </td><td>12             </td><td>18             </td></tr>\n",
       "\t<tr><td> 6             </td><td>Москва         </td><td>               </td><td>Людмила        </td><td>               </td><td> 71            </td><td>Романченко     </td><td>1              </td><td>  NA           </td><td> 2             </td><td> 7             </td></tr>\n",
       "\t<tr><td> 7             </td><td>Санкт-Петербург</td><td>               </td><td>Наташа         </td><td>               </td><td> 74            </td><td>Филимонова     </td><td>1              </td><td>1988           </td><td> 7             </td><td>18             </td></tr>\n",
       "\t<tr><td>10             </td><td>Санкт-Петербург</td><td>               </td><td>Михаил         </td><td>               </td><td>175            </td><td>Захаренков     </td><td>2              </td><td>1981           </td><td>11             </td><td>23             </td></tr>\n",
       "\t<tr><td>13             </td><td>Turku          </td><td>               </td><td>Павел          </td><td>St. Petersburg </td><td>208            </td><td>Антипов        </td><td>2              </td><td>  NA           </td><td>11             </td><td>30             </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " X & city & deactivated & first\\_name & home\\_town & id & last\\_name & sex & byear & bmonth & bday\\\\\n",
       "\\hline\n",
       "\t  0              & Москва          &                 & Илья            &                 &   5             & Перекопский     & 2               &   NA            & 11              & 18             \\\\\n",
       "\t  2              & Санкт-Петербург &                 & Михаил          & Санкт-Петербург &  11             & Петров          & 2               &   NA            & 12              & 18             \\\\\n",
       "\t  6              & Москва          &                 & Людмила         &                 &  71             & Романченко      & 1               &   NA            &  2              &  7             \\\\\n",
       "\t  7              & Санкт-Петербург &                 & Наташа          &                 &  74             & Филимонова      & 1               & 1988            &  7              & 18             \\\\\n",
       "\t 10              & Санкт-Петербург &                 & Михаил          &                 & 175             & Захаренков      & 2               & 1981            & 11              & 23             \\\\\n",
       "\t 13              & Turku           &                 & Павел           & St. Petersburg  & 208             & Антипов         & 2               &   NA            & 11              & 30             \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| X | city | deactivated | first_name | home_town | id | last_name | sex | byear | bmonth | bday |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "|  0              | Москва          |                 | Илья            |                 |   5             | Перекопский     | 2               |   NA            | 11              | 18              |\n",
       "|  2              | Санкт-Петербург |                 | Михаил          | Санкт-Петербург |  11             | Петров          | 2               |   NA            | 12              | 18              |\n",
       "|  6              | Москва          |                 | Людмила         |                 |  71             | Романченко      | 1               |   NA            |  2              |  7              |\n",
       "|  7              | Санкт-Петербург |                 | Наташа          |                 |  74             | Филимонова      | 1               | 1988            |  7              | 18              |\n",
       "| 10              | Санкт-Петербург |                 | Михаил          |                 | 175             | Захаренков      | 2               | 1981            | 11              | 23              |\n",
       "| 13              | Turku           |                 | Павел           | St. Petersburg  | 208             | Антипов         | 2               |   NA            | 11              | 30              |\n",
       "\n"
      ],
      "text/plain": [
       "  X  city            deactivated first_name home_town       id  last_name   sex\n",
       "1  0 Москва                      Илья                         5 Перекопский 2  \n",
       "2  2 Санкт-Петербург             Михаил     Санкт-Петербург  11 Петров      2  \n",
       "3  6 Москва                      Людмила                     71 Романченко  1  \n",
       "4  7 Санкт-Петербург             Наташа                      74 Филимонова  1  \n",
       "5 10 Санкт-Петербург             Михаил                     175 Захаренков  2  \n",
       "6 13 Turku                       Павел      St. Petersburg  208 Антипов     2  \n",
       "  byear bmonth bday\n",
       "1   NA  11     18  \n",
       "2   NA  12     18  \n",
       "3   NA   2      7  \n",
       "4 1988   7     18  \n",
       "5 1981  11     23  \n",
       "6   NA  11     30  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2. Дропаем NA по дням и месяцам\n",
    "df_dropna = df_clean %>% filter(!is.na(bday),!is.na(bmonth))\n",
    "\n",
    "dim(df_dropna)  # число строк довольно сильно упало :(\n",
    "head(df_dropna)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ Постройте гистограмму, на которой было бы понятно в какой месяц родилось какое количество людей. Команда для этого приведена ниже. Как считате, помесячная рождаемость имеет равномерное распределение?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAYAAACYBpIxAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA\nOI2NVV1oHFUUPrtzZyMkzlNsNIV0qD8NJQ2TVjShtLp/3d02bpZJNtoi6GT27s6Yyc44M7v9\noU9FUHwx6psUxL+3gCAo9Q/bPrQvlQol2tQgKD60+INQ6Ium65k7M5lpurHeZe58853vnnvu\nuWfvBei5qliWkRQBFpquLRcy4nOHj4g9K5CEh6AXBqFXUR0rXalMAjZPC3e1W99Dwntf2dXd\n/p+tt0YdFSBxH2Kz5qgLiI8B8KdVy3YBevqRHz/qWh72Yui3MUDEL3q44WPXw3M+fo1pZuQs\n4tOIBVVTaoiXEI/MxfhGDPsxsNZfoE1q66ro5aJim3XdoLFw72H+n23BaIXzbcOnz5mfPoTv\nYVz7KzUl5+FRxEuqkp9G/Ajia219thzg25abkRE/BpDc3pqvphHvRFys2weqvp+krbWKIX7n\nhDbzLOItiM8358pTwdirqpPFnMF2xLc1WvLyOwTAibpbmvHHcvttU57y5+XqNZrLe3lE/Pq8\neUj2fXKfOe3pfOjzhJYtB/yll5SDFcSDiH+hRkH25+L+sdxKEAMZahrlSX8ukqMOWy/jXW2m\n6M9LDBc31B9LFuv6gVKg/0Szi3KAr1kGq1GMjU/aLbnq6/lRxc4XfJ98hTargX++DbMJBSiY\nMIe9Ck1YAxFkKEAG3xbYaKmDDgYyFK0UGYpfoWYXG+fAPPI6tJnNwb7ClP7IyF+D+bjOtCpk\nhz6CFrIa/I6sFtNl8auFXGMTP34sNwI/JhkgEtmDz14ySfaRcTIBInmKPE32kxyyE2Tv+thK\nbEVePDfW/byMM1Kmm0XdObS7oGD/MypMXFPXrCwOtoYjyyn7BV29/MZfsVzpLDdRtuIZnbpX\nzvlf+ev8MvYr/Gqk4H/kV/G3csdazLuyTMPsbFhzd1UabQbjFvDRmcWJxR3zcfHkVw9GfpbJ\nmeev9F08WW8uDkaslwX6avlWGU6NRKz0g/SHtCy9J30o/ca9zX3Kfc19zn3BXQKRO8ud477h\nLnAfc1/G9mrzGlrfexZ5GLdn6ZZrrEohI2wVHhZywjbhUWEy8icMCGNCUdiBlq3r+xafL549\nHQ5jH+an+1y+LlYBifuxAvRN/lVVVOlwlCkdVm9NOL5BE4wkQ2SMlDZU97hX86EilU/lUmkQ\nUztTE6mx1EEPh7OmdqBtAvv8HdWpbrJS6tJj3n0CWdM6busNzRV3S9KTYhqvNiqWmuroiKgY\nhshMjmhTh9ptWhsF7970j/SbMrsPE1suR5z7DMC+P/Hs+y7ijrQAlhyAgccjbhjPygfeBTjz\nhNqy28EdkUh8C+DU9+z2v/oyeH791OncxHOs5y2AtTc7nb/f73TWPkD/qwBnjX8BoJ98VVBg\n/m8AAEAASURBVHgB7d0JnBTlnf/x3zAzXMN93wiJiEIEEhFFo5IgEk6XKMEVjIGIGILE4x+N\nugrqglEDYhITNxhiXDeA4Jpdr0SyHgE0JDFA5Agol8ol933z5/uYmumerp7qwZ7p6q7P83pB\nVz1Pne+q7ulfP0flnTyVjIQAAggggAACCCCAAAIIIIBAjgtUyfHz4/QQQAABBBBAAAEEEEAA\nAQQQcAIEwNwICCCAAAIIIIAAAggggAACkRAgAI7EZeYkEUAAAQQQQAABBBBAAAEECIC5BxBA\nAAEEEEAAAQQQQAABBCIhQAAcicvMSSKAAAIIIIAAAggggAACCBAAcw8ggAACCCCAAAIIIIAA\nAghEQoAAOBKXmZNEAAEEEEAAAQQQQAABBBAgAOYeQAABBBBAAAEEEEAAAQQQiIRAQSTOMoMn\nuWfPHjt06FAGjyB413l5eVa3bl07evSo7d+/P3iFCC1RtWpVq1mzph04cMCOHDkSoTMPPtWi\noiIrLCy03bt328mTJ4NXiNAS9erVs2PHjtm+ffsidNbBp6r7RffNwYMH7fDhw8ErRGgJfc7o\n80Z/M06cOBGhMw8+Vf190meMbEglAvn5+Va7dm33XtJ7ilQiUL16ddM/fQbrs5hUIqB7pkqV\nKu5vd0kuUzKpU6eO+66n73ykEoFq1apZjRo1XIygWCHMSZ+LDRs2DDzEUATAutEWLlxoGzdu\ntM6dO9sXv/jFuANfsGBBQmB29tlnW+vWrd1yx48ft8WLF9vy5cutY8eO1r1797j1NbNhwwa3\njwYNGljPnj2tVq1accsEle/du9d0HHrt0aOHtWnTJm79ZDP6IqPjC3PSm15fvLLhWDPhKBvd\no2G/jpVtow8Z2ciFADheXy5K3DPxLgUFBe6e0Y+C2MTbeJ/Dei9hE2+j+waXeBPNefeMfpzl\nnon38Wy4b+JdNKf3k/5+c88k2njfabDxt1ElWa7YZDwAfvXVV+2RRx6xL3zhC66m7Ze//KUN\nGDDAbr/9dqcv6Hvvvdf9yqk3rZdGjx7tAmCVjxkzxjZt2mQXX3yxzZ4923r16mW33nqrt6g9\n88wzNn36dLv00ktdkK35xx9/3OrXr++WCSpfu3atjRo1ytq3b28tW7a0J5980h588EG74IIL\nivfBBAIIIIAAAggggAACCCCAQLgFSiLKDBynahyffvppF8BeffXV7gjeeustu/vuu+3KK6+0\nz3/+8/bhhx+65ghPPfWUb5W2Al41cZk1a5ZrWrd+/XobMWKE9e/f38466yxX8ztjxgybNm2a\nde3a1TWFUcCs5fWqmt+yynVQkydPtkGDBtn48eNNzYV1zFOnTrWZM2e6+QzQsUsEEEAAAQQQ\nQAABBBBAAIFyCmR0EKwdO3a45sqXX3558WF369bNTas5tNLq1autUaNGvsGvyufPn29aX/3K\nlNq2beuaUb/22mtuftGiRdaiRQsX/CpDtch9+/a1VMu3b99uK1assMGDBxcHu6qh1vGpyTUJ\nAQQQQAABBBBAAAEEEEAgOwQyWgOswDa2qbLI/vCHP7i+Caq9VXr//fdd8+cpU6a4Prhqtnzd\nddfZJZdc4srV9FkBbmzS/NatW4vL1Ww5Nql827Ztrs+r1i+rfPPmzW7V2H2oc7X6CWgfnTp1\nKt605tXUOjapOfa5554bmxXaaf04oAEASCUCXrN7df7XAD6kEgHPRgNqkBIF1MeK91O8i0yU\nNDiNNx2/RHTnvM8X/ZhLn/r4+0D9OWXC+ynRRTkaoEat00glAt77SYPL6fOGVCKgz17dL7yf\nSkw05b2HdO9gE2/jfd/Td2FvjJP4JcIzl+ogkhkNgEtzffDBB65/7bXXXmtNmzZ1xatWrTLV\nFHfo0MENXvXKK6+4JtIPP/ywqz1WIFv6RtW81lNSAFu6XF/YBaTRa4PKFSDrj4v+xSZtY+fO\nnbFZ7jjVPDo2tWvXzi688MLYrNBO6wb3bvLQHmSGDszvHsjQoYRut17ri9AdWIYPSF8ysPG/\nCPoDGvY/ov5HXvG5+sJOShTQl1PeT4kuytEXdi/g818iurn6wk7yF+D95O/Cd2F/F+Vmw49J\nqT6xJTQB8NKlS+3OO++0r3zlK27AKY9/woQJLlj1BqzSwFOqFVYfXk3rl+HSQ9xr3ntj64+C\nX7m2ry8ap1OudTX4VukvKmeccYYbhEvlXtLjUBSkhznpi4VqtfVYEo1yTSoRUOCrHzvkwmNb\nSlw0JRf5qJsANVbxNmrdokcF6Ec2UomAgl79IKmRJHlsS4mLpvRkAn250A+ruTLKZvwZnv6c\nnt6gz5jSPzqf/hZzY019Udd3DL2XeIRh/DXV9zP902dw2B/bEn/kFT+ne0bfnVW5RCoRkIk+\na/SUAh5hWOKiKf1t0t8oPYou1QAzfguVN+fFNEF7DEUArH689913nw0dOtRuvPHGuGPW8/9K\nJ9Wo/vGPf3TNFXSzlg7adIGaNWvmVtMX0XXr1sVtQuUKqPXlPZVyfRnRY3BiA15to3nz5nHb\n1Q3SpUuXuLxdu3aF/oue3vRK+oLBH4q4y1dcI657AJt4Gy/olYs3Hb9EtOd4PyVef++zhvdT\noo3XbEs/2Jb+0TZx6Wjl6L3E+yn5Nef9lGgT+37ib3e8j/f3Gpd4F69bDp818S6a81qYZMNn\njXcdE88iPiejg2DpUF5//XX3mKObb745IfhV+R133GFz5szRZHFasmRJcb9fPZpo2bJlxWWa\n0OBUXr9eNUFeuXJl3BcKLZ9qeatWrVwQFLsPDYqlD9fYfsFxB8AMAggggAACCCCAAAIIIIBA\n6AQyGgCr6eRDDz1kl112man5sAJb75/XNEOjQus5vRoNWk1Q586d6wJa1RYrXXXVVTZv3jwX\n9OpXG5Wrer5fv36uvHfv3u712WefdUHrmjVr7OWXX3aPSlJBULlqoPv06eMelaQmEWoaoYGu\nNJJ048aN3bb5DwEEEEAAAQQQQAABBBBAIPwCGW0CrQGt1LRYjyTyHkvkkak/sJ7lq8cPqX/w\nyJEj3aAparas5wR7A0upH/CwYcNs7NixropeNbv33HOPa6uubWn5Bx54wCZOnGgKgjUgwpAh\nQ9yAWqmUaxk9L1jrDxw40G1PzZzHjRunIhICCCCAAAIIIIAAAggggECWCOSdqjU9mQ3HqgEe\n1NdXo0N7Q5XHHrdqfdUvV316k6UtW7a4WluvH1rp5YLKtf3yjuyaLX2A5arabQYZib8r9IOJ\nBozIhusYf+QVP6d+9Or3rpHUs+RjpOJR/rkHjQ+gzyS1ciGVCOgHSY3boM9SBu0pcdGUWhtp\nnIlPPvkkrstO/FLRnGvSpIn7jJENqURA/fL0nUet00qPhVKyVDSnNEijBu3RZ3DYB+2p7Cuk\ne0bfZfWdl1QiIBN91mhQOX3nI5UI6G+T/kYpRlCsEObkXcegY8xoDXDQwcWWa1Rnb2Tn2Hxv\nWqOLlhX8ajnv0UreOqVfg8pLP06p9PrMI4AAAggggAACCCCAAAIIhFcgawLg8BJWzpENeej1\nytlRBe/l+Tt7VfAe2DwCCCCAAAIIIIAAAggg4C+Q0UGw/A+JXAQQQAABBBBAAAEEEEAAAQTS\nL0AAnH5TtogAAggggAACCCCAAAIIIBBCAQLgEF4UDgkBBBBAAAEEEEAAAQQQQCD9AvQBTr8p\nW0QgFAL0Gw/FZeAgEEAAAQQQQAABBEIkQA1wiC4Gh4IAAggggAACCCCAAAIIIFBxAgTAFWfL\nlhFAAAEEEEAAAQQQQAABBEIkQAAcoovBoSCAAAIIIIAAAggggAACCFScAAFwxdmyZQQQQAAB\nBBBAAAEEEEAAgRAJEACH6GJwKAgggAACCCCAAAIIIIAAAhUnQABccbZsGQEEEEAAAQQQQAAB\nBBBAIEQCBMAhuhgcCgIIIIAAAggggAACCCCAQMUJ8BzgirNlywgggEDWCeTC86Ofv7NX1rlz\nwAgggAACCCBQOQLUAFeOM3tBAAEEEEAAAQQQQAABBBDIsAABcIYvALtHAAEEEEAAAQQQQAAB\nBBCoHAEC4MpxZi8IIIAAAggggAACCCCAAAIZFqAPcIYvALv/7AL0WfzshmwBAQQQQAABBBBA\nAIEoCFADHIWrzDkigAACCCCAAAIIIIAAAggYATA3AQIIIIAAAggggAACCCCAQCQEaAJdwZe5\nSpUqVrNmzQreS/ZsHgv/a4WLv4tys9WG937ya1rRJdl4zxQUfPrnuHr16nbixImKJsqq7efl\n5bnjzcbrWpHQ+fn5bvOFhYVZ+zlZUT7e+6latWrmTVfUvrJtu/rbpPcU76f4KycXJb2vsIm3\nqVq1qsvQ+8lzil8i++YIgCvhmnl/vCthV6HfBRb+lwgXfxflVoTNFf/2YvIdZlHJ7x4YkEVH\nW3mHWhH3TGUdvY49m4+/opxwSZSNvU9ipxOXjF6O58F9k/zae0bJl4hmCfdM4nWPvVdipxOX\nzHzOyZMnUzoIAuCUmE5/If2Sf/DgwdPfQI6tuX///hw7o/ScDi7JHbHBJrmAf0k23jOqpdKv\n7Pp7cezYMf8TC2luLgxEKNrn7+wVUmH/w1LNb1FRkR09etSy8Z73P6v05KqWSrVVhw4dsiNH\njqRnozmylRo1argf2bhn4i+oan5r167tPn+xibdRUKnWSYcPH3bvqfjScM15LWOCjoo+wEFC\nlCOAAAIIIIAAAggggAACCOSEADXAOXEZOQkEEEAAgYoWyIWazmyr5azoa8r2EUAAAQSiJ0AN\ncPSuOWeMAAIIIIAAAggggAACCERSgAA4kpedk0YAAQQQQAABBBBAAAEEoidAABy9a84ZI4AA\nAggggAACCCCAAAKRFCAAjuRl56QRQAABBBBAAAEEEEAAgegJEABH75pzxggggAACCCCAAAII\nIIBAJAUIgCN52TlpBBBAAAEEEEAAAQQQQCB6AgTA0bvmnDECCCCAAAIIIIAAAgggEEkBAuBI\nXnZOGgEEEEAAAQQQQAABBBCIngABcPSuOWeMAAIIIIAAAggggAACCERSoCCSZ81JI4AAAggg\ngAACFSww5KHXK3gPFb/55+/sVfE7YQ8IIIBAJQpQA1yJ2OwKAQQQQAABBBBAAAEEEEAgcwIE\nwJmzZ88IIIAAAggggAACCCCAAAKVKEAAXInY7AoBBBBAAAEEEEAAAQQQQCBzAgTAmbNnzwgg\ngAACCCCAAAIIIIAAApUoQABcidjsCgEEEEAAAQQQQAABBBBAIHMCBMCZs2fPCCCAAAIIIIAA\nAggggAAClShAAFyJ2OwKAQQQQAABBBBAAAEEEEAgcwIEwJmzZ88IIIAAAggggAACCCCAAAKV\nKFBQiftKuqsDBw7YwoULbePGjda5c2f74he/GLfs8ePHbfHixbZ8+XLr2LGjde/evVzlWnjD\nhg1uHw0aNLCePXtarVq14rYRVL53715bsGCB6bVHjx7Wpk2buPWZQQABBBBAAAEEEEAAAQQQ\nCLdAxmuAX331VRs4cKC9+OKLtnLlSrv11lvt0UcfLVZT8DtmzBi777777OOPP7b777/fpkyZ\nknK5FnzmmWdsxIgRLoCePXu23XTTTbZz587ibQSVr1271gYPHmxz5syx9957z0aOHGnvvPNO\n8fpMIIAAAggggAACCCCAAAIIhF8gozXAJ06csKefftoFuFdffbXTeuutt+zuu++2K6+80j7/\n+c+bAtZ9+/bZrFmzrKioyNavX++C2f79+9tZZ50VWK6a3RkzZti0adOsa9euduzYMbc/bU+B\ndVC5Dmry5Mk2aNAgGz9+vOXl5bljnjp1qs2cOdPNh/8yc4QIIIAAAggggAACCCCAAAIZrQHe\nsWOHa858+eWXF1+Jbt26uWk1h1aaP3++qVzBr1Lbtm1dM+nXXnvNzQeVL1q0yFq0aOGCX61Q\nUFBgffv2NW/9oPLt27fbihUrXA2wgl+lAQMGuObaapJNQgABBBBAAAEEEEAAAQQQyA6BjNYA\nN2rUyDV5jqX6wx/+YPn5+a52V/mbNm1yAWzsMgpot27d6rJSKW/ZsmXs6m5727ZtM9VAa/2y\nyjdv3uzW1T691LBhQ6tatao7hk6dOnnZdvjwYVuzZk3xvCYUuNeoUSMuL8oz+gGClCiAS6KJ\nl4ONJ5H4ik2iiXJw8XfBJrkLNsltsvH9VKXKp/U7+j6Zjcef/Gp89hKvMgeXeEvvnpEPNvE2\neh8pZcP7ybuO8WeQOBeqaOSDDz6wJ5980q699lpr2rSpa66sQLVOnTpxR675VatWBZZrJQWw\npdevXbu2C353794dWK4AuVq1au5f7EFoG7H9iFWmvsJquh2bJkyYYNdcc01sVqSnGzduHOnz\nT3byuCSTMcMGm+QC/iXcM/4uysUGm+QC/iXZfM/Uq1fP/6TI5bMgyT1QvXp10z9SokDpeCpx\nicznHDlyJKWDCE0AvHTpUrvzzjvtK1/5io0aNcodvH5pUCSvfruxSfOqWQ0q1zqFhYW+66us\nZs2ap1WudTU4l9aPTfXr108IdjVa9P79+2MXi/Q0Fv6XHxd/F+Vig01yAf8S7hl/F+Vig01y\nAf+SbLxn9N1PLfUOHjzoKjz8zyyauWqVqFpOPYGFVCIgE32vV4yhFp2kEgHViKsy8NChQy7+\nKSkJ35Ra9+q9H5RCEQCrH69GeR46dKjdeOONxcesm1GPLdKjh2LTnj17rFmzZu4NXFa51lEz\n63Xr1sWublpfwaouZirlCnb1QREb8GobzZs3j9uuaq1V4xubdu3a5fYXmxflabmREgVwSTTx\ncrDxJBJfsUk0UQ4u/i7YJHfBJrlNNr6f1EpPX4L13S3VGqHkArlVIhdVIGXjda3IKyETfc8/\nevQoNqWg5aKYST8oKQgOc9J11Ps/KGV0ECwd3Ouvv2733nuv3XzzzXHBr3fg7du3t2XLlnmz\n7lWDT3n9doPK27Vr5x6vFFuLrO156weVt2rVyvUFiD0GDYqlXxhi+wXHHSAzCCCAAAIIIIAA\nAggggAACoRPIaACsEZYfeughu+yyy+yMM86wJUuWFP/TCNFKV111lc2bN889w/fkyZM2d+5c\n92tev379Uirv3bu3W+7ZZ591QasGqXr55Zfdo5RUEFRet25d69Onj3uUkh7HpF8+pk+f7kaS\nzuZ+MQ6F/xBAAAEEEEAAAQQQQACBCAlktAn0K6+84pqn6JFE3mOJPHv1B9azfi+44AIbNmyY\njR071vXXVc3tPffcY7Vq1XKLBpWryv6BBx6wiRMnmoJg9X0YMmSI9ezZ060fVK6F9LxgrT9w\n4EDXBKBLly42btw4tz7/IYAAAggggAACCCCAAAIIZIdARgPg4cOHm/4FpZEjR7rl1F9BfXZL\np6ByPVv4hRdesC1btrhR70oPkR1Urv7Cjz32mOsToLbl3jOJSx8H8wgggAACCCCAAAIIIIAA\nAuEVyGgAXB4Wddr3C369bQSVazkNUlVWCirPhuG/yzo/yhBAAAEEEEAAAQQQQACBKAtktA9w\nlOE5dwQQQAABBBBAAAEEEEAAgcoVIACuXG/2hgACCCCAAAIIIIAAAgggkCEBAuAMwbNbBBBA\nAAEEEEAAAQQQQACByhXImj7AlcvC3hBAAAEEEEAAAQQqSmDIQ69X1KYrbbvP39mr0vbFjhBA\nIH0CBMDps2RLCCCAAAIIIIAAAggggEClCvCDUvm4aQJdPi+WRgABBBBAAAEEEEAAAQQQyFIB\nAuAsvXAcNgIIIIAAAggggAACCCCAQPkEaAJdPi+WRgABBBBAAAEEEECgQgRyoSmrYOgfXSG3\nBxtNkwA1wGmCZDMIIIAAAggggAACCCCAAALhFiAADvf14egQQAABBBBAAAEEEEAAAQTSJEAA\nnCZINoMAAggggAACCCCAAAIIIBBuAQLgcF8fjg4BBBBAAAEEEEAAAQQQQCBNAgTAaYJkMwgg\ngAACCCCAAAIIIIAAAuEWIAAO9/Xh6BBAAAEEEEAAAQQQQAABBNIkQACcJkg2gwACCCCAAAII\nIIAAAgggEG4BAuBwXx+ODgEEEEAAAQQQQAABBBBAIE0CBMBpgmQzCCCAAAIIIIAAAggggAAC\n4RYgAA739eHoEEAAAQQQQAABBBBAAAEE0iRAAJwmSDaDAAIIIIAAAggggAACCCAQboGCcB9e\nbhxdXl5ebpxIGs4CC39EXPxdlIsNNskF/Eu4Z/xdlIsNNskF/Eu4Z/xdlItN7tjEXsvY6eRn\nSEm6BSrTnQA43Vev1PYKCwutqKioVG50Zxs2bBjdky/jzHFJjoMNNskF/Eu4Z/xdlIsNNskF\n/Eu4Z/xdlItN5dpccvtzyXeYJSVvPXp1lhxp5R9mOt5Px44dS+nACYBTYjr9hY4ePWp79uw5\n/Q3k2Jrbtm3LsTNKz+ngktwRG2ySC/iXcM/4uygXG2ySC/iXcM/4uygXG2ySC/iXcM/4uyg3\nHTb5+flWo0aN5Dv5Zwl9gAOJWAABBBBAAAEEEEAAAQQQQCAXBAiAc+Eqcg4IIIAAAggggAAC\nCCCAAAKBAgTAgUQsgAACCCCAAAIIIIAAAgggkAsCBMC5cBU5BwQQQAABBBBAAAEEEEAAgUAB\nAuBAIhZAAAEEEEAAAQQQQAABBBDIBQEC4Fy4ipwDAggggAACCCCAAAIIIIBAoAABcCARCyCA\nAAIIIIAAAggggAACCOSCAAFwLlxFzgEBBBBAAAEEEEAAAQQQQCBQgAA4kIgFEEAAAQQQQAAB\nBBBAAAEEckGAADgXriLngAACCCCAAAIIIIAAAgggEChAABxIxAIIIIAAAggggAACCCCAAAK5\nIEAAnAtXkXNAAAEEEEAAAQQQQAABBBAIFCAADiRiAQQQQAABBBBAAAEEEEAAgVwQIADOhavI\nOSCAAAIIIIAAAggggAACCAQKEAAHErEAAggggAACCCCAAAIIIIBALggQAOfCVeQcEEAAAQQQ\nQAABBBBAAAEEAgUIgAOJWAABBBBAAAEEEEAAAQQQQCAXBAiAc+Eqcg4IIIAAAggggAACCCCA\nAAKBAgTAgUQsgAACCCCAAAIIIIAAAgggkAsCBMC5cBU5BwQQQAABBBBAAAEEEEAAgUABAuBA\nIhZAAAEEEEAAAQQQQAABBBDIBYGCMJ3EW2+9ZbVr17Zu3brFHdaCBQts//79cXlnn322tW7d\n2uUdP37cFi9ebMuXL7eOHTta9+7d45bVzIYNG2zhwoXWoEED69mzp9WqVStumaDyvXv3mo5D\nrz169LA2bdrErc8MAggggAACCCCAAAIIIIBAuAVCEwArgL333nvthhtuiAuAFdwqX4FxQUHJ\n4Y4ePdoFwCofM2aMbdq0yS6++GKbPXu29erVy2699dZi+WeeecamT59ul156qW3cuNE0//jj\nj1v9+vXdMkHla9eutVGjRln79u2tZcuW9uSTT9qDDz5oF1xwQfE+mEAAAQQQQAABBBBAAAEE\nEAi3QElEmaHjPHbsmAtIFYTm5eUlHMWHH35oR44csaeeesoaNmyYUK6Ad9++fTZr1iwrKiqy\n9evX24gRI6x///521llnuZrfGTNm2LRp06xr166m/Slg1vJ6Vc1vWeXa4eTJk23QoEE2fvx4\nd4xPP/20TZ061WbOnOl7zAkHSQYCCCCAAAIIIIAAAggggEDGBTLeB/jll1+2l156ySZNmlTc\npDlWZfXq1daoUSPf4FfLzZ8/3y6//HIX/Gq+bdu21rlzZ3vttdc0a4sWLbIWLVq44FfzqkXu\n27dvyuXbt2+3FStW2ODBg4uD3QEDBriaZDW5JiGAAAIIIIAAAggggAACCGSHQMZrgC+66CLr\n16+fC0yfeOKJBLX333/fNX+eMmWK64OrZsvXXXedXXLJJW5ZNX1WgBubNL9169bicjVbjk0q\n37Ztm504ccI1nS6rfPPmzW7V2H2oJrpq1apuH506dSre9Lp16+zmm28unteEmmpfccUVcXlR\nntGPGaREAVwSTbwcbDyJxFdsEk2Ug4u/CzbJXbBJbsP7CZvkAslLuG/8bXDxd1FuOmzU0jeV\nlPEA2K9Zc+yBr1q1ynbs2GEdOnRwg1e98sordvfdd9vDDz/sBrtSIFunTp3YVdy81lNSAFu6\nXP2JFfzu3r07sFwBdrVq1dy/2J1oGzt37ozNck211QQ7Nmnwrti+y7FlUZzGwv+q4+Lvolxs\nsEku4F/CPePvolxssEku4F/CPePvolxssEku4F/CPePvotx02Ci+SyVlPAAOOsgJEya4YNUb\nsEoDT6lWWH14NV2lShXXrzd2O4r+1R9YqbCw0LdcZTVr1jytcq2rwbe0fmxSkL5kyZLYLNu1\na5cLsuMyIzzj1ahHmMD31HHxZXGZ2GCTXMC/hHvG30W52GCTXMC/hHvG30W52GCTXMC/hHvG\n30W56bDJz8+3Jk2aJN/JP0sy3gc46Ajr1q1bPFqzt+yFF17omi5r0Cw91kiPJopNe/bssWbN\nmrksVaf7lSugVs1uKuUKdg8cOBC7C9M+mjdvHpfHDAIIIIAAAggggAACCCCAQHgFQh8A33HH\nHTZnzpw4QdWyen1y9WiiZcuWxZVrcCqvX2+7du1s5cqVcbXAWj7V8latWrkq+dh9aFAsVbF7\nxxC3c2YQQAABBBBAAAEEEEAAAQRCKRD6ALhbt27uMUkaDfrw4cM2d+5cF9AOHTrUgV511VU2\nb948U9B78uRJV67HJmlgLaXevXu712effdYFrWvWrDGNPK1HJaVSrhroPn36uEcl6XFLhw4d\ncs8U1kjSjRs3dtvgPwQQQAABBBBAAAEEEEAAgfALhL4PsB4/tHTpUhs5cqQbeVnNljUIlppB\nK6kf8LBhw2zs2LGuP69qdu+55x6rVauWK9fyDzzwgE2cONEUBNeoUcOGDBniBtTSAkHlWkbP\nC9b6AwcOdMt36dLFxo0bpyISAggggAACCCCAAAIIIIBAlgiEKgD+9a9/ncCmgFXPCNZoyurL\n27Rp0+Ln8XoLKzgePny465frN4S2apFfeOEF27Jli6u11cBZsSmoXP2FH3vsMbd9da72BtiK\n3QbTCCCAAAIIIIAAAggggAAC4RYIVQBcFpWCzrICTz2X1y/4jd2mgueyUlB56ccplbUtyhBA\nAAEEEEAAAQQQQAABBMIlEF8VmsKxqZb2+9//ftIlVdPatm1bO3jwYNJlKEAAAQQQQAABBBBA\nAAEEEECgsgVSqgH+5JNPTANLKf3tb3+zRYsW2ccff5xwrFpGA0xt2LDBDRal5sskBBBAAAEE\nEEAAAQQQQAABBMIgkFIAPGPGDNPjiGKTHg+ULHXt2jXh2b3JliUfAQQQQAABBBBAAAEEEEAA\ngcoQSCkAvuWWW9xzdI8ePWqvv/66rV+/3q6//vqE4ysoKHCB79VXX51QRgYCCCCAAAIIIIAA\nAggggAACmRRIKQAuLCy0u+66yx1nx44d3TN377vvvkweN/tGAAEEEEAAAQQQQAABBBBAoFwC\nKQXAsVv8xje+ETvLNAIIIIAAAggggAACCCCAAAJZIVDuAFhnNXfuXPvRj37kmkJrtOeTJ08m\nnOzOnTsT8shAAAEEEEAAAQQQQAABBBBAIFMC5Q6AFy5caKoF1gjPXbp0sSZNmlheXl6mjp/9\nIoAAAggggAACCCCAAAIIIJCSQLkD4Oeee86qV69u7777rp155pkp7YSFEEAAAQQQQAABBBBA\nAAEEEMi0QJXyHsCmTZvsvPPOI/gtLxzLI4AAAggggAACCCCAAAIIZFSg3AGwgl/V/h44cCCj\nB87OEUAAAQQQQAABBBBAAAEEECiPQLkDYD3/t0WLFjZhwgQ7cuRIefbFsggggAACCCCAAAII\nIIAAAghkTKDcfYBff/11a9y4sT3yyCP2+OOPW6tWrayoqCjhBJYsWZKQRwYCCCCAAAIIIIAA\nAggggAACmRIodwCsxxsdPnzYunfvnqljZr8IIIAAAggggAACCCCAAAIIlFug3AHw6NGjTf9I\nCCCAAAIIIIAAAggggAACCGSTQLn7AGfTyXGsCCCAAAIIIIAAAggggAACCHgC5a4BnjJlik2b\nNs1bP+nr+vXrk5ZRgAACCCCAAAIIIIAAAggggEBlC5Q7AG7UqJF16NAh7jiPHz9uGzZsMAW9\n9evXt2uvvTaunBkEEEAAAQQQQAABBBBAAAEEMi1Q7gD4uuuuM/3zS2vWrLErrrjCmjdv7ldM\nHgIIIIAAAggggAACCCCAAAIZEyh3AFzWkbZv397uvvtuu/nmm+22226z/Pz8shaPRFlBQYGr\nFY/EyaZwkmohQEoUwCXRxMvBxpNIfMUm0UQ5uPi7YJPcBZvkNryfsEkukLyE+8bfBhd/F+Wm\nw0atklNJaQ2AtcPWrVvb3r17bfXq1daxY8dUjiGnl9GFOHjwYE6fY3lOTvcGKVEAl0QTLwcb\nTyLxFZtEE+Xg4u+CTXIXbJLb8H7CJrlA8hLuG38bXPxdlJsOmypVqlhRUVHynfyzJK0B8IED\nB+yJJ55wNb9t2rQJ3HkUFjh58qQdO3YsCqea0jli4c+Ei7+LcrHBJrmAfwn3jL+LcrHBJrmA\nfwn3jL+LcrHBJrmAfwn3jL+LctNhk2rr43IHwL/4xS/sqaeeSjj6o0ePukGwtm/fbtdff73V\nrFkzYRkyEEAAAQQQQAABBBBAAAEEEMiUQLkD4CNHjtj+/fsTjlcRd+fOnd0gWOPHj08oJwMB\nBBBAAAEEEEAAAQQQQACBTAqUOwAeO3as6R8JAQQQQAABBBBAAAEEEEAAgWwSKHcA7J2c2mm/\n8cYb9o9//MPU/Llr167uX7169bxFeEUAAQQQQAABBBBAAAEEEEAgNAKnFQD/9a9/df1833vv\nvYQTmTRpkv3gBz9IyCcDAQQQQAABBBBAAAEEEEAAgUwKlDsA3rVrlw0ePNiN1DVlyhTr0aOH\n1apVy9atW2e//OUv7a677rLq1avbLbfcksnzYt8IIIAAAggggAACCCCAAAIIxAmUOwDWKNAK\ngt99913r0KFD8cbOPfdcGzRokN144432s5/9jAC4WIYJBBBAAAEEEEAAAQQQQACBMAhUKe9B\nLFmyxC677LK44Dd2G6NHj7bVq1fbxo0bY7OZRgABBBBAAAEEEEAAAQQQQCCjAuUOgPW4Iz0K\nKVnyyo4fP55sEfIRQAABBBBAAAEEEEAAAQQQqHSBcgfA5513nr355pu2aNGihIM9efKkPfzw\nw9aoUSNr3bp1QjkZCCCAAAIIIIAAAggggAACCGRKoNx9gL/97W+bBr9SM+gbbrjBzj//fKtT\np44bBOtXv/qV6xuswbBICCCAAAIIIIAAAggggAACCIRJoNwBcI0aNWzBggU2atQoe/zxx+PO\npX79+vbTn/7UvvWtb8XlM4MAAggggAACCCCAAAIIIIBApgXKHQDrgFu0aGGvvPKKffTRR7Zi\nxQrbvn27fe5zn7Ozzz7bPRIp0yfF/hFAAAEEEEAAAQQQQAABBBAoLVCuAFh9fLds2WLNmjVz\n22nVqpXpnwLhDz74gOC3tC7zCCCAAAIIIIAAAggggAACoRFIeRAsDXx1zjnn2Pjx4xMO/re/\n/a3rE6xnAa9atSqhnAwEEEAAAQQQQAABBBBAAAEEMi2QUgD81ltvWd++fW3lypXWoEGDhGPu\n2bOnXX/99bZs2TLTtGqDSQgggAACCCCAAAIIIIAAAgiESSClAPiWW26xoqIie/HFF+1nP/tZ\nwvF369bNZsyY4cp37dpld911V8IyZCCAAAIIIIAAAggggAACCCCQSYHAAPgf//iHe7TR8OHD\nrX///mUe69e+9jVXEzx37lw7cuRImctSiAACCCCAAAIIIIAAAggggEBlCgQGwF5z5gEDBqR0\nXF/96lft+PHjNINOSYuFEEAAAQQQQAABBBBAAAEEKksgMAD2Rnw+ePBgSsfkLZeXl5fS8iyE\nAAIIIIAAAggggAACCCCAQGUIBD4GqWvXrlavXj333N+BAwcGHtPvfvc7U/DbunXrwGVLL6DB\ntmrXrm3qUxybVKO8ePFiW758uXXs2NG6d+8eW+xqnMsq18IbNmywhQsXukG8NFBXrVq14rYR\nVL53715bsGCB6bVHjx7Wpk2buPWZQQABBBBAAAEEEEAAAQQQCLdAYA1wlSpV7Mtf/rK98MIL\ntmbNmjLPRgHmK6+8Yr1793aDZpW5cKlCBbD33nuvC3JjixT8jhkzxu677z77+OOP7f7777cp\nU6YULxJUrgWfeeYZGzFihNv27Nmz7aabbrKdO3cWbyOofO3atTZ48GCbM2eOvffeezZy5Eh7\n5513itdnAgEEEEAAAQQQQAABBBBAIPwCgQGwTkFB59GjR13N7H/913+56dhT08jPGh26V69e\nVlhYaA8++GBscZnTx44dcyNI33rrra7muPTCClj37dtns2bNsjvvvNN+8pOfuGBcg3MpBZWr\nZlcjVE+bNs2dx89//nOrVq2a257WDyrXMpMnT7ZBgwbZL37xC5s4caILpqdOnWonT55UMQkB\nBBBAAAEEEEAAAQQQQCALBFIKgNUM+o033rCaNWvatdde617POeccF/C2bNnS6tevb9/5znes\nQ4cO9uc//9nOP//8lE/95ZdftpdeeskmTZrk22x6/vz5dvnllxfXKLdt29Y6d+5sr732mttH\nUPmiRYusRYsWpnNQKigocM809tYPKt++fbutWLHC1QB7/Zo1INjGjRsTaqvdDvgPAQQQQAAB\nBBBAAAEEEEAglAKBfYC9o+7UqZO9/fbbrsZVr2oCvHLlSvvc5z5nQ4cOtfPOO881LS7dt9Zb\nP9nrRRddZP369XOB6RNPPJGw2KZNm1wAG1uggHbr1q0uK5VyBemxSetv27bNTpw4YVq/rPLN\nmze7VbWOlxo2bGhVq1Z1xyAXL+3YscPVTnvzelV/ZhmRPhXQ86RJiQK4JJp4Odh4Eomv2CSa\nKAcXfxdskrtgk9yG9xM2yQWSl3Df+Nvg4u+i3HTYpNo6N+UAWAd2xhln2Pe//31NuqQRn2vU\nqOHNntargslkSc2jFajWqVMnbhHNr1q1yoLKtZIC2NLra6AtBb+7d+8OLFeArCbT+hebtI3Y\nfsQqU1D+wx/+MHYxmzBhQsKgXnELRGym9LWI2OknPV1cktIkvH+TLxm9Eu4b/2uOi7+LcrHB\nJrmAfwn3jL+LcrHBJrmAfwn3jL+LctNhc+TIkeQ7iCkpVwAcs56b/KzBb+ntlZ7Pz883DcKl\nQDc2aV6/EgSVax31SfZbX2Vq0n065VpXg29p/dikmmT1NY5N+tGgdKAcWx61aSz8rzgu/i7K\nxQab5AL+Jdwz/i7KxQab5AL+Jdwz/i7KxQab5AL+Jdwz/i7KTZeNWukGpc8UAAdt/LOWq89t\ngwYN3KOHYre1Z88e0/OJg8q1TqNGjWzdunWxq5vWV79l1eqmUq5g98CBA3EBr7bRvHnzuO2q\nVrhv375xeRogzHs2clxBRGcOHToU0TMv+7RxSe6DDTbJBfxLuGf8XZSLDTbJBfxLuGf8XZSL\nDTbJBfxLuGf8XZSbDhtVjqaSUhoEK5UNVdQy7du3t2XLlsVtXs8D9vrtBpW3a9fO9VWOrQXW\n9rz1g8pbtWrl+ifHHoMGxVIT6th+wXEHyAwCCCCAAAIIIIAAAggggEDoBEIfAF911VU2b948\nN+KyOjbPnTvX1L5bA2cpBZXrmcRKzz77rAta9SxjjTyt5wIrBZXXrVvX+vTp4x6lpMcx6deJ\n6dOnu5rexo0bu23wHwIIIIAAAggggAACCCCAQPgFQt0EWnwXXHCBDRs2zMaOHev666rm9p57\n7jFvtOmgcjVzfuCBB9zzexUEq9/ykCFDrGfPnu7qBJVroTFjxrj1Bw4c6JpNd+nSxcaNG+fW\n5z8EEEAAAQQQQAABBBBAAIHsEAhVAPzrX//aV23kyJE2fPhw13dXfXZLp6ByPYrohRdesC1b\ntphqbTWwVmwKKld/4ccee8ztX23L0zFMd+z+mUYAAQQQQAABBBBAAAEEEKh4gVAFwGWdrkb0\n8gt+vXWCyrVc06ZNvcV9X4PK0zE8t++OyUQAAQQQQAABBBBAAAEEEKhwgfiq0ArfHTtAAAEE\nEEAAAQQQQAABBBBAIDMCBMCZcWevCCCAAAIIIIAAAggggAAClSxAAFzJ4OwOAQQQQAABBBBA\nAAEEEEAgMwIEwJlxZ68IIIAAAggggAACCCCAAAKVLEAAXMng7A4BBBBAAAEEEEAAAQQQQCAz\nAgTAmXFnrwgggAACCCCAAAIIIIAAApUsQABcyeDsDgEEEEAAAQQQQAABBBBAIDMCBMCZcWev\nCCCAAAIIIIAAAggggAAClSxAAFzJ4OwOAQQQQAABBBBAAAEEEEAgMwIEwJlxZ68IIIAAAggg\ngAACCCCAAAKVLEAAXMng7A4BBBBAAAEEEEAAAQQQQCAzAgTAmXFnrwgggAACCCCAAAIIIIAA\nApUsQABcyeDsDgEEEEAAAQQQQAABBBBAIDMCBMCZcWevCCCAAAIIIIAAAggggAAClSxAAFzJ\n4OwOAQQQQAABBBBAAAEEEEAgMwIEwJlxZ68IIIAAAggggAACCCCAAAKVLEAAXMng7A4BBBBA\nAAEEEEAAAQQQQCAzAgTAmXFnrwgggAACCCCAAAIIIIAAApUsQABcyeDsDgEEEEAAAQQQQAAB\nBBBAIDMCBZnZbXT2mpeXZ9WqVYvOCQecKRb+QLj4uygXG2ySC/iXcM/4uygXG2ySC/iXcM/4\nuygXG2ySC/iXcM/4uyg3HTaKu1JJBMCpKH2GZapUqWIFBTB7hOm4ub1t5dIrLsmvJjbYJBfw\nL+Ge8XdRLjbYJBfwL+Ge8XdRLjbYJBfwL+Ge8XdRbjpsTpw4kXwHMSVEZjEYFTF5/Phx27dv\nX0VsOiu3uWfPnqw87oo+aFySC2ODTXIB/xLuGX8X5WKDTXIB/xLuGX8X5WKDTXIB/xLuGX8X\n5abDJj8/32rXrp18J/8soQ9wIBELIIAAAggggAACCCCAAAII5IIAAXAuXEXOAQEEEEAAAQQQ\nQAABBBBAIFCAADiQiAUQQAABBBBAAAEEEEAAAQRyQYAAOBeuIueAAAIIIIAAAggggAACCCAQ\nKEAAHEjEAggggAACCCCAAAIIIIAAArkgQACcC1eRc0AAAQQQQAABBBBAAAEEEAgUIAAOJGIB\nBBBAAAEEEEAAAQQQQACBXBAgAM6Fq8g5IIAAAggggAACCCCAAAIIBAoQAAcSsQACCCCAAAII\nIIAAAggggEAuCBAA58JV5BwQQAABBBBAAAEEEEAAAQQCBQiAA4lYAAEEEEAAAQQQQAABBBBA\nIBcECIBz4SpyDggggAACCCCAAAIIIIAAAoECBMCBRCyAAAIIIIAAAggggAACCCCQCwIEwLlw\nFTkHBBBAAAEEEEAAAQQQQACBQAEC4EAiFkAAAQQQQAABBBBAAAEEEMgFAQLgXLiKnAMCCCCA\nAAIIIIAAAggggECgAAFwIBELIIAAAggggAACCCCAAAII5IIAAXAuXEXOAQEEEEAAAQQQQAAB\nBBBAIFCAADiQiAUQQAABBBBAAAEEEEAAAQRyQYAAOBeuIueAAAIIIIAAAggggAACCCAQKEAA\nHEjEAggggAACCCCAAAIIIIAAArkgUJANJ7FgwQLbv39/3KGeffbZ1rp1a5d3/PhxW7x4sS1f\nvtw6duxo3bt3j1tWMxs2bLCFCxdagwYNrGfPnlarVq24ZYLK9+7dazoOvfbo0cPatGkTtz4z\nCCCAAAIIIIAAAggggAAC4RYIfQCs4Pbee++12rVrW0FByeGOHj3aBcAqHzNmjG3atMkuvvhi\nmz17tvXq1ctuvfXWYvlnnnnGpk+fbpdeeqlt3LjRNP/4449b/fr13TJB5WvXrrVRo0ZZ+/bt\nrWXLlvbkk0/agw8+aBdccEHxPphAAAEEEEAAAQQQQAABBBAIt0BJRBnS4/zwww/tyJEj9tRT\nT1nDhg0TjlIB7759+2zWrFlWVFRk69evtxEjRlj//v3trLPOcjW/M2bMsGnTplnXrl3t2LFj\nLmDW8gqcVfNbVrl2OHnyZBs0aJCNHz/e8vLy7Omnn7apU6fazJkz3XzCQZGBAAIIIIAAAggg\ngAACCCAQOoHQ9wFevXq1NWrUyDf4leb8+fPt8ssvd8Gv5tu2bWudO3e21157TbO2aNEia9Gi\nhQt+Na9a5L59+6Zcvn37dluxYoUNHjy4ONgdMGCAq0lWk+vYpNroHTt2xP1T8K6g+bP+i91P\nNk9/Vge/9bPZwzt2v/P6rHnetrP99bM6+K2f7Sbe8fud22fN87adza+f1SDZ+tls4h17snP7\nLPnetrP99bMYJFs32010/MnO7bPmY+P/3TAXXCrqvskFm8/6vkm2PjYl76dULEJfA/z++++7\n5s9TpkxxfXDVbPm6666zSy65xJ2fmj4rwI1Nmt+6dWtxuZotxyaVb9u2zU6cOOGaTpdVvnnz\nZrdq7D5UE121alW3j06dOhVvWsG6AuXYNGHCBLvmmmtisyI93axZs0iff7KTxyWZjBk22CQX\n8C/hnvF3US422CQX8C/hnvF3US422CQX8C/hnvF3UW46bFTxmEoKfQC8atUqV6PaoUMHN3jV\nK6+8Ynfffbc9/PDDbrArBbJ16tSJO1fNaz0lBbCly9WfWMHv7t27A8sVYFerVs39i92JtrFz\n587YLDew1mWXXRaX16RJEzt06FBcXpRnsPC/+rj4uygXG2ySC/iXcM/4uygXG2ySC/iXcM/4\nuygXG2ySC/iXcM/4uyg3HTZqjatKyqAU+gBYNagKVr0BqzTwlGqF1YdX01WqVHH9emNPVP18\n1R9YqbCw0LdcZTVr1jytcq0rYK0fm1q1auUGyIrN27VrV0KgHFsetenSPxpE7fyTnS8uyWSM\n909yGmyS2PB+SgJzKhsbbJIL+Jdwz/i7KBcbbJIL+Jdwz/i7KDcdNvn5+cUxYPI9mYW+D3Dd\nunWLg1/vRC688ELXdFnt4PVYIz2aKDbt2bOnuBpd/Yf9yhVQq2Y3lXIFuwcOHIjdhWkfzZs3\nj8tjBgEEEEAAAQQQQAABBBBAILwCoQ+A77jjDpszZ06c4JIlS4r7/erRRMuWLYsr1+BUXr/e\ndu3a2cqVK+NqgbV8quWq1dXAWbH70KBYqpWO7RccdwDMIIAAAggggAACCCCAAAIIhE4g9AFw\nt27d3HN7NcDU4cOHbe7cuS6gHTp0qMO86qqrbN68eaag9+TJk65cHaD79evnynv37u1en332\nWRe0rlmzxl5++WX3qCQVBJWrBrpPnz7uUUl63JLap+uZwhpJunHjxm7b/IcAAggggAACCCCA\nAAIIIBB+gdD3AdaoykuXLrWRI0e6Ts1qtqxBsNQMWkn9gIcNG2Zjx451/XlVs3vPPfe4AalU\nruUfeOABmzhxoikIrlGjhg0ZMsQNqJVKuZbR84K1/sCBA932unTpYuPGjVMRCQEEEEAAAQQQ\nQAABBBBAIEsEQh8AK2CdNGmS7d+/3/Xlbdq0afHzeD1jBcfDhw93/XLVp7d0Ui3yCy+8YFu2\nbHG1tho4KzYFlau/8GOPPea2n2rn6tjtM40AAggggAACCCCAAAIIIJB5gdAHwB6RRnX2Rnb2\n8mJfNeS1X/Abu4yC57JSUHnpxymVtS3KEEAAAQQQQAABBBBAAAEEwiUQXxUarmPjaBBAAAEE\nEEAAAQQQQAABBBBImwABcNoo2RACCCCAAAIIIIAAAggggECYBQiAw3x1ODYEEEAAAQQQQAAB\nBBBAAIG0CRAAp42SDSGAAAIIIIAAAggggAACCIRZgAA4zFeHY0MAAQQQQAABBBBAAAEEEEib\nAAFw2ijZEAIIIIAAAggggAACCCCAQJgFCIDDfHU4NgQQQAABBBBAAAEEEEAAgbQJEACnjZIN\nIYAAAggggAACCCCAAAIIhFmAADjMV4djQwABBBBAAAEEEEAAAQQQSJsAAXDaKNkQAggggAAC\nCCCAAAIIIIBAmAUIgMN8dTg2BBBAAAEEEEAAAQQQQACBtAkQAKeNkg0hgAACCCCAAAIIIIAA\nAgiEWYAAOMxXh2NDAAEEEEAAAQQQQAABBBBImwABcNoo2RACCCCAAAIIIIAAAggggECYBQiA\nw3x1ODYEEEAAAQQQQAABBBBAAIG0CRAAp42SDSGAAAIIIIAAAggggAACCIRZgAA4zFeHY0MA\nAQQQQAABBBBAAAEEEEibAAFw2ijZEAIIIIAAAggggAACCCCAQJgFCIDDfHU4NgQQQAABBBBA\nAAEEEEAAgbQJFKRtS2zIV6CwsNBq167tWxbFzCZNmkTxtAPPGZfkRNhgk1zAv4R7xt9Fudhg\nk1zAv4R7xt9Fudhgk1zAv4R7xt9FuemwOXr0aPIdxJQQAMdgVMSkLsSePXsqYtNZuc2tW7dm\n5XFX9EHjklwYG2ySC/iXcM/4uygXG2ySC/iXcM/4uygXG2ySC/iXcM/4uyg3HTb5+flWvXr1\n5Dv5ZwlNoAOJWAABBBBAAAEEEEAAAQQQQCAXBAiAc+Eqcg4IIIAAAggggAACCCCAAAKBAgTA\ngUQsgAACCCCAAAIIIIAAAgggkAsCBMC5cBU5BwQQQAABBBBAAAEEEEAAgUABAuBAIhZAAAEE\nEEAAAQQQQAABBBDIBQEC4Fy4ipwDAggggAACCCCAAAIIIIBAoAABcCARCyCAAAIIIIAAAggg\ngAACCOSCAAFwLlxFzgEBBBBAAAEEEEAAAQQQQCBQgAA4kIgFEEAAAQQQQAABBBBAAAEEckGA\nADgXriLngAACCCCAAAIIIIAAAgggEChAABxIxAIIIIAAAggggAACCCCAAAK5IEAAnAtXkXNA\nAAEEEEAAAQQQQAABBBAIFCAADiRiAQQQQAABBBBAAAEEEEAAgVwQIADOhavIOSCAAAIIIIAA\nAggggAACCAQKEAAHErEAAggggAACCCCAAAIIIIBALggQAOfCVeQcEEAAAQQQQAABBBBAAAEE\nAgUIgAOJWAABBBBAAAEEEEAAAQQQQCAXBAiAc+Eqcg4IIIAAAggggAACCCCAAAKBAgTAgUQs\ngAACCCCAAAIIIIAAAgggkAsCBMC5cBU5BwQQQAABBBBAAAEEEEAAgUABAuBAIhZAAAEEEEAA\nAQQQQAABBBDIBYGCXDiJyjiHvXv32oIFC0yvPXr0sDZt2lTGbtkHAggggAACCCCAAAIIIIBA\nmgSoAU4Bcu3atTZ48GCbM2eOvffeezZy5Eh75513UliTRRBAAAEEEEAAAQQQQAABBMIiQA1w\nCldi8uTJNmjQIBs/frzl5eXZ008/bVOnTrWZM2e6+RQ2wSIIIIAAAggggAACCCCAAAIZFqAG\nOOACbN++3VasWOFqgBX8Kg0YMMA2btxoy5cvD1ibYgQQQAABBBBAAAEEEEAAgbAIUAMccCU2\nb97slmjRokXxkg0bNrSqVava1q1brVOnTsX5H330kU2cOLF4XhPDhg2ziy66KC4vyjP169eP\n8uknPXdcktIYNtgkF/Av4Z7xd1EuNtgkF/Av4Z7xd1EuNtgkF/Av4Z7xd1FuOmyOHz+efAcx\nJXknT6WYeSZLCcybN88eeugh02tsuvLKK+26666zIUOGFGevXLnS1RQXZ5yamDBhgl1zzTWx\nWUwjgAACCCCAAAIIIIAAAgikUeDIkSOukjJok9QABwgVFhbasWPHEpbSLww1a9aMyz/zzDPt\nT3/6U1ze0aNHzatFjisI0UyVKlWsSZMmdujQIdu1a1eIjizzh1KjRg2rW7eu7d692w4ePJj5\nAwrREdSrV8+qV69uW7ZsMX5Hi78wzZo1M30I79ixI74g4nPVqlVzv/BqNP39+/dHXCP+9OvU\nqeP+pnzyySeW6i/Y8VvI3Tn9fTpx4oRt27Ytd0/yNM6mBym/AAAWPElEQVRM30/UIk3vJb2n\nSCUCtWrVMv3TZ7A+i0klArpn8vPzXSvGklymZNK4cWP3XU/f+UglAop39DdKMYJihTAn7zoG\nHSMBcIBQo0aN3JeRAwcOxAW8e/bssebNm8etLXQFBbFJN4tfAB27TKanY4OX2OlMH1cY9u95\n6NWbDsNxhekYsEl+Nbhn4m08D+6ZeJfSc55T6fyoznse3mtUHUqft+ehV2+69DJRn8cm+R3A\nPRNvE+sROx2/VDTnPA+9etNhlUj1+BgEK+AKtmrVygoKCmzZsmXFS2pQLP0aHdsvuLiQCQQQ\nQAABBBBAAAEEEEAAgVAKEAAHXBY1f+3Tp4/NmDHD9u3b56r+p0+fbn379nVNJQJWpxgBBBBA\nAAEEEEAAAQQQQCAkAgTAKVyIMWPGuA7VAwcONA1+pRrhcePGpbAmiyCAAAIIIIAAAggggAAC\nCIRFgD7AKVwJDcv92GOPmfr9qp9vUVFRCmuxCAIIIIAAAggggAACCCCAQJgECIDLcTU0AhoJ\nAQQQQAABBBBAAAEEEEAgOwVoAp2d142jRgABBBBAAAEEEEAAAQQQKKcAAXA5wVgcAQQQQAAB\nBBBAAAEEEEAgOwUIgLPzunHUCCCAAAIIIIAAAggggAAC5RQgAC4nGIsjgAACCCCAAAIIIIAA\nAghkpwABcHZeN44aAQQQQAABBBBAAAEEEECgnAJ5J0+lcq7D4uUQ2L9/vx05cqQca1T+ojq+\nt99+2xo1amSdOnWq/AMI8R43bdpkq1atsg4dOljz5s1DfKSVf2jvvfeebd++3Xr27GmFhYWV\nfwAh3uObb75pGjW+W7duIT7Kyj803S+6b9q3b2+tW7eu/AMI8R71OaPPm/POO49H7ZW6TgsX\nLrSCggI7//zzS5VEe1aPZvzb3/7m3kt6T5FKBNauXWsbNmywLl26WL169UoKmLK//OUvdujQ\nIbv44ovRiBE4ePCgLVq0yJo2bWodO3aMKWHy448/tvfff9/OOecca9y4cahBqlSpYnXr1g0+\nRgXApGgLbNu27eSpAO/kTTfdFG0In7OfNWuWs3nuued8SqOddeONNzqbU0FNtCF8zl7vp6FD\nh/qURDtr3rx57p75+c9/Hm0In7O/6667nM3q1at9SqOd1aNHj5Nf/epXo43gc/angl93z0ya\nNMmnNNpZjz76qLN55513og3hc/b9+vU7eerHWZ+SaGed+sHE3TO33XZbtCF8zn7GjBnO5qWX\nXvIpzc4smkAH/0bAEggggAACCCCAAAIIIIAAAjkgQACcAxeRU0AAAQQQQAABBBBAAAEEEAgW\nIAAONmIJBBBAAAEEEEAAAQQQQACBHBBgEKwcuIif9RSOHTtmf//7312ncQbSiNfUoD0aSKNt\n27bWoEGD+MKIz61Zs8Z2795tX/jCF9wANRHniDt9DUxTVFTkBk+LK4j4jO4X3TctWrRwA41E\nnCPu9D/88EM7NR6DnX322Va9evW4sqjP6O9Tfn6+G4Al6hax569BNjV4WpMmTaxly5axRZGf\n1oBymzdvtjPPPNNq1aoVeY9YgJUrV7rBWc8999zY7MhPa0DYZcuWue96+s5HKhHYunWraSCs\nM844w+rXr19SkMVTBMBZfPE4dAQQQAABBBBAAAEEEEAAgdQFaAKduhVLIoAAAggggAACCCCA\nAAIIZLEAAXAWXzwOHQEEEEAAAQQQQAABBBBAIHWBgtQXZclcFjh+/Lj953/+p/3Lv/yL1alT\nJ5dPNeVzO3HihOsbvXjxYtdfsVevXlatWrWU18/lBXft2mVvvfWWnXr6m51//vnWvHnzXD7d\n0zq3v/zlLyan3r17n9b6ubbSggULTH0WY5P6u7Zu3To2K5LTuk8WLlxoe/bssS9/+cv05zx1\nFyxdutTUj9MvXXzxxa6PvV9ZVPL02au+0StWrHD3jPrVkz4VUL/oP//5z9awYUM79QzpnOmz\neLrXt6zvd3v37jV9NutVVm3atDnd3WTleurXqs/eq6++2vf4y7LzXSGHMvUdr3bt2nbqmdFx\nZ5Ur343pAxx3WaM78+Mf/9hmz55ts2bNcgPURFfi0zPXYDTf/va3XcDbpUsXe/vtt91AGk8+\n+WTkfyD4v//7P5s0aZILfA8ePGjLly+3f//3f7fzzjsv6rdN8flv2bLFvvnNb5runR/+8IfF\n+VGd0JeIPn36uD+mBQUlv7uOHj3a5UfVRef9wQcf2O233+5+RGratKm9+eabNmLECPvWt74V\nZRZ7/PHH3Y9ssQj6kn7gwAGbM2dOpAdR0+CMY8eOtby8PDcI4fz5892X1AceeMCqVIl2w765\nc+fatGnT7KyzznKfN0uWLHH3UqdOnWJvpUhNJ/t+t3btWhs1apRp8FMNoqZA+MEHH7QLLrgg\nEj779u2zm266yX3Pmz59uu85J7PzXTiHMlXx873vfc9uuOEGu/baa4vPLJe+G5d8Eyk+PSai\nJKAv6o8++qi9++67UTrtwHPVFyz9ov7EE0+4ZRXoDRkyxP1AoA+EqKajR4/az3/+c/fjwLBh\nwxzD5MmT7Re/+AUB8D9vCv06qi+i+nJK+lRAIxxrhM2nnnrK1crgUiLws5/9zI38rB+VlN55\n5x2777777KqrrnJf4EuWjNbUzTffbPrnJQW+119/vQ0cODDSwa88nn/+efdDgIK9wsJCNxK0\nApm//vWv1r17d48scq/6cv7Tn/7Uhg8fbvpxTem5556zu+++25599tnItRoI+n6nv92DBg2y\n8ePHu79XTz/9tE2dOtVmzpyZ83+//vSnP9nDDz/sWmm1a9cu4b0SZJewQo5k6KkwzzzzjPvn\n9x0ml74bR/unwhy5YT/LaTz00EOuGSu1VPGKNWvWtOuuu644s0aNGtaxY0fbuHFjcV4UJ1ST\n993vftf90fTOX0Pi79ixw5uN/OtvfvMb9+XhK1/5SuQtPIDVq1dbo0aNCH49kH++6vNEX8TG\njBlTXKJmiDNmzOBRSMUin07ox0h9DnuBTaniSM3qxyR97ir4VWrWrJl7TJR+qI1yUnNw/Uir\nH0m8pC4oO3fujOSP/GV9v1MrAnkNHjy4ONgdMGCA+46jVl25nNSS5K677rKvfe1rds011/ie\nall2vivkSObLL79sL730kmvl59c9KZe+G1MDnCM37emexp133ul+TV+/fv3pbiIn14sNfnWC\nCvD0bFc1O4ty0vNJL7nkEkegP6CLFi2y//7v/3bNqKLs4p37P/7xD1MArOZU6lNP+lTg/fff\nd7WZU6ZMcc3s9OVd7zHvXoqqk2rG9Xxb/dL+yCOPmD6HzznnHFfT6QU3UbWJPW999v72t791\nLQiqVq0aWxTJ6SuuuMJeffVV+8lPfuJa3rzwwgvuWfV0QzH3XtJ7yksKiNUqR309o5bK+n6n\nZyQrxfYdV59pvb/0zNdcbjKuH9LU5U/n+6tf/co5lP6vLLvSy+bS/EUXXWT9+vUzdVXyWkDG\nnl8ufTemBjj2ykZwWn3OSGUL6Nf2CRMmuC8YV155ZdkLR6j0/vvvd02IVLOngXuing4fPuya\nPutHEtXIkEoENCiNfkTq0KGD/b//9/9cfzM1S1Tf+ignNdnUj0oyURD8pS99yX7/+9+7vlf6\n0k76VEBjU3zxi1909w8m5vpsquZOLv/2b//m3kc33nijqXYmykmD6umHIzXhVVNOtVhSc3El\nNaGPWirr+50GmNOgnqUH9tSgR6oxz+Wk4E7Bb1mpLLuy1sv2MrnEjtNR1vlk+3djaoDLurqU\nRV5Ao7L+4Ac/cKOzqm8MtTIlt4QGGtHoter/q0F71B+tbt26JQtEbEp9z9q2beuaVUXs1ANP\nVz8gKaBTza+SBllRrbC+wF944YWB6+fqAvqSrpGxR44caUOHDnWnqVq873znO65pdJRtvGuu\nHwn0Q4l+cCN9KqCWFBpl/j/+4z/szDPPdK0q9IOSguEod73Qj7HqN66/1RqsUTXB6t+pz2XV\n+pFKBPRdRp8/pZN+NIj6DymlTZhPFMiF78bUACdeV3IQcAL64qUvovojoaZm+uNKiheoV6+e\n65OnP5pRrs3TgBlqCq5fzu+44w73T4MZqY+V5vVDQZSTfhjxgl/PQcFdssfceMvk+mvjxo3d\nKV566aXFp9q5c2c30vxHH31UnBflCfVHU62EmuaRzP2Q9MYbb7hBGVXjqdoa3T89e/Z0rQei\nbqSa8V//+tdu9FoNJqfxTXbv3h1Y4xc1N32f0d/t0jXjCmx4rGHU7obynW+ufDcmAC7fdWfp\niAgooFHwq0EA9DiOKNdsxl7ydevW2de//vW4wcAOHTrk/pDquZRRTapd0GOzNICR+nDqnwK+\nWrVquemotxzQjwAaPTI26fEksf3PYsuiMn3GGWe4U/X642nmk08+cS1OvDK3QIT/0yBheu5v\nqs3yokClz9yioqK4U1VtZ+nnbMctEIEZuahPpz53+/fvb+eee65raaIAWNOkEoFWrVq599Sy\nZcuKM/WDrVrqRP1zuRiEiQSBXPpuTBPohMtLBgJmP/rRj1xQp4ejr1y5spikTp06rklVcUbE\nJvSlXH1j9Cik2267zfSFQwMl6AeCqDw70O+S677Qc39jkwIZ/SudH7tMVKa7devmHqug5yK3\nadPGXnzxRfe+0mMoopz0RfOyyy5zzy3VIFgK8vSoqCZNmuT0IDTlueb60e3yyy8vzyo5vaye\n86t7RrWcej9pvIGFCxe6ZybrcTZRTupPr0c6qoZq3LhxrnZTzaH/9V//lXEZSt0Y+putZ7Nr\nxHmvJYEGb+zbt695LVNKrcIsAjn13ZgAmBsagVICejSJ15y39BcK1fDpuclRTrfccoupT6cG\nBNOvxepfpS/vpZu4RtmIc48XULPEpUuXur6uGmVUA6+ozyJ9XM2+//3vm57HqZYVqsVr2bKl\n+5JBPzxzXQr0yJL27dvH31ARn/ve977n7hE9wkVBnz6HNTorgzSae1KDuizpUUhqeaMBGtU6\nh5QooMevTZw40VnpM1k/qOiHAxICfgK59t0471Szxei2W/S7wuQhgEBKAnpUgmqsGjRokNLy\nLISAmmgqoFErAo16TCoRUF88tajg/VRiwlTZArpfNLq6WgzQRDzeSuMuqCk0LvEufnPq96sf\n30o3q/dbljwEckWAADhXriTngQACCCCAAAIIIIAAAgggUKYAg2CVyUMhAggggAACCCCAAAII\nIIBArggQAOfKleQ8EEAAAQQQQAABBBBAAAEEyhQgAC6Th0IEEEAAAQQQQAABBBBAAIFcESAA\nzpUryXkggAACCCCAAAIIIIAAAgiUKUAAXCYPhQgggAACCCCAAAIIIIAAArkiQACcK1eS80AA\nAQQQQAABBBBAAAEEEChToKDMUgoRQAABBBBAIHQC27ZtMz1XWalt27ZJj0/P+Ny5c6d7HmrL\nli2TLpfugoMHD5qeFd64cWOrWbNmujfP9hBAAAEEEDhtAWqAT5uOFRFAAAEEEMiMwC233GJn\nnHGG+7d06dKkB/Htb3/bLXPhhRcmXSYdBX//+99t+vTpxZt6/fXX3X5/97vfFecxgQACCCCA\nQBgECIDDcBU4BgQQQAABBE5DIC8vz2bPnu275r59++zFF1/0LUt35pe+9CX705/+lO7Nsj0E\nEEAAAQTSLkAAnHZSNogAAggggEDlCKhm97nnnvPd2f/8z//Y8ePH7fOf/7xveTozjx07ls7N\nsS0EEEAAAQQqTIAAuMJo2TACCCCAAAIVK/CNb3zDVq1aZUuWLEnY0W9+8xvr27ev1a9fP6FM\nfXR//OMf2ze/+U0bPny4PfLII7Zr16645VavXm333Xefqb+xmjKPHz/errnmGpsyZYppfaUt\nW7a4ZU6ePGl//etf3fSHH34Ytx2tO3bsWBsxYoT99Kc/Le67HLcQMwgggAACCFSSAAFwJUGz\nGwQQQAABBNItMGTIEDfAVelm0Br46ve//70NGzYsYZcbN260c845x26//XbbtGmT7d692yZO\nnGidO3d2Qay3ggLg+++/3+644w4XSL/11lv2t7/9zW677Ta7+OKL7cSJE3bgwAFTvtLmzZvd\ntAbe8tLDDz9sAwcOdAH6H/7wB/vud7/r5o8cOeItwisCCCCAAAKVKkAAXKnc7AwBBBBAAIH0\nCTRq1Mh69+6d0Az6+eeft8LCQhs0aFDCzkaNGuVqbv/4xz+6IPl///d/7d133zU1Y77++uvd\na+xKL730kmmQKwW/K1eutNGjR7vl582bZ+3atTMNeKW+yP3793fTnTp1Kl5dQbTWnT9/vqlm\n+Nprr3XLaH8kBBBAAAEEMiFAAJwJdfaJAAIIIIBAmgTUDFqB5uLFi4u3OHPmTFfTWlRUVJyn\niY8++sheffVVu+GGG+z8888vLuvQoYOr6X3vvffszTffLM7XxE033eRqh73Mq6++2k2uX7/e\ny0r6OmbMGDvrrLNceX5+vulYlRRIkxBAAAEEEMiEAAFwJtTZJwIIIIAAAmkSuPLKK61q1arF\ntcB6/q5qZdVft3RasWKFy4oNfr1levTo4SZLB6elB9Fq0qSJW87rB+yt7/eqwDo2nXnmmW52\n+/btsdlMI4AAAgggUGkCBMCVRs2OEEAAAQQQSL9AvXr17Iorrih+HJJGha5du7brt1t6b17g\nWadOndJFVqtWLZd39OjRuLKaNWvGzau5s5IGvgpKOg4SAggggAACYRIgAA7T1eBYEEAAAQQQ\nOA0BNS1+//333WBTGhDr61//uqsVLr2pz33ucy5r3bp1pYvMy+vatWtCGRkIIIAAAgjkigAB\ncK5cSc4DAQQQQCCyAhrsqnr16vaTn/zEDTjl1/xZOGeffbZ7LNKvfvWrhBrcX/7yl87vdAJg\n9e9lZOfI3n6cOAIIIJBVAgTAWXW5OFgEEEAAAQQSBdTU+Gtf+5o99dRTpj66l112WeJCp3LU\nzPnBBx90ozjrEUpvv/22e/TRjTfeaL/97W9t0qRJpibV5U161rD6HT/xxBNutOfyrs/yCCCA\nAAIIVJYAAXBlSbMfBBBAAAEEKlBAzaDVL1ejNKtGNln6zne+Y6rtXbBggfXs2dPOO+88e+ON\nN2zKlCn2gx/8INlqZebfc889pv7FY8eONT3vl4QAAggggEBYBfJO/bEMHsUirEfPcSGAAAII\nIIDAaQvo2bwKllu0aHHa2/BWPH78uO3YscP0bGJvoCyvjFcEEEAAAQTCIkAAHJYrwXEggAAC\nCCCAAAIIIIAAAghUqABNoCuUl40jgAACCCCAAAIIIIAAAgiERYAAOCxXguNAAAEEEEAAAQQQ\nQAABBBCoUAEC4ArlZeMIIIAAAggggAACCCCAAAJhESAADsuV4DgQQAABBBBAAAEEEEAAAQQq\nVIAAuEJ52TgCCCCAAAIIIIAAAggggEBYBAiAw3IlOA4EEEAAAQQQQAABBBBAAIEKFSAArlBe\nNo4AAggggAACCCCAAAIIIBAWAQLgsFwJjgMBBBBAAAEEEEAAAQQQQKBCBQiAK5SXjSOAAAII\nIIAAAggggAACCIRFgAA4LFeC40AAAQQQQAABBBBAAAEEEKhQAQLgCuVl4wgggAACCCCAAAII\nIIAAAmER+P/YGeaE+iZHSAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3. Гистограмма с рождаемостью по месяцам \n",
    "ggplot(df_dropna, aes(x=factor(bmonth)))+\n",
    "    geom_bar(stat=\"count\", width=0.7, fill=\"steelblue\") + \n",
    "    xlab('Month') + ylab('Count')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Такс такс такс, что тут у нас. Учитывая, что выборка довольно большого объёма, сложно списать разницу в высоте столбиков на случайность. Если мы будем проверять гипотезу о равномерности распределения, скорее всего, она будет отвергаться. Почему-то в конце года рождается меньше людей. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Постройте точно такую же гистограмму для дней рождений. Вас ждёт небольшой сюрприз. Избавьтесь от этого сюрприза, чтобы он не замусоривал данные. Как считате, подневная рождаемость имеет равномерное распределение? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAYAAACYBpIxAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 4. Аналогичная картинка для дней \n",
    "ggplot(df_dropna, aes(x=factor(bday)))+\n",
    "    geom_bar(stat=\"count\", width=0.7, fill=\"steelblue\") + \n",
    "    xlab('Days') + ylab('Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>bday</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>34</th><td>       1984</td></tr>\n",
       "\t<tr><th scope=row>35</th><td>        -99</td></tr>\n",
       "\t<tr><th scope=row>36</th><td>        666</td></tr>\n",
       "\t<tr><th scope=row>37</th><td>-1234567890</td></tr>\n",
       "\t<tr><th scope=row>38</th><td>        313</td></tr>\n",
       "\t<tr><th scope=row>39</th><td>       -111</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|l}\n",
       "  & bday\\\\\n",
       "\\hline\n",
       "\t34 &        1984\\\\\n",
       "\t35 &         -99\\\\\n",
       "\t36 &         666\\\\\n",
       "\t37 & -1234567890\\\\\n",
       "\t38 &         313\\\\\n",
       "\t39 &        -111\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | bday |\n",
       "|---|---|\n",
       "| 34 |        1984 |\n",
       "| 35 |         -99 |\n",
       "| 36 |         666 |\n",
       "| 37 | -1234567890 |\n",
       "| 38 |         313 |\n",
       "| 39 |        -111 |\n",
       "\n"
      ],
      "text/plain": [
       "   bday       \n",
       "34        1984\n",
       "35         -99\n",
       "36         666\n",
       "37 -1234567890\n",
       "38         313\n",
       "39        -111"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Что за?! \n",
    "df_dropna %>% select(bday) %>% distinct() %>% tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сюрприз! Вконтакте есть баги в записях. Служба поддержки отвечат, что в давнем времени была возможность обходить валидацию и писать некорректные данные в некоторые поля. Придётся нам отфильтровать это. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAYAAACYBpIxAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nIIAAAgiUlsD/B3k50NJWUerwAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_dropna = df_dropna %>% filter(bday >=0, bday <=31)\n",
    "\n",
    "ggplot(df_dropna, aes(x=factor(bday)))+\n",
    "    geom_bar(stat=\"count\", width=0.7, fill=\"steelblue\") + \n",
    "    xlab('Days') + ylab('Count')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Снова равномерное распределение не особо наблюдается. Почему-то дети любят рождаться в самом начале месяца. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Эмпирически оцените вероятность того, что в группе из 50 произвольных людей найдутся хотя бы двое с одинаковым днём рождения. Для этого напишите цикл, в ходе которого из таблички с помощью команды `sample` будет делаться подвыборка из 50 строк. Для этих 50 строк внутри условия вы должны проверить совпадение дней рождений. Если совпало, то нужно запомнить это в переменную счётчик, которую вы впоследствии, чтобы получить вероятность, поделите на длину цикла."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>X</th><th scope=col>city</th><th scope=col>deactivated</th><th scope=col>first_name</th><th scope=col>home_town</th><th scope=col>id</th><th scope=col>last_name</th><th scope=col>sex</th><th scope=col>byear</th><th scope=col>bmonth</th><th scope=col>bday</th><th scope=col>bdate</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 0             </td><td>Москва         </td><td>               </td><td>Илья           </td><td>               </td><td>  5            </td><td>Перекопский    </td><td>2              </td><td>  NA           </td><td>11             </td><td>18             </td><td>11-18-2000     </td></tr>\n",
       "\t<tr><td> 2             </td><td>Санкт-Петербург</td><td>               </td><td>Михаил         </td><td>Санкт-Петербург</td><td> 11            </td><td>Петров         </td><td>2              </td><td>  NA           </td><td>12             </td><td>18             </td><td>12-18-2000     </td></tr>\n",
       "\t<tr><td> 6             </td><td>Москва         </td><td>               </td><td>Людмила        </td><td>               </td><td> 71            </td><td>Романченко     </td><td>1              </td><td>  NA           </td><td> 2             </td><td> 7             </td><td>2-7-2000       </td></tr>\n",
       "\t<tr><td> 7             </td><td>Санкт-Петербург</td><td>               </td><td>Наташа         </td><td>               </td><td> 74            </td><td>Филимонова     </td><td>1              </td><td>1988           </td><td> 7             </td><td>18             </td><td>7-18-2000      </td></tr>\n",
       "\t<tr><td>10             </td><td>Санкт-Петербург</td><td>               </td><td>Михаил         </td><td>               </td><td>175            </td><td>Захаренков     </td><td>2              </td><td>1981           </td><td>11             </td><td>23             </td><td>11-23-2000     </td></tr>\n",
       "\t<tr><td>13             </td><td>Turku          </td><td>               </td><td>Павел          </td><td>St. Petersburg </td><td>208            </td><td>Антипов        </td><td>2              </td><td>  NA           </td><td>11             </td><td>30             </td><td>11-30-2000     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllll}\n",
       " X & city & deactivated & first\\_name & home\\_town & id & last\\_name & sex & byear & bmonth & bday & bdate\\\\\n",
       "\\hline\n",
       "\t  0              & Москва          &                 & Илья            &                 &   5             & Перекопский     & 2               &   NA            & 11              & 18              & 11-18-2000     \\\\\n",
       "\t  2              & Санкт-Петербург &                 & Михаил          & Санкт-Петербург &  11             & Петров          & 2               &   NA            & 12              & 18              & 12-18-2000     \\\\\n",
       "\t  6              & Москва          &                 & Людмила         &                 &  71             & Романченко      & 1               &   NA            &  2              &  7              & 2-7-2000       \\\\\n",
       "\t  7              & Санкт-Петербург &                 & Наташа          &                 &  74             & Филимонова      & 1               & 1988            &  7              & 18              & 7-18-2000      \\\\\n",
       "\t 10              & Санкт-Петербург &                 & Михаил          &                 & 175             & Захаренков      & 2               & 1981            & 11              & 23              & 11-23-2000     \\\\\n",
       "\t 13              & Turku           &                 & Павел           & St. Petersburg  & 208             & Антипов         & 2               &   NA            & 11              & 30              & 11-30-2000     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| X | city | deactivated | first_name | home_town | id | last_name | sex | byear | bmonth | bday | bdate |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "|  0              | Москва          |                 | Илья            |                 |   5             | Перекопский     | 2               |   NA            | 11              | 18              | 11-18-2000      |\n",
       "|  2              | Санкт-Петербург |                 | Михаил          | Санкт-Петербург |  11             | Петров          | 2               |   NA            | 12              | 18              | 12-18-2000      |\n",
       "|  6              | Москва          |                 | Людмила         |                 |  71             | Романченко      | 1               |   NA            |  2              |  7              | 2-7-2000        |\n",
       "|  7              | Санкт-Петербург |                 | Наташа          |                 |  74             | Филимонова      | 1               | 1988            |  7              | 18              | 7-18-2000       |\n",
       "| 10              | Санкт-Петербург |                 | Михаил          |                 | 175             | Захаренков      | 2               | 1981            | 11              | 23              | 11-23-2000      |\n",
       "| 13              | Turku           |                 | Павел           | St. Petersburg  | 208             | Антипов         | 2               |   NA            | 11              | 30              | 11-30-2000      |\n",
       "\n"
      ],
      "text/plain": [
       "  X  city            deactivated first_name home_town       id  last_name   sex\n",
       "1  0 Москва                      Илья                         5 Перекопский 2  \n",
       "2  2 Санкт-Петербург             Михаил     Санкт-Петербург  11 Петров      2  \n",
       "3  6 Москва                      Людмила                     71 Романченко  1  \n",
       "4  7 Санкт-Петербург             Наташа                      74 Филимонова  1  \n",
       "5 10 Санкт-Петербург             Михаил                     175 Захаренков  2  \n",
       "6 13 Turku                       Павел      St. Petersburg  208 Антипов     2  \n",
       "  byear bmonth bday bdate     \n",
       "1   NA  11     18   11-18-2000\n",
       "2   NA  12     18   12-18-2000\n",
       "3   NA   2      7   2-7-2000  \n",
       "4 1988   7     18   7-18-2000 \n",
       "5 1981  11     23   11-23-2000\n",
       "6   NA  11     30   11-30-2000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# создадим колонку с датами рождения, подпишем рандомный год, чтобы не париться\n",
    "df_dropna = df_dropna %>% mutate(bdate = paste(bmonth,bday,'2000',sep = '-')) \n",
    "head(df_dropna)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "48"
      ],
      "text/latex": [
       "48"
      ],
      "text/markdown": [
       "48"
      ],
      "text/plain": [
       "[1] 48"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sample_n  выбрала рандомные 50 строк \n",
    "# после мы выбрали колонку с датами\n",
    "# в колонке с датами оставили уникальные значения\n",
    "# подсчитали их количество \n",
    "# если уникальных значений меньше 50, значит два др совпали \n",
    "\n",
    "df_dropna %>% sample_n(50) %>% select(bdate) %>% distinct() %>% nrow()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Засунем всё это в функцию \n",
    "# Аргументы: \n",
    "#     df - таблица \n",
    "#     n_ppl - сколько случайных людей должно оказаться в комнате \n",
    "#     n_obs - сколько генераций с выбором людей надо сделать \n",
    "#     col_name - какая колонка нас интересует\n",
    "\n",
    "prob_estimator <- function(df, n_ppl, n_obs, colname){\n",
    "    \n",
    "    m = 0\n",
    "    for(i in 1:n_obs){\n",
    "        k = df %>% sample_n(n_ppl) %>% select(colname) %>% distinct() %>% nrow()\n",
    "        if(k != n_ppl){\n",
    "            m = m + 1\n",
    "        }\n",
    "    }\n",
    "\n",
    "    return(m/n_obs)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# для 100 человек\n",
    "prob_estimator(df_dropna, 100, 1000, 'bdate')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.547"
      ],
      "text/latex": [
       "0.547"
      ],
      "text/markdown": [
       "0.547"
      ],
      "text/plain": [
       "[1] 0.547"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Посмотрим то же самое для 23 человек \n",
    "prob_estimator(df_dropna, 23, 1000, 'bdate')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вроде бы всё более-менее согласуется с теорией и вероятности получаются похожими на неё, хоть и немного другими. Попробуем позапускать эксперимент на разном числе людей в группе. Оценки будем строить на основе $1000$ наблюдений. На основе запусков составим следущую забавную табличку: \n",
    "\n",
    "\n",
    "| Людей в группе |Теоретическая вероятность|Эмпирическая вероятность|\n",
    "|----------------|-------------------------|------------------------|\n",
    "|10              |0.12                     | 0.13                   |\n",
    "|20              |0.41                     | 0.45                   |\n",
    "|30              |0.70                     | 0.71                   |\n",
    "|50              |0.97                     | 0.98                   |\n",
    "|100             |0.99                     | 1                      |\n",
    "\n",
    "Поосторожнее с идеей проверить правильной ли получилась табличка. Код для оценивания всех вероятностей в ней работает довольно долго. \n",
    "\n",
    "В конечном счёте наши оценки довольно похожи на цифры, полученные в теории. Парадокс дней рождений разрешён в нашу пользу. На самом деле неплохо было бы построить для каждой из долей доверительный интервалы и чисто формально проверить гипотезу о том, что каждая из долей совпадает с теоретической, но это мы оставим до будущих занятий. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__6.__ Попробуйте проделать ту же оценку отдельно для подмножества женщин и подмножества мужчин. Насколько оценки вероятностей разнятся? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.981"
      ],
      "text/latex": [
       "0.981"
      ],
      "text/markdown": [
       "0.981"
      ],
      "text/plain": [
       "[1] 0.981"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.971"
      ],
      "text/latex": [
       "0.971"
      ],
      "text/markdown": [
       "0.971"
      ],
      "text/plain": [
       "[1] 0.971"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_male = df_dropna %>% filter(sex == 2)\n",
    "df_female = df_dropna %>% filter(sex == 1)\n",
    "\n",
    "prob_estimator(df_male,   50, 1000, 'bdate')\n",
    "prob_estimator(df_female, 50, 1000, 'bdate')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.55"
      ],
      "text/latex": [
       "0.55"
      ],
      "text/markdown": [
       "0.55"
      ],
      "text/plain": [
       "[1] 0.55"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.55"
      ],
      "text/latex": [
       "0.55"
      ],
      "text/markdown": [
       "0.55"
      ],
      "text/plain": [
       "[1] 0.55"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_estimator(df_male,   23, 1000, 'bdate')\n",
    "prob_estimator(df_female, 23, 1000, 'bdate')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Оценки разнятся не то чтобы особо сильно. Опять же, было бы неплохо проверить гипотезу о равенстве долей для мужчин и женщин. Но это тоже остаётся на будущее.\n",
    "\n",
    "На самом деле мы с вами только что впервые попробовали вскрыть внутренности сундука, о котором мы говорили на прошлой паре, по итоговой выборке. Закон больших чисел в форме Бернулли (помните из лекций по терверу?) позволил нам оценить вероятность события на основе его частоты. Очень круто, когда математика разрешает тебе сделать что-нибудь клёвое. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__[3] Простая часть, решения которой в домашке прошло года нет__\n",
    "\n",
    "__1.__ Сколько в итоговой, прошедшей все фильтры из предыдущего пункта, выборке есть уникальных имён? Какое мужское имя самое популярное? Какое женское имя самое популярное? Постройте гистограмму для 30 самых популярных имён.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "119378"
      ],
      "text/latex": [
       "119378"
      ],
      "text/markdown": [
       "119378"
      ],
      "text/plain": [
       "[1] 119378"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# уникальных имён\n",
    "df_dropna %>% select(first_name) %>% distinct() %>% nrow()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "77704"
      ],
      "text/latex": [
       "77704"
      ],
      "text/markdown": [
       "77704"
      ],
      "text/plain": [
       "[1] 77704"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# из них мужские\n",
    "df_male %>% select(first_name) %>% distinct() %>% nrow()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "49248"
      ],
      "text/latex": [
       "49248"
      ],
      "text/markdown": [
       "49248"
      ],
      "text/plain": [
       "[1] 49248"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# из них женские\n",
    "df_female %>% select(first_name) %>% distinct() %>% nrow()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Будем делать вид, что Максим - Макс и т.п это разные имена. Мы пока не умеем исправлять такие вещи. Но в будущем обязательно научимся на каком-нибудь курсе по анализу текстов. :3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>first_name</th><th scope=col>count</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Иван     </td><td>19541    </td></tr>\n",
       "\t<tr><td>Евгений  </td><td>20313    </td></tr>\n",
       "\t<tr><td>Денис    </td><td>20865    </td></tr>\n",
       "\t<tr><td>Никита   </td><td>22458    </td></tr>\n",
       "\t<tr><td>Максим   </td><td>31290    </td></tr>\n",
       "\t<tr><td>Дмитрий  </td><td>32661    </td></tr>\n",
       "\t<tr><td>Алексей  </td><td>33392    </td></tr>\n",
       "\t<tr><td>Сергей   </td><td>43808    </td></tr>\n",
       "\t<tr><td>Андрей   </td><td>44452    </td></tr>\n",
       "\t<tr><td>Александр</td><td>57455    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " first\\_name & count\\\\\n",
       "\\hline\n",
       "\t Иван      & 19541    \\\\\n",
       "\t Евгений   & 20313    \\\\\n",
       "\t Денис     & 20865    \\\\\n",
       "\t Никита    & 22458    \\\\\n",
       "\t Максим    & 31290    \\\\\n",
       "\t Дмитрий   & 32661    \\\\\n",
       "\t Алексей   & 33392    \\\\\n",
       "\t Сергей    & 43808    \\\\\n",
       "\t Андрей    & 44452    \\\\\n",
       "\t Александр & 57455    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| first_name | count |\n",
       "|---|---|\n",
       "| Иван      | 19541     |\n",
       "| Евгений   | 20313     |\n",
       "| Денис     | 20865     |\n",
       "| Никита    | 22458     |\n",
       "| Максим    | 31290     |\n",
       "| Дмитрий   | 32661     |\n",
       "| Алексей   | 33392     |\n",
       "| Сергей    | 43808     |\n",
       "| Андрей    | 44452     |\n",
       "| Александр | 57455     |\n",
       "\n"
      ],
      "text/plain": [
       "   first_name count\n",
       "1  Иван       19541\n",
       "2  Евгений    20313\n",
       "3  Денис      20865\n",
       "4  Никита     22458\n",
       "5  Максим     31290\n",
       "6  Дмитрий    32661\n",
       "7  Алексей    33392\n",
       "8  Сергей     43808\n",
       "9  Андрей     44452\n",
       "10 Александр  57455"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "        # группировка по именам    для каждого считаем число    потом сортируем   топ внизу \n",
    "df_male %>% group_by(first_name) %>% summarise(count = n()) %>% arrange(count) %>% tail(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>first_name</th><th scope=col>count</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Мария    </td><td>22829    </td></tr>\n",
       "\t<tr><td>Виктория </td><td>23204    </td></tr>\n",
       "\t<tr><td>Ольга    </td><td>23805    </td></tr>\n",
       "\t<tr><td>Юлия     </td><td>24084    </td></tr>\n",
       "\t<tr><td>Ирина    </td><td>24522    </td></tr>\n",
       "\t<tr><td>Екатерина</td><td>24988    </td></tr>\n",
       "\t<tr><td>Анна     </td><td>25332    </td></tr>\n",
       "\t<tr><td>Татьяна  </td><td>26215    </td></tr>\n",
       "\t<tr><td>Елена    </td><td>30588    </td></tr>\n",
       "\t<tr><td>Анастасия</td><td>37298    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " first\\_name & count\\\\\n",
       "\\hline\n",
       "\t Мария     & 22829    \\\\\n",
       "\t Виктория  & 23204    \\\\\n",
       "\t Ольга     & 23805    \\\\\n",
       "\t Юлия      & 24084    \\\\\n",
       "\t Ирина     & 24522    \\\\\n",
       "\t Екатерина & 24988    \\\\\n",
       "\t Анна      & 25332    \\\\\n",
       "\t Татьяна   & 26215    \\\\\n",
       "\t Елена     & 30588    \\\\\n",
       "\t Анастасия & 37298    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| first_name | count |\n",
       "|---|---|\n",
       "| Мария     | 22829     |\n",
       "| Виктория  | 23204     |\n",
       "| Ольга     | 23805     |\n",
       "| Юлия      | 24084     |\n",
       "| Ирина     | 24522     |\n",
       "| Екатерина | 24988     |\n",
       "| Анна      | 25332     |\n",
       "| Татьяна   | 26215     |\n",
       "| Елена     | 30588     |\n",
       "| Анастасия | 37298     |\n",
       "\n"
      ],
      "text/plain": [
       "   first_name count\n",
       "1  Мария      22829\n",
       "2  Виктория   23204\n",
       "3  Ольга      23805\n",
       "4  Юлия       24084\n",
       "5  Ирина      24522\n",
       "6  Екатерина  24988\n",
       "7  Анна       25332\n",
       "8  Татьяна    26215\n",
       "9  Елена      30588\n",
       "10 Анастасия  37298"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "         # группировка по именам    для каждого считаем число    потом сортируем   топ внизу \n",
    "df_female %>% group_by(first_name) %>% summarise(count = n()) %>% arrange(count) %>% tail(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Оцените вероятность того, что в группе из 50 произвольных людей найдутся хотя бы двое с одинаковыми именами. Она оказалась больше или меньше, чем в пункте про дни рождения?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.998"
      ],
      "text/latex": [
       "0.998"
      ],
      "text/markdown": [
       "0.998"
      ],
      "text/plain": [
       "[1] 0.998"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# используем ту же самую функцию,но меняем имя колонки \n",
    "prob_estimator(df_dropna, 50, 1000, 'first_name')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ Разнятся ли эти вероятности между мужчинами и женщинами? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# используем ту же самую функцию, но меняем имя колонки и имя таблиц\n",
    "prob_estimator(df_male, 50, 1000, 'first_name')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_estimator(df_female, 50, 1000, 'first_name')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2] Задачка 16\n",
    "\n",
    "Предположим, что рост $100$ второкурсников распределен нормально со средним $175$ см и стандартным отклонением $8$ см. Если сделать выборку в $5$ человек и посчитать по ней средний рост $\\bar x$, то какими будут $E(\\bar x)$ и $Var(\\bar x)$, если выборки делаются \n",
    "\t \n",
    "__а)__ с возвращением, то есть наблюдения $x_1, \\ldots, x_5$ производятся независимо;\n",
    "\t \t\n",
    "__б)__ без возвращения, то есть наблюдения зависимы.\n",
    "\n",
    "Решите задачу вручную и проверьте своё решение с помощью симуляций."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "175.530778716378"
      ],
      "text/latex": [
       "175.530778716378"
      ],
      "text/markdown": [
       "175.530778716378"
      ],
      "text/plain": [
       "[1] 175.5308"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "8.06896888495762"
      ],
      "text/latex": [
       "8.06896888495762"
      ],
      "text/markdown": [
       "8.06896888495762"
      ],
      "text/plain": [
       "[1] 8.068969"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(40)\n",
    "x <- rnorm(100, mean=175, sd=8)\n",
    "\n",
    "# Нужно сгенерить так, чтобы значения были близки к теории, \n",
    "# иначе дальнейшие сэмплы будут далеки от расчётов на бумажке\n",
    "mean(x)\n",
    "sd(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Cценарий 1: отбор без повторения.__\n",
    "\n",
    "Тут ничего особенного. Всё ровно как в лекциях. \n",
    "\n",
    "\\begin{equation} \n",
    "\\begin{aligned} \n",
    "& E(\\bar x) = \\frac{1}{n} \\sum_{i=1}^n E(x_i) = E(x_i) = 175 \\\\ \n",
    "& Var(\\bar x) = \\frac{1}{n^2} \\sum_{i=1}^n Var(x_i) = \\frac{Var(x_i)}{n} = \\frac{8^2}{5} = 12.8\n",
    "\\end{aligned}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "175.532200249253"
      ],
      "text/latex": [
       "175.532200249253"
      ],
      "text/markdown": [
       "175.532200249253"
      ],
      "text/plain": [
       "[1] 175.5322"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "12.8811143326075"
      ],
      "text/latex": [
       "12.8811143326075"
      ],
      "text/markdown": [
       "12.8811143326075"
      ],
      "text/plain": [
       "[1] 12.88111"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Делаем n_obs выборок с возвращением\n",
    "n_obs = 10^6\n",
    "\n",
    "mean_1 = rep(0, n_obs)\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    sample_1 = sample(x, size=5, replace = TRUE)\n",
    "    mean_1[i] = mean(sample_1)\n",
    "    }\n",
    "\n",
    "mean(mean_1)\n",
    "var(mean_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Cценарий 2: отбор c повторением.__\n",
    "\n",
    "Тут происходит несчастье. Раньше иы всегда пользовались тем, что выборка независимо одинаково распределена. Тут это неправда. Каждое наблюдение, которое мы вытягиваем не может быть вытянуто второй раз. Это влияет на следущее наблюдение. Между случайными величинами $X_1, \\ldots, X_n$ возникает связь. Давайте посмотрим что из-за этой связи произойдёт с дисперсией среднего. \n",
    "\n",
    "\\begin{equation} \n",
    "\\begin{aligned} \n",
    "& E(\\bar x) = \\frac{1}{n} \\sum_{i=1}^n E(x_i) = E(x_i) = 175 \\\\ \n",
    "& Var(\\bar x) = \\frac{n \\cdot Var(x_i) + 2 \\cdot C_n^2 \\cdot Cov(x_i,x_j)}{n^2}\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\n",
    "Ковариацию можно найти, вспомнив что сумма случайностей неслучайна, как в семинарской задачке с кубиком. У нас всего $100$ второкурсников. Это размер нашей генеральной совокупности. То есть $X_1 + \\ldots + X_{100}$ всегда будет какой-то константой. Ковариация случайной величины и константы это ноль. Получаем, что: \n",
    "\n",
    "\\begin{equation} \n",
    "\\begin{aligned} \n",
    "&Cov(X_1, X_1 + \\ldots + X_{100}) = 0 \\\\\n",
    "&Cov(X_1, X_1) + Cov(X_1,X_2) + \\ldots + Cov(X_1, X_{100}) = 0 \\\\\n",
    "&Var(X_1) + (n-1) \\cdot Cov(X_1,X_2) = 0 \\\\\n",
    "&Cov(X_1,X_2) = -\\frac{Var(X_1)}{n-1}\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\n",
    "Добиваем задачку. \n",
    "\n",
    "$$\n",
    "Var(\\bar x) = \\frac{n \\cdot Var(x_i) + 2 \\cdot C_n^2 \\cdot Cov(x_i,x_j)}{n^2}  = \\frac{5 \\cdot 8^2 + 5 \\cdot 4 \\cdot (- ^64/_{99})}{25} = 12.28 \n",
    "$$\n",
    "\n",
    "Получается, что при повторных выборках дисперсия меньше. Давайте сгенерируем это добро, а после обсудим что это всё означает с теоретической точки зрения. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "175.534453269664"
      ],
      "text/latex": [
       "175.534453269664"
      ],
      "text/markdown": [
       "175.534453269664"
      ],
      "text/plain": [
       "[1] 175.5345"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "12.3786128535239"
      ],
      "text/latex": [
       "12.3786128535239"
      ],
      "text/markdown": [
       "12.3786128535239"
      ],
      "text/plain": [
       "[1] 12.37861"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Делаем n_obs выборок без возвращения\n",
    "mean_2 = rep(0, n_obs)\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    sample_2 = sample(x, size=5, replace = FALSE)\n",
    "    mean_2[i] = mean(sample_2)\n",
    "    }\n",
    "\n",
    "mean(mean_2)\n",
    "var(mean_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Мораль:__  В матстате, перед построением оценки или доверительного интервала, мы постоянно предполагаем, что наши наблюдения $x_1, \\ldots, x_n$ одинаково и независимо распределены. В реальности это может быть не так. В задачке выше при большой выборке ковариация между соседними наблюдениями будет ничтожно маленькой и мы можем смело пренебрегать той маленькой взаимосвязью между наблюдениями, так как она никак не скажется на итоговых результатах. \n",
    "\n",
    "А, что если выборка очень маленькая? Мало ли ковариация будет положительной, а дисперсия большой... Тогда все предпосылке катятся в пекло.  Эта задачка именно об этом. Попытайтесь придумать ситуацию, когда в выборке между наблюдениями резко возникает зависимость, причём ещё и положительная. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2]  Задачка 17\n",
    "\n",
    "У Маши 30 разных пар туфель. И она говорит, что мало! Пёс Шарик утащил без разбору на левые и правые $17$ туфель. Какова вероятность того, что у Маши останется ровно $13$ полных пар? Пусть случайная величина $X$ — число полных пар у Маши. Найдите $E(X)$ и $Var(X)$.\n",
    "\n",
    "Решите задачу вручную и проверьте своё решение с помощью симуляций."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Найдём вероятность того, что у Маши останется 13 полных пар.__ Шарик тащит $17$ туфелек. Всего вариантов стащить туфли у него $C_{60}^{17}$, потому что всего у Маши туфелек $60$ штук. Чтобы у Маши осталось ровно $13$ пар, остальные $17$ Шарик должен подпортить. Значит он сначала выбирает $17$ пар из $30$, а после в каждой паре выбирает какую туфельку покорёжить. Получаем $C_{30}^{17} \\cdot 2^{17}$ способов. Итого:\n",
    "\n",
    "$$\n",
    "P(A) = \\frac{C_{30}^{17} \\cdot 2^{17}}{C_{60}^{17}} \\approx 0.04 \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Найдём теперь математическое ожидание числа оставшихся пар.__  Пусть $X$ - число полных пар у Маши. Разобьём эту случайную величину в сумму простейших $X = X_1 + \\ldots + X_{30}$, где \n",
    "\n",
    "\\begin{equation*}\n",
    "X_i = \n",
    " \\begin{cases}\n",
    "   1, &\\text{если i-ая пара осталась}\\\\\n",
    "   0, &\\text{если i-ая пара не осталась}\n",
    " \\end{cases}\n",
    "\\end{equation*}\n",
    "\n",
    "Найдём $P(X_i = 1)$. Для этого нужно, чтобы Шарик точно не трогал нашу пару, но трогал остальные. Это может произойти $C_{58}^{17}$ способами, то есть \n",
    "\n",
    "$$\n",
    "P(X_i = 1) = \\frac{C_{58}^{17}}{C_{60}^{17}} \\approx 0.51\n",
    "$$\n",
    "\n",
    "Получается, что \n",
    "\n",
    "$$\n",
    "E(X) = E(X_1) + \\ldots + E(X_{30}) = 30 \\cdot E(X_i) = 30 \\cdot P(X_i = 1) \\approx 15.3\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Теперь найдём дисперсию числа оставшихся пар.__\n",
    "\n",
    "$$\n",
    "Var(X) = Var(X_1 +....+ X_{30}) = Var(X_1) +....+ Var(X_{30}) + 2Cov(X_1,X_2) +.....+2Cov(X_{29},X_{30}) = 30 \\cdot Var(X1) + 2 \\cdot C_{30}^{2} \\cdot Cov(X_1,X_2)\n",
    "$$\n",
    "\n",
    "Найдём дисперсию $X_1$. \n",
    "\n",
    "$$\n",
    "Var(X_1) = E(X_1^2) - E(X_1)^2 = P(X_1 = 1) - (P(X_1 = 1))^2 \\approx  0.249\n",
    "$$\n",
    "\n",
    "Теперь нам нужно найти ковариацию. Для этого нам понадобится $E(X_1 \\cdot X_2) = P(X_1 = 1, X_2 = 1)$. Чтобы ни первая, ни вторая пара не оказались у Шарика, он должен вынести какие-то другие пары, получаетcя, что \n",
    "\n",
    "$$\n",
    "E(X_1 \\cdot X_2) = P(X_1 = 1, X_2 = 1) = \\frac{C_{56}^{17}}{C_{60}^{17}}\n",
    "$$\n",
    "\n",
    "Выходит, что \n",
    "\n",
    "$$\n",
    "Cov(X_1, X_2) = E(X_1 \\cdot X_2) - E(X_1) \\cdot E(X_2) \\approx -0.0071.\n",
    "$$\n",
    "\n",
    "В итоге получаем, что \n",
    "\n",
    "$$\n",
    "Var(X) = 30 \\cdot 0.038 - 2 \\cdot C_{30}^2 \\cdot 0.0072 \\approx 1.24\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Ну а теперь симуляции.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_obs <- 10^6\n",
    "\n",
    "# сколько и когда оставалось у Маши \n",
    "masha <- rep(0, n_obs)\n",
    "\n",
    "for(j in 1:n_obs){\n",
    "    # тут лежат туфли, первые 30 индексов - левые, вторые 30 - правые \n",
    "    # 0 означает, что туфля у Маши, 1 что у Шарика \n",
    "    shoes <- rep(0, 60) \n",
    "    \n",
    "    # Шарик делает свой ход\n",
    "    ind <- sample(1:60, size = 17, replace = FALSE)\n",
    "    shoes[ind] <- 1 # пометим единичкое все туфли, которые Шарик украл \n",
    "    \n",
    "    # смотрим какие туфли в одинаковом состоянии\n",
    "    both <- (shoes[1:30] == shoes[31:60])\n",
    "    \n",
    "    # при этом они должны быть у Маши \n",
    "    masha[j] = sum(shoes[1:30][both] != 1)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.040365"
      ],
      "text/latex": [
       "0.040365"
      ],
      "text/markdown": [
       "0.040365"
      ],
      "text/plain": [
       "[1] 0.040365"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "15.305673"
      ],
      "text/latex": [
       "15.305673"
      ],
      "text/markdown": [
       "15.305673"
      ],
      "text/plain": [
       "[1] 15.30567"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1.23578025285125"
      ],
      "text/latex": [
       "1.23578025285125"
      ],
      "text/markdown": [
       "1.23578025285125"
      ],
      "text/plain": [
       "[1] 1.23578"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(masha==13)  # вероятность, что у Маши останется ровно 13 пар\n",
    "mean(masha)      # среднее число пар у Маши\n",
    "var(masha)       # дисперсия числа пар "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [3]  Задачка 18 \n",
    "\n",
    "ЛСП постоянно подбрасывает монетку и орёт \"орёл - решка\". \n",
    "\t\n",
    "* Когда выпадает $OPOP$,  ЛСП успокаивается и ныряет в ванну. Сколько в среднем раз ему нужно подбросить монетку, чтобы нырнуть?\n",
    "* Когда выпадает комбинация $POPP$, ЛСП просто теряется в мире цифрового глянца. Сколько в среднем раз ему нужно подбросить монетку, чтобы потеряться? \n",
    "* Пусть теперь ЛСП хочет получить любую из этих двух комбинаций. Какова вероятность того, что ЛСП потеряется, а не нырнёт, то есть что $POPP$ появится раньше,  чем $OPOP$? \n",
    "\n",
    "Решите задачку вручную и проверьте своё решение с помощью симуляций."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Решение:__ \n",
    "\n",
    "* Нарисуем граф состояний для этой игры. Искать среднее число ходов будем методом первого шага. \n",
    "\n",
    "Такс. Мы подкинули монету. Выпал либо орел, либо решка. Если решка, то для нас ничего не поменялось и мы как будто бы в начале игры. Если орёл, то мы накопили одну полезную букву. Дальше монетку подкидываем второй раз. Есл орёл, то мы ничего не накопили, остаёмся в той же вершине. Если решка, то мы накопили вторую полезную букву и получили $OP$. \n",
    "\n",
    "Снова подкинули монетку. Если выпала решка, то все наши накопления пошли на смарку и мы откатились в начало игры. Если выпал орёл, мы получили $OPO$. Дальше снова кидаем монетку и илбо получаем $OPOP$, либо выпадает орёл, который портит наши накопления и мы откатываемся в состояние $O$, потому что мы получаем $OPOO$. И самое полезное для нас это первый орёл, который поможет начать копить историю заново. Граф готов. \n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/HW/images/lsp_1.png\" width=\"300\"> \n",
    "\n",
    "\n",
    "Теперь составим систему уравнений. Пусть $e_i$ - среднее число шагов до попадания в вершину $OPOP$ из вершины $i$. Пусть вершина $O$ - вторая, $OP$ - третья и так далее. Делаем шаг из первой вершины. \n",
    "\n",
    "$$\n",
    "e_1 = \\frac{1}{2} \\cdot (1 + e_1) + \\frac{1}{2} \\cdot (1 + e_2).\n",
    "$$\n",
    "\n",
    "Если выпал орёл, мы сделали один шаг и остались в $1$. Если выпала решка, мы сделали один шаг и попали в $2$. Уравнение для первой вершины готово, нужно ещё три. Составляем их по аналогии. \n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "e_1 =& \\frac{1}{2} \\cdot (1 + e_1) + \\frac{1}{2} \\cdot (1 + e_2) \\\\ \n",
    "e_2 =& \\frac{1}{2} \\cdot (1 + e_2) + \\frac{1}{2} \\cdot (1 + e_3) \\\\ \n",
    "e_3 =& \\frac{1}{2} \\cdot (1 + e_1) + \\frac{1}{2} \\cdot (1 + e_4) \\\\ \n",
    "e_4 =& \\frac{1}{2} \\cdot (1 + e_2) + \\frac{1}{2} \\cdot 1  \\\\ \n",
    "\\end{cases} \n",
    "$$\n",
    "\n",
    "Решаем систему, получаем, что $e_1 = 20$. Теперь симуляции. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "7"
      ],
      "text/latex": [
       "7"
      ],
      "text/markdown": [
       "7"
      ],
      "text/plain": [
       "[1] 7"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Сначала код для одной симуляции! \n",
    "# Пущай 1 - орёл, 0 - решка, мы хотим 1010 \n",
    "\n",
    "k = 4 # сколько сделано шагов\n",
    "x = sample(x = c(1,0), size = 4, replace=TRUE)\n",
    "\n",
    "# пока последние 4 символа не такие как нам надо, подбрасываем монетку\n",
    "while(sum(x[(k-3):k] == c(1,0,1,0)) !=4 ){\n",
    "    x = append(x, sample(x = c(1,0), size = 1))\n",
    "    k = k + 1\n",
    "}\n",
    "\n",
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Теперь повторяем симуляцию много раза \n",
    "n_obs = 10^5\n",
    "\n",
    "T <- rep(0, n_obs)\n",
    "for(i in 1:n_obs){\n",
    "    k = 4 # сколько сделано шагов\n",
    "    x = sample(x = c(1,0), size = 4, replace=TRUE)\n",
    "\n",
    "    # пока последние 4 символа не такие как нам надо, подбрасываем монетку\n",
    "    while(sum(x[(k-3):k] == c(1,0,1,0)) !=4 ){\n",
    "        x = append(x, sample(x = c(1,0), size = 1))\n",
    "        k = k + 1\n",
    "    }\n",
    "    T[i] = k\n",
    "}\n",
    "\n",
    "# P.S. Осторожнее с while! Случайно можно впасть в вечный цикл..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "20.02384"
      ],
      "text/latex": [
       "20.02384"
      ],
      "text/markdown": [
       "20.02384"
      ],
      "text/plain": [
       "[1] 20.02384"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAYAAACYBpIxAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\n6zH1JUCAAAECBAgQIECAAIFCAv8PvQpRT7aeR50AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(T) \n",
    "qplot(T, bins=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Снова рисуем граф состояний. \n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/HW/images/lsp_2.png\" width=\"300\"> \n",
    "\n",
    "По аналогии с тем, что было в предыдущем пункте, составляем систему и решаем её. \n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "e_1 =& \\frac{1}{2} \\cdot (1 + e_1) + \\frac{1}{2} \\cdot (1 + e_2) \\\\ \n",
    "e_2 =& \\frac{1}{2} \\cdot (1 + e_2) + \\frac{1}{2} \\cdot (1 + e_3) \\\\ \n",
    "e_3 =& \\frac{1}{2} \\cdot (1 + e_1) + \\frac{1}{2} \\cdot (1 + e_4) \\\\ \n",
    "e_4 =& \\frac{1}{2} \\cdot (1 + e_3) + \\frac{1}{2} \\cdot 1  \\\\ \n",
    "\\end{cases} \n",
    "$$\n",
    "\n",
    "Получаем, что $e_1 = 18$. Обратите внимание, что разница между двумя графами в четвёртом уравнении. Из-за этого разные результаты. Пункт с симуляциями пропустим, так как они один в один такие же, как в предыдущем пункте, но надо последовательность прсото заменить на другую. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Ну и ещё разок нарисуем граф состояний. \n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/HW/images/lsp_3.png\" width=\"450\"> \n",
    "\n",
    "Тут нас уже интересуют не математические ожидания, а вероятности. Судя \n",
    "\n",
    "\n",
    "Пусть $p_i$ - вероятность оказаться в $OPOP$, находясь при этом в вершине $i$. Составляем систему уравнений: \n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "p_1 = \\frac{1}{2} \\cdot p_2 + \\frac{1}{2} \\cdot p_3 \\\\ \n",
    "p_2 = \\frac{1}{2} \\cdot p_2 + \\frac{1}{2} \\cdot p_4 \\\\ \n",
    "p_3 = \\frac{1}{2} \\cdot p_5 + \\frac{1}{2} \\cdot p_3 \\\\ \n",
    "p_4 = \\frac{1}{2} \\cdot p_6 + \\frac{1}{2} \\cdot p_3 \\\\\n",
    "p_5 = \\frac{1}{2} \\cdot p_2 + \\frac{1}{2} \\cdot p_7 \\\\\n",
    "p_6 = \\frac{1}{2} \\cdot p_2 + \\frac{1}{2} \\cdot 1 \\\\ \n",
    "p_7 = \\frac{1}{2} \\cdot p_6 + \\frac{1}{2} \\cdot 0 \\\\ \n",
    "\\end{cases} \n",
    "$$\n",
    "\n",
    "Решаем систему, получаем что $P(OPOP) = \\frac{9}{14}.$ При этом $P(POPP) = 1 - P(OPOP) = \\frac{5}{14}$, так как игра не будет длиться вечно.  Теперь симуляции. Повторим код из первой симуляции и будем следить за появлением двух последовательностей. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.6428"
      ],
      "text/latex": [
       "0.6428"
      ],
      "text/markdown": [
       "0.6428"
      ],
      "text/plain": [
       "[1] 0.6428"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Теперь повторяем симуляцию много раза \n",
    "n_obs = 10^4\n",
    "\n",
    "m <- 0 # счётчик для ОРОР\n",
    "for(i in 1:n_obs){\n",
    "    k = 4 # сколько сделано шагов\n",
    "    x = sample(x = c(1,0), size = 4, replace=TRUE)\n",
    "    \n",
    "    # проверка того, что произошло в первые шаги (иначе оценка сильно ниже!!!)\n",
    "    if(sum(x[(k-3):k] == c(1,0,1,0)) == 4){\n",
    "        m = m + 1\n",
    "    }\n",
    "\n",
    "    # пока последние 4 символа не такие как нам надо, подбрасываем монетку\n",
    "    while((sum(x[(k-3):k] == c(1,0,1,0)) !=4)&(sum(x[(k-3):k] == c(0,1,0,0)) !=4)){\n",
    "        x = append(x, sample(x = c(1,0), size = 1))\n",
    "        k = k + 1\n",
    "        if(sum(x[(k-3):k] == c(1,0,1,0)) == 4){\n",
    "            m = m + 1\n",
    "        }\n",
    "    }\n",
    "}\n",
    "\n",
    "m/n_obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.642857142857143"
      ],
      "text/latex": [
       "0.642857142857143"
      ],
      "text/markdown": [
       "0.642857142857143"
      ],
      "text/plain": [
       "[1] 0.6428571"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "9/14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Мораль:__ в методе первого шага обычно просто достаточно понять как именно выглядит рекурентная связь внутри нашего графа. И задачка сразу же раскалывается :) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [2] Задачка 19\n",
    "\n",
    "Решите задачки вручную: \n",
    "\n",
    "* $k$ различных космонавтов собираются высадиться на $m$ различных планет. Каждый космонавт выбирает себе планету независимо и равновероятно. Пусть $X$ — количество планет, на которые никто не высадился. Найдите $E(X)$.\n",
    "\n",
    "* В ряд стоят $n$ гномов. Издали на них смотрит дракон. Гномы разной высоты. Сколько в среднем гномов видит дракон? Какова дисперсия числа увиденных гномов?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Решение:__ \n",
    "\n",
    "* Сначала про космонавтов. Пусть $k$ - число космонавтов, а $m$ - число различных планет. Построим случайную величину $X$ - число планет, на которых никто не высадился. Тогда $X = X_1 + \\ldots + X_m$.  Случайная величина $X_i$ будет принимать значение $1$, если на $i$-ую планету никто не высадился и $0$, если на $i-$ую планету кто-то высадился. Найдём вероятность того, что $X_i = 1$. На нашей планете никого быть не должно. Все должны быть на чужой. Значит \n",
    "\n",
    "$$\n",
    "P(X_i = 1) = \\left(\\frac{m-1}{m} \\right)^k.\n",
    "$$\n",
    "\n",
    "Мы готовы найти итоговый ответ: \n",
    "\n",
    "$$\n",
    "E(X) = E(X_1 + \\ldots + X_m) = E(X_1) + \\ldots + E(X_m) = m \\cdot E(X_i) = m \\cdot P(X_i = 1) = m \\cdot \\left(\\frac{m-1}{m} \\right)^k.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Теперь про гномов. Пусть $n$ - число гномов. Случайная величина $X$ - число тех гномов, которых видит дракон. Введём случайную величину $X_i$ по следующему правилу: \n",
    "\n",
    "$$\n",
    "\\begin{equation*}\n",
    "X_i = \n",
    " \\begin{cases}\n",
    "   1, &\\text{если дракон увидел i-го гнома по порядку}\\\\\n",
    "   0, &\\text{если не увидел}\n",
    " \\end{cases}\n",
    "\\end{equation*}\n",
    "$$\n",
    "\n",
    "Какова вероятность того, что дракон увидит самого мелкого гнома? Коненчо же, $P(X_1 = 1) = \\frac{(n-1)!}{n!} = \\frac{1}{n}$. Если он стоит первым, его видно. Иначе нет. Какова вероятность того, что дракон увидит предпоследнего по высоте гнома? Ну либо он до мелкого, либо после (но тогда оба в начале очереди). Остальные двигаются как угодно. Получаем, что $P(X_2 = 1) = \\frac{(n-2)!}{n!} + \\frac{(n-1)!}{n!} = \\frac{1}{n-1}$. По аналогии получаем остальные вероятности. Выходит, что \n",
    "\n",
    "$$\n",
    "E(X) = E(X_1) + \\ldots + E(X_n) = \\frac{1}{n}  + \\ldots + \\frac{1}{3} + \\frac{1}{2} + 1.\n",
    "$$\n",
    "\n",
    "Теперь дисперсия. Случайные величны $X_i$ и $X_j$ независимы. Например, возьмём первых двух гномов. Пусть $X_2 = 1$. Даёт ли это нам информацию о том, что происходит с первым гномом? Видит ли его дракон? \n",
    "\n",
    "$$\n",
    "P(X_1 = 1 \\mid X_2 = 1) = \\frac{P(X_1 = 1 \\cap X_2 = 1)}{P(X_2 = 1)} = \\frac{\\frac{(n-2)!}{n!}}{\\frac{1}{(n-1)}} = \\frac{1}{n} = P(X_1 = 1). \n",
    "$$\n",
    "\n",
    "Аналогичные рассуждения можно построить для любых $i,j$. Выходит, что случайные величины независимые. Осталось только заметить, что $E(X_i^2) = E(X_i)$ и получить, что \n",
    "\n",
    "$$\n",
    "Var(X_k) = E(X_k) - E(X_k)^2 = \\frac{1}{k} - \\frac{1}{k^2}.\n",
    "$$\n",
    "\n",
    "Тогда \n",
    "\n",
    "$$\n",
    " Var(X) = \\sum\\limits_{k=1}^{n}(\\frac{1}{k} - \\frac{1}{k^2})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [4]  Задачка 20\n",
    "\n",
    "Илье Муромцу предстоит дорога к камню. И от камня начинаются ещё три дороги. Каждая из тех дорог снова оканчивается камнем. И от каждого камня начинаются ещё три дороги. И каждые три дороги кончаются камнем.... И так далее до бесконечности. На каждой дороге можно встретить живущего на ней трёхголового Змея Горыныча с вероятностью (хм, вы не поверите!) одна третья. Какова вероятность того, что у Ильи Муромца существует возможность пройти свой бесконечный жизненный путь, так ни разу и не встретив Змея Горыныча? \n",
    "\n",
    "Решите задачу вручную и проверьте своё решение с помощью симуляции. \n",
    "\n",
    "**Hint:** наверное, лучше всего делать симуляции с помощью рекурсивной функции на походы Ильи Муромца."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Решение:__ Эта задачка была сложной. Для начала нарисуем граф состояний и попытаемся понять как именно в нём устроен метод первого шага. \n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/HW/images/stone.png\" width=\"450\"> \n",
    "\n",
    "Обозначим буквой $p$ вероятность того, что существует бесконечный жизненный путь из нашей стартовой точки. \n",
    "Проходим по первой дороге. Вероятность, что нас не сожрут равна $1 - \\frac{1}{3}$. Дальше нам надо пойти по одной из трёх дорог. Каждая из них ведет к новому камню. Получается, что мы оказались в той же самой ситуации, в которой были в самом начале. Вероятность выжить, путешествую по каждой из трёх дорог равна $p$. \n",
    "\n",
    "Нас интересует наличие дороги хотябы по одному из трёх путей. Чтобы получить вероятность этого, перейдём к противоположному событию. Дважды. С вероятнотью $(1 - p)^3$ ни по одной дороге жизненного пути нет. С вероятностью $1 - (1 - p)^3$ хотя бы по одной дороге он есть. Получается уравнение\n",
    "\n",
    "$$\n",
    "p = \\frac{1}{3} \\cdot 0 + \\frac{2}{3} \\cdot( 1 - (1 - p)^3 ) = \\frac{2}{3} \\cdot (1 - (1 - p)^3)\n",
    "$$\n",
    "\n",
    "Немного поколдуем надо ним \n",
    "\n",
    "$$\n",
    "\\begin{aligned} \n",
    "p &= \\frac{2}{3} \\cdot (1 - (1 - p)^3) \\\\\n",
    "1-p &= 1 - \\frac{2}{3} \\cdot (1 - (1 - p)^3) \\\\\n",
    "1-p &= \\frac{1}{3} + \\frac{2}{3} (1-p)^3 \\\\\n",
    "t &= \\frac{1}{3} + \\frac{2}{3} t^3 \\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "В итоге мы получили кубическое уравнение\n",
    "\n",
    "$$\n",
    "2t^3 - 3t + 1 = 0.\n",
    "$$\n",
    "\n",
    "Как мы решали такие уравнения на линале? Просто угадывали первый корень и сводили всё к квадратному. Сразу видно, что один из корней $t = 1$. Поделим уравнение на $(t - 1)$. Получим $(t-1) \\cdot (2t^2 + 2t - 1) = 0$. Решаем квадратное уравнение, получаем корни $\\frac{1}{2} \\cdot (-1 \\pm \\sqrt{3})$. Вспоминаем, что $t = 1 - p$. Получаем три решения: \n",
    "\n",
    "$$ \n",
    "p = 0, \\quad p = \\frac{1}{2} \\cdot (3 \\pm \\sqrt{3})\n",
    "$$\n",
    "\n",
    "Одно из решений больше $1$ и не подходит по ограничениям на вероятность. Решение с нулём скучное. Оно точно не будет правдой. При желании можно доказать это [(страница 39 культурного кода).](https://github.com/bdemeshev/probability_dna/raw/master/probability_dna.pdf)  Для этого просто нужно осознать, что в краевой ситуации, когда Змеев Горынычей нет, нелевое решение будет давать неадекватный результат. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.633974596215561"
      ],
      "text/latex": [
       "0.633974596215561"
      ],
      "text/markdown": [
       "0.633974596215561"
      ],
      "text/plain": [
       "[1] 0.6339746"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(3 - sqrt(3))/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь симуляции. Ключевая проблема для симуляций заключается в том, что Илья Муромец должен найти бесконечный жизненный путь. У нас нет столько компьютерных мощностей, чтобы бесконечные пути симулировать. Нам придётся доходить до какого-то определённого периода (например, сотого или тысячного) и начиная с него говорить, что Илья вышел на бесконечный путь. По-другому никак не выйдет. Давайте попробуем написать функцию, которая помогает Илье ходить по его жизненным дорогам. Можно сделать это с рекурсией, можно без. Мы попробуем с рекурсией. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0"
      ],
      "text/latex": [
       "0"
      ],
      "text/markdown": [
       "0"
      ],
      "text/plain": [
       "[1] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_recursion <- 5 # ограничение на количество походов Ильи вглубь\n",
    "\n",
    "life_path <- function(stone_number){\n",
    "    stone_number = stone_number + 1 # продвинулись на один камень вглубь\n",
    "    \n",
    "    # идём по нашим трём дорогам, если ещё не превысили максимальный путь \n",
    "    exist = TRUE\n",
    "    if(stone_number < max_recursion){\n",
    "        path_1 <- life_path(stone_number)\n",
    "        path_2 <- life_path(stone_number)\n",
    "        path_3 <- life_path(stone_number)  \n",
    "        \n",
    "        # если путь существует то хотя бы одна функция выдаст 1\n",
    "        exist <- (path_1 == 1)|(path_2 == 1)|(path_3 == 1)\n",
    "    }\n",
    "    \n",
    "    # сгенерировали змея горыныча на нашей дороге\n",
    "    x <- sample(size = 1, x = c(0,1), prob = c(2/3,1/3), replace = TRUE)\n",
    "    \n",
    "    if((x == 1)|(exist == FALSE)){\n",
    "        return(0)\n",
    "    } else {\n",
    "        return(1)\n",
    "    }    \n",
    "}\n",
    "\n",
    "life_path(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.6396"
      ],
      "text/latex": [
       "0.6396"
      ],
      "text/markdown": [
       "0.6396"
      ],
      "text/plain": [
       "[1] 0.6396"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs <- 10^4\n",
    "\n",
    "# сюда записываем ответ на вопрос \"а есть ли путь?\"\n",
    "ilusha <- rep(0, n_obs)\n",
    "\n",
    "# пошли симуляции\n",
    "for(i in 1:n_obs){\n",
    "    ilusha[i] <- life_path(0)\n",
    "}\n",
    "\n",
    "# даже при ограничении в глубине в 5 походов, получаем точность в два знака =)\n",
    "mean(ilusha) # вероятность того, что путь существует "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. [40+] Кит-рисёрчер\n",
    "\n",
    "**Добро пожаловать в Кита. Кит — это большая рисёрчерская задача с огромным количеством вопросов. В ките есть как ручные вопросы, так и вопросы для симуляций. За каждый вопрос даётся какое-то количество баллов. В каких-то вопросах требуется решить задачу руками на бумажке. В каких-то вопросах требуется произвести симуляцию в R. Продвинтесь в своём рисёрче над этим китом как можно глубже и срубите куш из баллов.** \n",
    "\n",
    "**Частично решение этого кита можно найти в логах предыдущего года. Если на вас нападёт отчаяние, можете заглянуть в них.** "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Эконом играет в киллера! Всего участие в игре принимает $100$ человек. Краткие правила игры: \n",
    "\n",
    "1. Каждый игрок одновременно и убийца и жертва. \n",
    "2. Игроку даётся конверт, в котором лежит имя человека, которого он должен убить. \n",
    "3. Сам игрок также находится у кого-то в конверте. Нужно не допустить своей смерти. \n",
    "4. Чтобы убить другого игрока, надо оказаться с ним наедине и застрелить из пальца. \n",
    "5. Жертва убитого становится новой жертвой игрока. \n",
    "6. Побеждает тот, кто совершит наибольшее число убийств. \n",
    "\n",
    "Организаторы игры сразу же столкнулись с несколькими проблемами. Первая проблема - это __суицидники.__ Если Максиму в конверте попался Максим, то Максим должен убить сам себя. Он - суицидник.  В такой ситуации организаторам придётся поменять конверт. Хотелось бы, чтобы подобных ситуаций было как можно меньше.\n",
    "\n",
    "**a)[1]** Какова вероятность, что суицидником окажется именно Максим? Найдите эту вероятность руками. \n",
    "\n",
    "__Ответ:__ Всего раздач конвертов может быть $n!$, вариантов, когда в конверте у Максима именно он, $(n-1)!$. Значит вероятность суицида для Максима $\\frac{1}{n}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**б) [1]** Оцените с помощью симуляций вероятность того, что хотя бы один человек получит в конверте сам себя."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.632123"
      ],
      "text/latex": [
       "0.632123"
      ],
      "text/markdown": [
       "0.632123"
      ],
      "text/plain": [
       "[1] 0.632123"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6  # устроим миллион раздач! \n",
    "n = 100       # число игроков\n",
    "\n",
    "x = rep(0, n_obs)  # сюда будем заносить число суицидников\n",
    "for(i in 1:n_obs){\n",
    "    konv = sample(1:n)      # раздача конвертов (случайная перестановка)\n",
    "    x[i] = sum(konv == 1:n) # число суицидников в раздаче \n",
    "}\n",
    "\n",
    "sum(x > 0)/n_obs  # вероятность хотя бы одного суицида "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**в) [2]** Найдите руками вероятность того, что хотя бы один человек получит сам себя. \n",
    "\n",
    "__Ответ:__ Это вопрос на беспорядки. Помните? Мы нахоидили их число на паре через формулу включений. Мы спрашивали, какова вероятность того, что никто в баре не сядет на своё место. В итоге мы выяснили, что это примерно $\\frac{1}{e}$. Тут один в один та же самая задачка. Вероятность, что ни один человек не получит в конверте себя это то же самое, что ни один человек не сядет на своё место. \n",
    "\n",
    "Нас интересует дополнение к беспорядку, что будет хотя бы один суицидник. Вычитаем $\\frac{1}{e}$ из $1$, получаем ответ. Точно такой же, как при генерации в пункте __б.__\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.632120558828558"
      ],
      "text/latex": [
       "0.632120558828558"
      ],
      "text/markdown": [
       "0.632120558828558"
      ],
      "text/plain": [
       "[1] 0.6321206"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1 - 1/exp(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**г) [2]** Пусть случайная величина $X$ - количество суицидников. Оцените $E(X)$ с помощью симуляций. Проинтерпретируйте величину $E(X)$. Что она означает для организаторов игры? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.000356"
      ],
      "text/latex": [
       "1.000356"
      ],
      "text/markdown": [
       "1.000356"
      ],
      "text/plain": [
       "[1] 1.000356"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(x) # среднее число суицидников\n",
    "\n",
    "# Организаторы должны быть готовы заменить один конверт. \n",
    "# Один из игроков достанет себя, и это тервер, а не закон подлости."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " **д) [2]** Найдите $E(X)$ руками.\n",
    " \n",
    "__Ответ:__  Мы можем разложить случайную величину $X$ в сумму индексов. Пусть \n",
    " \n",
    " $$\n",
    " X = X_1 + \\ldots + X_n, где \n",
    " $$\n",
    " \n",
    " случайная величина $X_i$ принимает значение $1$ только тогда, когда у человека в конверте он же сам. Вероятность этого события мы нашли в первом пункте на примере Максима. Выходит, что \n",
    " \n",
    "$$\n",
    "E(X_i) = P(X_i = 1) \\cdot 1 + P(X_i = 0) \\cdot 0 = P(X_i = 1) = \\frac{1}{n}.\n",
    "$$\n",
    "\n",
    "Ещё мы знаем, что $E(X_1 + X_2 + \\ldots + X_n) = E(X_1) + \\ldots + E(X_n)$ всегда. Значит $E(X) = n \\cdot E(X_1) = 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вторая проблема - это __мэтчинги__. Если у Глеба в конверте оказалась Аня, а у Ани в конверте оказался Глеб, то между ними возник мэтчинг. Когда игроки останутся наедине, они попробуют убить друг друга, и у них ничего не выйдет. Организаторам придётся заменить Ане и Глебу конверты с жертвами. \n",
    "\n",
    "**е) [1]**  Какова вероятность того, что мэтчинг возникнет именно между Аней и Глебом? \n",
    "\n",
    "__Ответ:__ нужно зафиксировать двоих. Они друг у друга, остальных можно двигать как угодно.\n",
    "\n",
    "$$\n",
    "P(\\text{мэтчинг у Ани и Глеба}) = \\frac{(n-2)!}{n!} = \\frac{1}{n \\cdot (n-1)} = 0.0001\n",
    "$$\n",
    "\n",
    "**ж) [3]** Оцените вероятность того, что в раздаче возник хотя бы один мэтчинг. \n",
    "\n",
    "__Внимание!__ В решении прошлого года, в этом пункте была ошибка! Я забыл удалить из раздач суицидников. Спасибо Юре Белякову, что нашёл эту ошибку. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2"
      ],
      "text/latex": [
       "2"
      ],
      "text/markdown": [
       "2"
      ],
      "text/plain": [
       "[1] 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "5"
      ],
      "text/latex": [
       "5"
      ],
      "text/markdown": [
       "5"
      ],
      "text/plain": [
       "[1] 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Мэтчинги это уже чуть более серьёзный разговор. На позиции i должно оказаться j, а на позиции j i\n",
    "\n",
    "# Простой пример: [3,5,1,2,4]\n",
    "# Между 3 и 1 игроком мэтчинг, так как x[1] = 3, а x[3] = 1\n",
    "# это то же самое что и x[x[1]] = 1 или x[x[3]] = 3\n",
    "\n",
    "z = c(3,5,1,2,4)\n",
    "sum(z[z] == 1:5) # получается двойка\n",
    "                 \n",
    "z = c(3,2,1,5,4) # два мэтчинга и суицидник\n",
    "sum(z[z] == 1:5) # нечётное число "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "konv = sample(1:n)            # раздача конвертов\n",
    "sum(konv[konv] == 1:n) %/% 2  # число мэтчингов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.393501"
      ],
      "text/latex": [
       "0.393501"
      ],
      "text/markdown": [
       "0.393501"
      ],
      "text/plain": [
       "[1] 0.393501"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# А теперь всё вместе! \n",
    "\n",
    "n_obs = 10^6  # устроим миллион раздач! \n",
    "n = 100       # число игроков\n",
    "\n",
    "y = rep(0, n_obs)  # сюда будем заносить число мэтчингов в раздаче\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    konv = sample(1:n)              # раздача конвертов \n",
    "    match = konv[konv] == 1:n       # есть мэтчинг\n",
    "    suic = konv != 1:n              # не суицидники\n",
    "    y[i] = sum(suic & match)  %/% 2 # число мэтчингов\n",
    "}\n",
    "\n",
    "sum(y > 0)/n_obs  # вероятность хотя бы одного мэтчинга"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**з) [3]** Пусть случайная величина $Y$ - количество мэтчингов. Оцените $E(Y)$. Проинтерпретируйте величину $E(Y)$. Что она означает для организаторов?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.500288"
      ],
      "text/latex": [
       "0.500288"
      ],
      "text/markdown": [
       "0.500288"
      ],
      "text/plain": [
       "[1] 0.500288"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(y)\n",
    "\n",
    "# В среднем мэтчинг будет возникать в одной из двух игр, \n",
    "# не такая страшная проблема как суицид, но надо быть готовым"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**и) [3]** Найдите $E(Y)$ руками.\n",
    "\n",
    "__Ответ:__ Поступим точно такжеб как и с суицидами. Разобьём $Y$ в сумму простейших. Пусть случайные величины $Y_{1,2}, Y_{1,3} \\ldots Y_{99,100}$ устроены как: \n",
    "\n",
    "\\begin{equation*}\n",
    "Y_{i,j} = \n",
    " \\begin{cases}\n",
    "   1 &\\text{, если у $i$-го игрока есть мэтчинг с $j$-им игроком}\\\\\n",
    "   0 &\\text{, иначе,}\n",
    " \\end{cases}\n",
    "\\end{equation*}\n",
    "\n",
    "тогда $Y = Y_{1,2} + \\ldots + Y_{99,100}$. Вероятность мэтчинга мы уже нашли выше. Оказалось, что это $p(Y_{i,j} = 1) = \\frac{1}{(n-1)\\cdot n}$. В итоге получаем, что \n",
    "\n",
    "$$\n",
    "E(Y) = E(Y_{1,2} + Y_{1,3} + \\ldots + Y_{99,100}) = E(Y_{1,2}) + \\ldots + E(Y_{99,100}) = C_{100}^2 \\cdot E(Y_{1,2}) = \\frac{4950} {99 \\cdot 100} = 0.5\n",
    "$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__к) [1]__  Кроме мэтчингов в игре существуют цепи. Например, у Ахмеда в конверте могла оказаться Рита, у Риты Максим, а у Максима Ахмед. Игроки выстраиваются в цепь. После того как Рита убьёт Максима, а затем Ахмеда, цепь замкнётся, и у Риты окажется она же сама. Какова вероятность того, что в игре ни один игрок в ходе замыкания такой цепи не окажется сам у себя? \n",
    "\n",
    "__Ответ:__  Тем, кто написал 0 и пояснили, что в конце то пара полюбак будет, балл не снимал. На самом деле подразумевалось, что последние два человека не могут убить друг-друга и игра прекращается. Фактически в пункте спрашивается какова вероятность того, что все игроки выстроятся в одну огромную цепь. \n",
    "\n",
    "Введем событие A - вся игра - большая цепь. Игроки получают конверты по-очереди. Нужно, чтобы первый человек получил не себя. Пусть первый игрок - Рита. Вероятность, что Рита получит не себя = $\\frac {99}{100}$. Пусть это произошло и она получила Ахмеда. Теперь необходимо, чтобы Ахмед получил не Риту, а себя он уже получить не может, тк он у Риты. Вероятность получить не Риту = $\\frac{98}{99}$. Пусть Ахмед получил Олю. Тогда чтобы цепь сохранялась, она должна получить не Риту, не Ахмеда и не себя. Себя она получить не может тк она попалась Ахмеду, Ахмеда она тоже не может получить, тк он у Риты. Тогда необходимо получить не Риту, вероятность этого = $\\frac{97}{98}$. И так далее. Пусть предпоследним получил конверт Максим, чтобы цепь сохранилась, он должен получить не Риту. Так как все до этого получали не Риту, то она находится где-то в одном из двух оставшихся конвертов. Вероятность получить не Риту = $\\frac{1}{2}$. И наконец бедный Олег получает конверт последним в котором находится именно Рита, вероятность этого = 1.\n",
    "\n",
    "Таким образом $P(A) = \\frac{99}{100} \\cdot \\frac{98}{99} \\ldots \\cdot \\frac{1}{2} \\cdot 1 = \\frac{1}{100}$\n",
    "\n",
    "\n",
    "__л) [х.з.]__ Вы понимаете, что любая раздача конвертов приводит к появлению какого-то количества подобных цепей. Каждая цепь — это какой-то граф. В итоговом графе может существовать различное количество компонент связности. Когда цепь в каждой из них замыкается, у человека в конверте оказывается он сам. Пусть случайная величина $Z$ — количество таких компонент, возникшее в игре при раздаче. Найдите $E(Z)$. Постройте для $Z$ гистограмму. \n",
    "\n",
    "Именно это я попросил сделать в прошлом году. Моё решение получилось довольно убойным. Его можно найти в прошлогодней домашке. Если вы сможете сделать это проще, накину баллов.\n",
    "\n",
    "__Для полноты картины воспроизведу тут код из прошлого года:__ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>3</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3\n",
       "2. 2\n",
       "3. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 3 2 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 2 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Можно было бы конечно написать огромную функцию с огромными циклами, но мы не будем\n",
    "# Немного пораскинем мозгами и придумаем более простой алгоритм поиска цепей. \n",
    "# При решении прошлого пункта мы с вами начились искать пары делая z[z]\n",
    "\n",
    "z = c(3,2,1)\n",
    "z\n",
    "z[z]  # Пары меняются местами => profit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3\n",
       "2. 1\n",
       "3. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 3 1 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 3\n",
       "3. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 3 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 2 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# По аналогии можно искать и тройки\n",
    "z = c(3,1,2)\n",
    "z\n",
    "x = z[z]\n",
    "x\n",
    "x[z]  # Но для поиска троек придется сделать z[z] два раза"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4\n",
       "2. 1\n",
       "3. 2\n",
       "4. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4 1 2 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3\n",
       "2. 4\n",
       "3. 1\n",
       "4. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 3 4 1 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 3\n",
       "3. 4\n",
       "4. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 3 4 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "4. 4\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 2 3 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Соответственно z[z] три раза поможет нам найти четвёрки\n",
    "z = c(4,1,2,3)\n",
    "x = z[z]\n",
    "z\n",
    "x\n",
    "y = x[z]\n",
    "y\n",
    "y[z]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4</li>\n",
       "\t<li>5</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4\n",
       "2. 5\n",
       "3. 2\n",
       "4. 1\n",
       "5. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4 5 2 1 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>4</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\item 4\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 3\n",
       "3. 5\n",
       "4. 4\n",
       "5. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 3 5 4 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>5</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4\n",
       "2. 2\n",
       "3. 3\n",
       "4. 1\n",
       "5. 5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4 2 3 1 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>5</li>\n",
       "\t<li>2</li>\n",
       "\t<li>4</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 5\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 5\n",
       "3. 2\n",
       "4. 4\n",
       "5. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 5 2 4 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Кажется, что алгоритм готов! На самом деле не совсем. \n",
    "# Давайте посмотрим на случай из тройки и пары: \n",
    "z = c(4,5,2,1,3)\n",
    "z\n",
    "x = z[z] # При первой махинации пара встанет на свои места\n",
    "x\n",
    "y = x[z] # При второй махинации тройка встанет на свои места, а пара испортится\n",
    "y\n",
    "y[z]     # При третьей махинации тройка испотится, а пара встанет на места"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4</li>\n",
       "\t<li>5</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4\n",
       "2. 5\n",
       "3. 2\n",
       "4. 1\n",
       "5. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4 5 2 1 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>4</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\item 4\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 3\n",
       "3. 5\n",
       "4. 4\n",
       "5. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 3 5 4 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "\t<li>5</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "4. 4\n",
       "5. 5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 2 3 4 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Проблема в том, что у перестановок разный цикл и когда одна из них входит \n",
    "# в норму, другая неизбежно портится. Но выход есть. Будем искуственно вмешиваться\n",
    "# в работу перестановок и не давать двигаться тем позициям, которые уже оказались \n",
    "# на своих местах. \n",
    "\n",
    "z = c(4,5,2,1,3)\n",
    "z\n",
    "yp = z==1:5  # смотрим кто уже на своих местах\n",
    "y = z[yp]  # запоминаем их \n",
    "\n",
    "x = z[z]   # При первой махинации пара встанет на свои места\n",
    "x[yp] = y  # Выправляем то, что уже было на своих местах, но перемешалось\n",
    "x\n",
    "\n",
    "yp = x==1:5  # снова смотрим кто на своих местах\n",
    "y = x[yp]  # запоминаем их \n",
    "x = x[z]   # на своих местах оказываются тройки, пара смешивается\n",
    "x[yp] = y  # исправляем это\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>4</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\item 4\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 3\n",
       "3. 5\n",
       "4. 4\n",
       "5. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 3 5 4 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "\t<li>5</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "4. 4\n",
       "5. 5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 2 3 4 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Напишем функцию для одной перестановки \n",
    "\n",
    "permutation <- function(vect, z){\n",
    "    yp = vect==1:length(vect)\n",
    "    y = vect[yp]\n",
    "    \n",
    "    x = vect[z]\n",
    "    x[yp] = y\n",
    "    return(x) \n",
    "}\n",
    "\n",
    "z = c(4,5,2,1,3)\n",
    "x = permutation(z,z)\n",
    "x\n",
    "x = permutation(x,z)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Число суицидников: 0 \n",
      "\n",
      " Длина цепи: 14 \n",
      " Число цепей: 1 \n",
      "\n",
      " Длина цепи: 42 \n",
      " Число цепей: 1 \n",
      "\n",
      " Длина цепи: 44 \n",
      " Число цепей: 1 \n",
      "\n",
      "Всего цепей в игре: 3"
     ]
    }
   ],
   "source": [
    "# Отлично! Функция готова, остался цикл.\n",
    "n = 100 \n",
    "konv = sample(1:n)  \n",
    "\n",
    "i_iter = 1                 # счётчик для итераций (цепи такого размера мы сейчас нашли)\n",
    "i_chain = sum(konv == 1:n) # число цепей, суицидники - цепи длины 1\n",
    "i_sum = sum(konv == 1:n)   # люди, которые на текущей итерации на своей позиции\n",
    "\n",
    "x = konv  # Копируем раздачу, чтобы был вектор, который мы будем менять \n",
    "\n",
    "cat(' Число суицидников:', i_chain, '\\n\\n')\n",
    "while(i_sum != n){ # цикл идёт пока все не встанут на свои места\n",
    "    \n",
    "    x = permutation(x,konv)  # сделали перестановку \n",
    "    i_iter = i_iter + 1      # плюс одна итерация\n",
    "    \n",
    "    # выяснили сколько цепей было обнаружено на данном шаге\n",
    "    chain_count = (sum(x == 1:n) - i_sum) / i_iter \n",
    "    \n",
    "    # увеличили счётчик цепей на число найденных цепей\n",
    "    i_chain = i_chain + chain_count\n",
    "    \n",
    "    # увеличили сумму с людьми на своих же позициях\n",
    "    i_sum = i_sum + (sum(x == 1:n) - i_sum) \n",
    "    if(chain_count > 0){\n",
    "        cat(' Длина цепи:', i_iter, '\\n', 'Число цепей:', chain_count, '\\n\\n')\n",
    "    }\n",
    "       \n",
    "}\n",
    "\n",
    "cat('Всего цепей в игре:',i_chain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Нам нужно узнать среднее число цепей в игре. Значит цикл по размотке придётся \n",
    "# запускать много-много раз. Давайте оформим его как функцию. \n",
    "\n",
    "one_chain <- function(konv){\n",
    "    n = length(konv)\n",
    "    \n",
    "    i_iter = 1                 # счётчик для итераций (цепи такого размера мы сейчас нашли)\n",
    "    i_chain = sum(konv == 1:n) # число цепей, суицидники - цепи длины 1\n",
    "    i_sum = sum(konv == 1:n)   # люди, которые на текущей итерации на своей позиции\n",
    "\n",
    "    x = konv  # Копируем раздачу, чтобы был вектор, который мы будем менять \n",
    "\n",
    "    while(i_sum != n){ # цикл идёт пока все не встанут на свои места\n",
    "\n",
    "        x = permutation(x,konv)  # сделали перестановку \n",
    "        i_iter = i_iter + 1      # плюс одна итерация\n",
    "\n",
    "        # выяснили сколько цепей было обнаружено на данном шаге\n",
    "        chain_count = (sum(x == 1:n) - i_sum) / i_iter \n",
    "\n",
    "        # увеличили счётчик цепей на число найденных цепей\n",
    "        i_chain = i_chain + chain_count\n",
    "\n",
    "        # увеличили сумму с людьми на своих же позициях\n",
    "        i_sum = i_sum + (sum(x == 1:n) - i_sum) \n",
    "    }\n",
    "    \n",
    "    return(i_chain)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_obs = 10^5\n",
    "s = rep(0,n_obs) # вектор для числа цепей\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    s[i] = one_chain(sample(1:n))   \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>3</li>\n",
       "\t<li>6</li>\n",
       "\t<li>4</li>\n",
       "\t<li>6</li>\n",
       "\t<li>9</li>\n",
       "\t<li>9</li>\n",
       "\t<li>4</li>\n",
       "\t<li>5</li>\n",
       "\t<li>4</li>\n",
       "\t<li>6</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3\n",
       "\\item 6\n",
       "\\item 4\n",
       "\\item 6\n",
       "\\item 9\n",
       "\\item 9\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\item 4\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3\n",
       "2. 6\n",
       "3. 4\n",
       "4. 6\n",
       "5. 9\n",
       "6. 9\n",
       "7. 4\n",
       "8. 5\n",
       "9. 4\n",
       "10. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 3 6 4 6 9 9 4 5 4 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s[1:10] # вот оно, количество цепей в каждой игре :) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "5.18634"
      ],
      "text/latex": [
       "5.18634"
      ],
      "text/markdown": [
       "5.18634"
      ],
      "text/plain": [
       "[1] 5.18634"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(s)  # вот и получили среднее число цепей"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAYAAACYBpIxAAAEDWlDQ1BJQ0MgUHJvZmlsZQAA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\nAAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(s, bins=15)  # ну и, конечно, гистограмка "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.01032"
      ],
      "text/latex": [
       "0.01032"
      ],
      "text/markdown": [
       "0.01032"
      ],
      "text/plain": [
       "[1] 0.01032"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ради интереса для пункта к) можно найти оценку вероятности, что в игре будет одна цепь \n",
    "mean(s == 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Усложняем ситуацию! Предположим, что на игру отводится $24 \\cdot 60$ часов. Последовательность убийств — это поток событий. Время, которое проходит между убийствами описывается экспоненциальным распределением с параметром $\\alpha = 0.08$.\n",
    "\n",
    "__м) [1]__  Сколько в среднем проходит часов между убийствами? \n",
    "\n",
    "__Ответ:__ Если $X \\sim Exp(0.08)$, тогда $E(X) = \\frac{1}{0.08} = 12.5$. Выходит, что между убийствами в среднем проходит $12.5$ часов."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__н) [5]__  Какова вероятность того, что через $30$ дней в игре останется меньше $50$ человек? При симуляциях можно считать, что если в какой-то момент человек оказался в конверте сам у себя, он умирает. Если возник мэтчинг, умирают оба человека. Цепочку, на которой происходит убийство, выбирайте случайно на основе равномерного распределения.\n",
    "\n",
    "__Ответ:__ По условию время убийства никак не зависит от того, как именно произошла раздача конвертов и сколько человек на данный момент остаётся в игре. Возникает мысль, что для того, чтобы понять с какой вероятностью через $30$ дней в игре останется меньше $50$ человек, нам вообще не нужно генерировать раздачи конвертов. Более того, нам вообще не нужно выбирать какой именно человек умрёт. Потому что для нас важен только факт того, что человек умер.\n",
    "\n",
    "Если так сделать, можно получить близкий к ответу результат, но оценка будет завышена, потому что по условию пункта, люди у которых мэтчинг, умирают. В ходе выбора той пары, где происходит выстрел, могут возникать такие мэтчинги. Будут умирать лишние люди. Интересно насколько большим будет эффект от них. Попробуем реализовать оба варианта. С завязкой на игру, и без завязки на игру. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.8586"
      ],
      "text/latex": [
       "0.8586"
      ],
      "text/markdown": [
       "0.8586"
      ],
      "text/plain": [
       "[1] 0.8586"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs <- 10^5 \n",
    "died_cnt <- rep(0, n_obs) # тут колекционируем мёртвых\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    time <- 24*30    # время на половину игры\n",
    "    k <- 0           # число мёртвых\n",
    "\n",
    "    while(time > 0){\n",
    "        pau <- rexp(1, rate = 0.08) # время между убийствами в часах\n",
    "        k = k + 1\n",
    "        time = time - pau\n",
    "    }\n",
    "    \n",
    "    died_cnt[i] = k\n",
    "}\n",
    "\n",
    "mean(died_cnt > 50) # так как всего у нас 100 человек в игре"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Хорошо, теперь абсолютно то же самое, но в этот раз будем внимательно наблюдать за мэтчингами и выбирать тех, кто умрёт в текущую итерацию, случайно. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Смертей должно быть: 67 \n",
      "Реально умерло: 67"
     ]
    }
   ],
   "source": [
    "# шаг первый - понимаем сколько людей должно умереть в течение разадчи \n",
    "n = 100          # число игроков \n",
    "time <- 24*30    # время на половину игры\n",
    "k <- 0           # число убийств\n",
    "\n",
    "while(time > 0){\n",
    "    pau <- rexp(1, rate = 0.08) # время между убийствами в часах\n",
    "    k = k + 1\n",
    "    time = time - pau\n",
    "}\n",
    "\n",
    "# шаг второй - раздаём конверты и убиваем людей \n",
    "konv = sample(1:n)   # раздача конвертов\n",
    "died_ppl = 1:n       # вектор, куда будем писать мёртвых\n",
    "\n",
    "# все суицидники и мэтчинги мертвы \n",
    "died_ppl[konv[konv] == 1:n] = 0 \n",
    "\n",
    "cat('Смертей должно быть:', k, '\\n')\n",
    "while((k > 0)&(sum(died_ppl == 0) < 100)){\n",
    "    # выбираем индекс живого человека, который сделает свой выстрел в нашей цепи\n",
    "    idx = sample(died_ppl[died_ppl != 0],size = 1)\n",
    "\n",
    "    # выстрел идёт в человека konv[idx], помечаем его как мёртвого \n",
    "    died_ppl[konv[idx]] = 0\n",
    "    # отбираем у него конверт и отдаем его idx \n",
    "    konv[idx] = konv[konv[idx]]\n",
    "\n",
    "    # если вдруг возникли мэтчинги или суициды, зануляем их\n",
    "    died_ppl[konv[konv] == 1:n] = 0 \n",
    "    k = k - 1 # сколько убийств осталось сделать  \n",
    "}\n",
    "\n",
    "cat('Реально умерло:', sum(died_ppl == 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Оформим второй кусок кода как функцию. В пунктах ниже мы будем его переиспользовать. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "kill_people <- function(n, k){\n",
    "    # шаг второй - раздаём конверты и убиваем людей \n",
    "    konv = sample(1:n)   # раздача конвертов\n",
    "    died_ppl = 1:n       # вектор, куда будем писать мёртвых\n",
    "\n",
    "    # все суицидники и мэтчинги мертвы \n",
    "    died_ppl[konv[konv] == 1:n] = 0 \n",
    "\n",
    "    while((k > 0)&(sum(died_ppl == 0) < 100)){\n",
    "        # выбираем индекс живого человека, который сделает свой выстрел в нашей цепи\n",
    "        idx = sample(died_ppl[died_ppl != 0],size = 1)\n",
    "\n",
    "        # выстрел идёт в человека konv[idx], помечаем его как мёртвого \n",
    "        died_ppl[konv[idx]] = 0\n",
    "        # отбираем у него конверт и отдаем его idx \n",
    "        konv[idx] = konv[konv[idx]]\n",
    "\n",
    "        # если вдруг возникли мэтчинги или суициды, зануляем их\n",
    "        died_ppl[konv[konv] == 1:n] = 0 \n",
    "        k = k - 1 # сколько убийств осталось сделать  \n",
    "    }\n",
    "    \n",
    "    return(sum(died_ppl == 0))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь цикл! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_obs = 10^4  # число симуляций \n",
    "\n",
    "died_cnt <- rep(0, n_obs)\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    # шаг первый - понимаем сколько людей должно умереть в течение разадчи \n",
    "    n = 100          # число игроков \n",
    "    time <- 24*30    # время на половину игры\n",
    "    k <- 0           # число убийств\n",
    "\n",
    "    while(time > 0){\n",
    "        pau <- rexp(1, rate = 0.08) # время между убийствами в часах\n",
    "        k = k + 1\n",
    "        time = time - pau\n",
    "    }\n",
    "    \n",
    "    died_cnt[i] = kill_people(n, k) \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.9249"
      ],
      "text/latex": [
       "0.9249"
      ],
      "text/markdown": [
       "0.9249"
      ],
      "text/plain": [
       "[1] 0.9249"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(died_cnt > 50) # так как всего у нас 100 человек в игре"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__о) [5]__ Найдите математическое ожидание числа игроков, выживших после $30$ дней. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "37.5237"
      ],
      "text/latex": [
       "37.5237"
      ],
      "text/markdown": [
       "37.5237"
      ],
      "text/plain": [
       "[1] 37.5237"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "100 - mean(died_cnt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Предположим, что со временем игра протухает. Поначалу всем весело и все хотят убивать, но ближе к середине энтузиазм скатывается в ноль. Пусть $\\alpha$ в самом начале равна $0.08$. Каждые 48 часов она уменьшается в два раза.\n",
    "\n",
    "__п) [5]__ Какова вероятность того, что через $30$ дней в игре останется меньше $50$ человек? Каково математическое ожидание выживших? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Ответ:__ Ну, всё что тут требуется это поменять код, который генерирует время между убийствами. Остальное остаётся прежним. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_obs = 10^4\n",
    "died_cnt <- rep(0, n_obs)\n",
    "\n",
    "for(i in 1:n_obs){\n",
    "    n = 100         \n",
    "    time <- 24*30\n",
    "    k <- 0\n",
    "\n",
    "    while(time > 0){\n",
    "        # делим параметр на число прошедших 48-часовок\n",
    "        alpha = 0.08/(2*((24*30 - time)%/%48))\n",
    "        pau <- rexp(1, rate = alpha)\n",
    "        k = k + 1\n",
    "        time = time - pau\n",
    "    }\n",
    "    \n",
    "    died_cnt[i] = kill_people(n, k) \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean(died_cnt > 50) # так как всего у нас 100 человек в игре"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "100 - mean(died_cnt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Организаторы игры не хотят, чтобы игра протухла. Перед тем как запустить игру, они построили кучу симуляций и решили, что каждые $7$ дней в полночь они будут награждать самого топового убийцу специальным призом. Каждый раз, когда происходит награждение, $\\alpha$ подскакивает на $0.02$. \n",
    "\n",
    "__р) [5]__ Какова вероятность того, что через $30$ дней в игре останется меньше $50$ человек? Каково математическое ожидание выживших?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# тот же код, что и в предыдущем пункте, но с условием на альфу."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}