end_seminars_2019/sem_1/presa_intro/1. Intro,generation.ipynb

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   "source": [
    "<center>\n",
    "\n",
    "# R для тервера и матстата  <br> <br> Шо за случайности да как их генерить \n",
    "\n",
    "<br> \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars/sem_2/yYGiBqtirSM.jpg\" height=\"300\" width=\"500\"> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   },
   "source": [
    "Данный ноутбук является конспектом 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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Чем будем заниматься \n",
    "\n",
    "- Посмотрим на то, что уже заботали под новым углом\n",
    "\n",
    "- Немного углубим знания, выработаем интуицию\n",
    "\n",
    "- Будем смотреть презы, писать код, болтать, решать задачки на доске\n",
    "\n",
    "- Посмотрим на примеры задач, которые приходится решать аналитикам\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## В чём будем заниматься \n",
    "\n",
    "- Конечно же в R\n",
    "\n",
    "- R очень лёгок в освоении\n",
    "\n",
    "- Одна из самыз красивых визуализаций данных \n",
    "\n",
    "- Очень хорош в работе со статистикой \n",
    "\n",
    "- Много готовых пакетов и большое комьюнити\n",
    "\n",
    "- Используется многими компаниями в работе, вот устаревший [мини-список](https://blog.revolutionanalytics.com/2014/05/companies-using-r-in-2014.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Чему мы хотим научиться\n",
    "\n",
    "* Увидеть картину мира целиком, а не отдельные её части\n",
    "* Чётко осознавать какие именно методы из статистики можно применить к задаче\n",
    "* Понимать что за задача перед нами стоит и уметь переводить её на язык математики \n",
    "* Использовать всю мощь R для этих целей"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Про активности \n",
    "\n",
    "- Не делаешь сам $\\Rightarrow$ никогда не научишься $\\Rightarrow$ $4$ ~~большие~~ огромные домашки, за каждую можно набрать $100$ баллов\n",
    "\n",
    "- Домашки делаются в командах по три человека\n",
    "\n",
    "- Баллы ставятся на команду\n",
    "\n",
    "- Для зачёта и оценки $10$ надо набрать на команду $100$ баллов\n",
    "\n",
    "- В каждой домашке много рыбёшек и большой кит, можно решать только то, к чему лежит душа  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Регистрация команд \n",
    "\n",
    "* Нужно разбиться на команды по три человека и [зарегистрироваться в форме](https://docs.google.com/forms/d/e/1FAIpQLSfW1e5wSWF42xlYxjE-XpXusxd7BMKROrdaiz2lPPio_OPsqw/viewform)\n",
    "* Название своей команды нужно держать в тайне, у нас анонимное состязание, потому что есть супер-приз"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Суперприз\n",
    "    \n",
    "- Две команды, набравшие наибольшее количество баллов свожу почилить с винишком, пиццей и настолками на крышу Яндекса\n",
    "\n",
    "- Команда может претендовать на крышу, если она набрала больше $100$ баллов\n",
    "\n",
    "<center>\n",
    "<img src=\"https://webpromoexperts.com.ua/images/uploads/blogs/skorostnaa-ekskursia-po-moskovskomu-ofisu-and-/UPijZLN5vs.jpg\"  width=\"500\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Страничка курса со всей инфой: \n",
    "\n",
    "https://fulyankin.github.io/r_probability/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "# Показать как сдавать домашки! \n",
    "\n",
    "* __Опасность:__ не смочь собрать в R домашку \n",
    "* __Лечение:__ написать мне и попросить помочь, я всегда отвечу \n",
    "* Я в академии в четверг весь день, иногда в пятницу, можно подойти с ноутом\n",
    "* В команде вас трое, а файл на всех один: разделение труда. Кто-то решает, кто-то вбивает. \n",
    "* [Видео с запуском R и созданием pdf с домашкой](https://yadi.sk/i/Pxp_pByP6Em9-A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/laba.jpg\"  width=\"1000\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/laba_2.jpg\"  width=\"1000\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "# 1. Зачем мы учили тервер?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Теория вероятностей \n",
    "\n",
    "- Мы изучали вероятности\n",
    "\n",
    "- Мы изучали события \n",
    "\n",
    "- Мы изучали случайные величины и их распределения \n",
    "\n",
    "- __ЗАЧЕМ МЫ ЭТО ДЕЛАЛИ?__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Случайные ли величины? \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_vinsent.png\"  width=\"1000\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_1.png\"  width=\"3000\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Демон Лапласа \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_laplas.png\" width=\"1000\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Байесовский взгляд на вероятность \n",
    "\n",
    "- Лаплас: детерминизм, мы могли бы идеально прогнозировать вселенную, если бы измерили точное положение каждого атома. Издержки этого огромны. \n",
    "\n",
    "- Между совершенством природы и несовершенством человеческого познания огромный разрыв. \n",
    "\n",
    "- Неопределённость — результат этого разрыва. Случайность — это результат нашего невежества, а вероятность способ это невежество измерить. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Частотный взгляд на вероятность \n",
    "\n",
    "- Наука не может рассматривать вероятность как субъективную меру невежества.\n",
    "\n",
    "- Можно оценивать вероятности только тех событий, которые происходят более одного раза.\n",
    "\n",
    "- Вопрос «Какова вероятность, что кандидат N победит на выборах?» не имеет ответа, так как событие уникально и не обладает «частотой».\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Что мы имеем \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_sunduk.png\" width=\"900\"> \n",
    "</center>\n",
    "\n",
    "- <font size=\"5.5\"> Сундук — различные процесс порождения данных. Теория вероятностей изучает этот сундук. В реальности мы его не видим. </font>\n",
    "\n",
    "- <font size=\"5.5\"> В реальном мире мы видим выборки, которые сундук выплёвывает на нас. Математическая статистика изучает испражнения сундука и по ним пытается восстановить его внутренности. </font> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Хлам из сундука\n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_inside_sunduk.png\" width=\"1000\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Чем плюётся сундук \n",
    "\n",
    "- Выборки, по которым можно попробовать восстановить его внутренности \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_inside_sunduk_2.png\" width=\"1000\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Базовые теоремы \n",
    "\n",
    "- Все манипуляции по восстановлению внутренностей сундука по его испражнениям позволяет делать ряд теорем.\n",
    "\n",
    "- Некоторые из них вы уже выучили!\n",
    "\n",
    "- __Что это за теоремы?__ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 2. Закон больших чисел"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Закон больших чисел \n",
    "\n",
    "- ЗБЧ утверждает, что среднее арифметическое большого числа похожих случайных величин «стабилизируется» с рочтом их числа\n",
    "\n",
    "- Как бы сильно случайные величины не отклонялись от своего среднего значения, эти отклонения взаимно гасятся и среднее арифметическое приближается к постоянной величине\n",
    "\n",
    "$$\n",
    "\\frac{X_1 + \\ldots + X_n}{n} - \\frac{E(X_1) + \\ldots + E(X_n)}{n} \\overset{p}{\\to} 0\n",
    "$$\n",
    "\n",
    "- ЗБЧ сформулировано довольно много: Чебышёва,Хинчина и тд\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Закон больших чисел \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/gif_creator/animation_LLN.gif\" width=\"800\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Вопрос про больницы\n",
    "\n",
    "- Есть две больницы: маленькая и большая \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_ill.png\" width=\"600\"> \n",
    "</center>\n",
    "\n",
    "- В обеих принимают роды, выяснилось, что в одной из больниц оценка вероятности появления мальчика составила $0.7$\n",
    "\n",
    "- В какой из больниц это произошло и почему? \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Вопрос про больницы\n",
    "\n",
    "Есть две больницы: маленькая и большая \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_ill.png\" width=\"600\"> \n",
    "</center>\n",
    "\n",
    "- Скорее всего, это произошло в маленькой больнице. При малых объёмах выборки вероятность отклониться от $0.5$ больше. Именно это нашёптывает нам ЗБЧ. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "### Слабая форма ЗБЧ (Пафнутий Львович Чебышёв)\n",
    "\n",
    "Пусть $X_1, \\ldots, X_n$ попарно независимые и одинаково распределённые случайные величины с конечным вторым моментом, $E(X_i^2) < \\infty$, тогда имеет место сходимость:\n",
    "\n",
    "$$\n",
    "\\frac{X_1 + \\ldots + X_n}{n} \\overset{p}{\\to} E(X_1)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Сильная форма ЗБЧ\n",
    "\n",
    "Пусть $X_1, \\ldots, X_n$ попарно независимые и одинаково распределённые случайные величины с конечным вторым моментом, $E(X_i^2) < \\infty$, причём $\\sum_{k=1}^{\\infty} \\frac{Var(X_k)}{k^2} < \\infty$, тогда имеет место сходимость \n",
    "\n",
    "$$\n",
    "\\frac{X_1 + \\ldots + X_n}{n} \\overset{п.н.}{\\to} E(X_1)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Страховые компании \n",
    "\n",
    "- Примерно с $1600$-х годов ЗБЧ позволяет зарабатывать деньги на страховании\n",
    "\n",
    "- __Упражнение:__ для $25$-летней девушки вероятность прожить ещё год составляет $0.9$. Страховка в год стоить $1000$ рублей при взносе в $110$ рублей. Какой будет средняя прибыль компании с одной страховки? \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Страховые компании \n",
    "\n",
    "$X_i$ — прибыль с одной страховки \n",
    "\n",
    "  $X_i$     | $110$  | $-890$\n",
    " ---------- | ------ | -------------\n",
    "$P(\\ldots)$ | $0.9$  | $0.1$\n",
    "\n",
    "Средняя прибыль компании составит $\\frac{1}{n} \\sum X_i$. По закону больших чисел:\n",
    "\n",
    "$$\n",
    "\\frac{1}{n} \\sum_{i=1}^n X_i \\overset{p}{\\to} E(X_1) = 0.9 \\cdot 110 - 0.1 \\cdot 890 = 10\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Генерации разных штук\n",
    "\n",
    "- Другой ништяк, который нам разрешает ЗБЧ — генерация случайных величин для оценки разных математических ожиданий и т.п.\n",
    "\n",
    "- Не можешь посчитать? Сгенерируй! \n",
    "\n",
    "- Обычно такие генерации называют методом Монте-Карло \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Метод Монте-Карло\n",
    "\n",
    "- __Метод Монте-Карло__ это общее название группы численных методов, основанных на получении большого числа реализаций случайного процесса, который формируется таким образом, чтобы его вероятностные характеристики совпадали с аналогичными величинами решаемой задачи \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 3. Генерации в R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "library(\"ggplot2\")  # Пакет для красивых графиков \n",
    "     \n",
    "# Если вы работаете в R-studio, вы можете избежать подгрузки пакетов ниже\n",
    "# Отрегулируем размер картинок, которые будут выдаваться в нашей тетрадке\n",
    "library('repr') \n",
    "library(\"grid\")  # Пакет для субплотов\n",
    "options(repr.plot.width=4, repr.plot.height=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Генерации в R \n",
    "\n",
    "Чтобы сварить в R любую случайную величину, нужно знать четыре буквы: $r$, $d$, $p$ и $q$. \n",
    "\n",
    "* `rnorm` эта команда сгенерирует выборку из нормального распределения\n",
    "* `dnorm` эта команда вычислит значение плотности в указанной точке\n",
    "* `pnorm` эта команда находит вероятность \n",
    "* `qnorm` эта команда находит квантили "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Генерируем нормальную выборку\n",
    "\n",
    "Хочу сгенерировать нормальную случайную величину $X \\sim N(\\mu, \\sigma^2)$:\n",
    "\n",
    "$$\n",
    "f(x) = \\frac{1}{\\sigma \\sqrt{2 \\pi}} \\cdot  e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>3.44389035979933</li>\n",
       "\t<li>7.59097440961776</li>\n",
       "\t<li>3.6506566737062</li>\n",
       "\t<li>4.72979997241011</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3.44389035979933\n",
       "\\item 7.59097440961776\n",
       "\\item 3.6506566737062\n",
       "\\item 4.72979997241011\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3.44389035979933\n",
       "2. 7.59097440961776\n",
       "3. 3.6506566737062\n",
       "4. 4.72979997241011\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 3.443890 7.590974 3.650657 4.729800"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- rnorm(4, mean=5, sd=3)  # если дисперсия 9, \n",
    "x                            # то стандартное отклонение 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Хочу узнать $f(3)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.106482668507451"
      ],
      "text/latex": [
       "0.106482668507451"
      ],
      "text/markdown": [
       "0.106482668507451"
      ],
      "text/plain": [
       "[1] 0.1064827"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dnorm(3, mean=5, sd=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Хочу узнать $F(3) = P(X < 3) = \\int_{-\\infty}^3 f(x)dx$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.252492537546923"
      ],
      "text/latex": [
       "0.252492537546923"
      ],
      "text/markdown": [
       "0.252492537546923"
      ],
      "text/plain": [
       "[1] 0.2524925"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pnorm(3, mean=5, sd=3)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Хочу узнать $P(4 < X < 9)$ - ? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Хочу узнать \n",
    "\n",
    "$$P(4 < X < 9) =  \\int_4^9 f(x) dx = F(9) - F(4)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.539347440092368"
      ],
      "text/latex": [
       "0.539347440092368"
      ],
      "text/markdown": [
       "0.539347440092368"
      ],
      "text/plain": [
       "[1] 0.5393474"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pnorm(9, mean=5, sd=3) - pnorm(4, mean=5, sd=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Квантиль уровня $\\gamma$ это такое число $q$, что:\n",
    "\n",
    "$$\n",
    "P(X < q) = \\gamma\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.95996398454005"
      ],
      "text/latex": [
       "1.95996398454005"
      ],
      "text/markdown": [
       "1.95996398454005"
      ],
      "text/plain": [
       "[1] 1.959964"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qnorm(1 - 0.05/2, mean=0, sd=1)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1.64485362695147</li>\n",
       "\t<li>1.95996398454005</li>\n",
       "\t<li>2.5758293035489</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1.64485362695147\n",
       "\\item 1.95996398454005\n",
       "\\item 2.5758293035489\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1.64485362695147\n",
       "2. 1.95996398454005\n",
       "3. 2.5758293035489\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1.644854 1.959964 2.575829"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- c(0.95, 0.975, 0.995)\n",
    "qnorm(x, mean = 0, sd = 1)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1.81246112281168</li>\n",
       "\t<li>2.22813885198627</li>\n",
       "\t<li>3.16927267261695</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1.81246112281168\n",
       "\\item 2.22813885198627\n",
       "\\item 3.16927267261695\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1.81246112281168\n",
       "2. 2.22813885198627\n",
       "3. 3.16927267261695\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1.812461 2.228139 3.169273"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# квантили для другого распределения!\n",
    "x <- c(0.95, 0.975, 0.995)\n",
    "qt(x, df = 10)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Что сгенерирует код? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>-0.707120663342578</li>\n",
       "\t<li>-0.980011188525533</li>\n",
       "\t<li>0.396645732489923</li>\n",
       "\t<li>-0.839942216948569</li>\n",
       "\t<li>1.75183863777376</li>\n",
       "\t<li>1.08577247385991</li>\n",
       "\t<li>-0.396472256977632</li>\n",
       "\t<li>-0.893778576611249</li>\n",
       "\t<li>-0.274953778469149</li>\n",
       "\t<li>-0.630480321588603</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -0.707120663342578\n",
       "\\item -0.980011188525533\n",
       "\\item 0.396645732489923\n",
       "\\item -0.839942216948569\n",
       "\\item 1.75183863777376\n",
       "\\item 1.08577247385991\n",
       "\\item -0.396472256977632\n",
       "\\item -0.893778576611249\n",
       "\\item -0.274953778469149\n",
       "\\item -0.630480321588603\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -0.707120663342578\n",
       "2. -0.980011188525533\n",
       "3. 0.396645732489923\n",
       "4. -0.839942216948569\n",
       "5. 1.75183863777376\n",
       "6. 1.08577247385991\n",
       "7. -0.396472256977632\n",
       "8. -0.893778576611249\n",
       "9. -0.274953778469149\n",
       "10. -0.630480321588603\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] -0.7071207 -0.9800112  0.3966457 -0.8399422  1.7518386  1.0857725\n",
       " [7] -0.3964723 -0.8937786 -0.2749538 -0.6304803"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rnorm(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Характеристики случайных величин"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "4.86203937386118"
      ],
      "text/latex": [
       "4.86203937386118"
      ],
      "text/markdown": [
       "4.86203937386118"
      ],
      "text/plain": [
       "[1] 4.862039"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "9.36098544923856"
      ],
      "text/latex": [
       "9.36098544923856"
      ],
      "text/markdown": [
       "9.36098544923856"
      ],
      "text/plain": [
       "[1] 9.360985"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "3.05957275599692"
      ],
      "text/latex": [
       "3.05957275599692"
      ],
      "text/markdown": [
       "3.05957275599692"
      ],
      "text/plain": [
       "[1] 3.059573"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "4.8395876699123"
      ],
      "text/latex": [
       "4.8395876699123"
      ],
      "text/markdown": [
       "4.8395876699123"
      ],
      "text/plain": [
       "[1] 4.839588"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- rnorm(1000, mean=5, sd=3)\n",
    "\n",
    "mean(x) # среднее\n",
    "\n",
    "var(x) # выборочная дисперсия\n",
    "\n",
    "sd(x) # выборочное стандартное отклонение\n",
    "\n",
    "median(x) # выборочная медиана"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Гистограмма "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": 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jyzRQABBBBIbwECcHq3P7VHAAEEEEiS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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(\"ggplot2\")  # пакет для красивых картинок\n",
    "\n",
    "x <- rnorm(1000, mean=5, sd=3)\n",
    "\n",
    "qplot(x) # гистограма "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Плотность распределения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2IGH1Wt3arce++9kpeXJz/96U9l+/bt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\nJuhgXNFOO7TlktZzX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d9G58hw4dZP78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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(\"ggplot2\")  # пакет для красивых картинок\n",
    "\n",
    "x <- seq(-5, 15, by=0.01)\n",
    "y <- dnorm(x, mean=5, sd=3)\n",
    "\n",
    "qplot(x, y, geom=\"line\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Функция распределения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RPtLgIUYHflN1NLAo4kcP78ecGqVzExMdK1a1dH2kijSMBqAhRgq4kyPBIggaAJ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\nTZz0xwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(\"ggplot2\")  # пакет для красивых картинок\n",
    "\n",
    "x <- seq(-5, 15, by=0.01)\n",
    "y <- pnorm(x, mean=5, sd=3)\n",
    "\n",
    "qplot(x, y, geom=\"line\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Зачем всё это надо?!\n",
    "\n",
    "- Чтобы решать реальные проблемы! Например, пусть $X \\sim N(5,3)$. Как найти $E \\left(\\frac{1}{X} \\right)$? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Спосбо первый: \n",
    "\n",
    "$$\n",
    "E \\left(\\frac{1}{X} \\right) = \\int_{-\\infty}^{+\\infty} \\frac{1}{x} \\cdot \\frac{1}{\\sigma \\sqrt{2 \\pi}} \\cdot  e^{-\\frac{(x - 5)^2}{2 \\cdot 3^2}} dx\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Чтобы решать реальные проблемы! Например, пусть $X \\sim N(5,3)$. Как найти $E \\left(\\frac{1}{X} \\right)$? \n",
    "\n",
    "- Спосбо второй (ЗБЧ разрешает нам так делать): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0767308182919124"
      ],
      "text/latex": [
       "0.0767308182919124"
      ],
      "text/markdown": [
       "0.0767308182919124"
      ],
      "text/plain": [
       "[1] 0.07673082"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs <- 10^6 # число наблюдений \n",
    "\n",
    "x <- rnorm(n_obs, mean = 5, sd = 3)\n",
    "\n",
    "mean(1/x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Зачем всё это надо?\n",
    "\n",
    "- $X_1, X_2, X_3 \\sim U[0;2]$, независимые\n",
    "\n",
    "- Хотим знать $P(X_1 + X_2 + X_3^2 > 5)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. FALSE\n",
       "2. FALSE\n",
       "3. FALSE\n",
       "4. FALSE\n",
       "5. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] FALSE FALSE FALSE FALSE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.147573"
      ],
      "text/latex": [
       "0.147573"
      ],
      "text/markdown": [
       "0.147573"
      ],
      "text/plain": [
       "[1] 0.147573"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs <- 10^6\n",
    "x_1 <- runif(n_obs, min = 0, max = 2)\n",
    "x_2 <- runif(n_obs, min = 0, max = 2)\n",
    "x_3 <- runif(n_obs, min = 0, max = 2)\n",
    "\n",
    "success <- x_1 + x_2 + x_3^2 > 5\n",
    "success[1:5]\n",
    "sum(success) / n_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Зачем всё это надо?\n",
    "\n",
    "- $X_1, X_2, X_3 \\sim U[0;2]$, независимые\n",
    "\n",
    "- Хотим знать $$P(X_1 + X_2 > 0.8 \\mid X_3 < 0.1)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.415671448688954</li>\n",
       "\t<li>0.721095726825297</li>\n",
       "\t<li>1.74133329978213</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.415671448688954\n",
       "\\item 0.721095726825297\n",
       "\\item 1.74133329978213\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.415671448688954\n",
       "2. 0.721095726825297\n",
       "3. 1.74133329978213\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.4156714 0.7210957 1.7413333"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. FALSE\n",
       "2. FALSE\n",
       "3. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] FALSE FALSE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1.74133329978213</li>\n",
       "\t<li>1.82215116219595</li>\n",
       "\t<li>0.446165119297802</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1.74133329978213\n",
       "\\item 1.82215116219595\n",
       "\\item 0.446165119297802\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1.74133329978213\n",
       "2. 1.82215116219595\n",
       "3. 0.446165119297802\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1.7413333 1.8221512 0.4461651"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs <- 10^6\n",
    "x_1 <- runif(n_obs, min = 0, max = 2)\n",
    "x_2 <- runif(n_obs, min = 0, max = 2)\n",
    "x_3 <- runif(n_obs, min = 0, max = 2)\n",
    "\n",
    "uslovie <- x_3 < 0.1\n",
    "x_1[1:3]\n",
    "uslovie[1:3]\n",
    "x_1[uslovie][1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.045767"
      ],
      "text/latex": [
       "0.045767"
      ],
      "text/markdown": [
       "0.045767"
      ],
      "text/plain": [
       "[1] 0.045767"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs <- 10^6\n",
    "x_1 <- runif(n_obs, min = 0, max = 2)\n",
    "x_2 <- runif(n_obs, min = 0, max = 2)\n",
    "x_3 <- runif(n_obs, min = 0, max = 2)\n",
    "\n",
    "uslovie <- x_3 < 0.1\n",
    "\n",
    "success <- x_1[uslovie] + x_2[uslovie] > 0.8\n",
    "\n",
    "sum(success)/n_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Генерация выборок \n",
    "\n",
    "- С такой же лёгкостью можно генерировать любые выборки"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4</li>\n",
       "\t<li>3</li>\n",
       "\t<li>6</li>\n",
       "\t<li>10</li>\n",
       "\t<li>5</li>\n",
       "\t<li>8</li>\n",
       "\t<li>1</li>\n",
       "\t<li>7</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4\n",
       "\\item 3\n",
       "\\item 6\n",
       "\\item 10\n",
       "\\item 5\n",
       "\\item 8\n",
       "\\item 1\n",
       "\\item 7\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4\n",
       "2. 3\n",
       "3. 6\n",
       "4. 10\n",
       "5. 5\n",
       "6. 8\n",
       "7. 1\n",
       "8. 7\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  4  3  6 10  5  8  1  7"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample(1:10, size = 8)  # выборка без повторений"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>8</li>\n",
       "\t<li>10</li>\n",
       "\t<li>3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>9</li>\n",
       "\t<li>9</li>\n",
       "\t<li>6</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 8\n",
       "\\item 10\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\item 9\n",
       "\\item 9\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 8\n",
       "2. 10\n",
       "3. 3\n",
       "4. 5\n",
       "5. 6\n",
       "6. 9\n",
       "7. 9\n",
       "8. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  8 10  3  5  6  9  9  6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample(1:10, size = 8, replace = TRUE) # с повторениями"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'Решка'</li>\n",
       "\t<li>'Решка'</li>\n",
       "\t<li>'Решка'</li>\n",
       "\t<li>'Решка'</li>\n",
       "\t<li>'Решка'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Решка'\n",
       "\\item 'Решка'\n",
       "\\item 'Решка'\n",
       "\\item 'Решка'\n",
       "\\item 'Решка'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Решка'\n",
       "2. 'Решка'\n",
       "3. 'Решка'\n",
       "4. 'Решка'\n",
       "5. 'Решка'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Решка\" \"Решка\" \"Решка\" \"Решка\" \"Решка\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# неправильная монетка \n",
    "sample(c(\"Орёл\", \"Решка\"), size = 5, replace = TRUE, prob = c(0.3, 0.7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ЗБЧ и монетка"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.299637"
      ],
      "text/latex": [
       "0.299637"
      ],
      "text/markdown": [
       "0.299637"
      ],
      "text/plain": [
       "[1] 0.299637"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <-  sample(c(\"Орёл\", \"Решка\"), size = 10^6, replace = TRUE, prob = c(0.3, 0.7))\n",
    "\n",
    "sum(x == 'Орёл')/length(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 4. Центральная предельная теорема (ЦПТ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ЦПТ \n",
    "\n",
    "- При определённых условиях сумма достаточно большого числа случайных величин имеет распределение близкое к нормальному \n",
    "\n",
    "- __Главное:__ чтобы случайные величины были похожи и не было такого, что одна резко выделяется на фоне остальных \n",
    "\n",
    "- Есть много разных ЦПТ с разными условиями "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Классическая формулировка ЦПТ \n",
    "\n",
    "Пусть $X_1, \\ldots, X_n, \\ldots$ — последовательность независимых одинаковых случайных велчин с конечным вторым моментом $E(X_i^2) < \\infty$. Тогда \n",
    "\n",
    "<br>\n",
    "\n",
    "$$\n",
    "\\frac{(X_1 + \\ldots + X_n) - n \\cdot E(X_1)}{\\sqrt{n \\cdot Var(X_1)}} \\overset{d}{\\to} N(0,1)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ЦПТ и равномерное распределение\n",
    "\n",
    "- Пусть $X \\sim U[-1;1]$, пусть $Y = X_1 + \\ldots + X_n$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n = 10^4\n",
    "X1 <- runif(n, min = -1, max = 1)\n",
    "X2 <- runif(n, min = -1, max = 1)\n",
    "X3 <- runif(n, min = -1, max = 1)\n",
    "X4 <- runif(n, min = -1, max = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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AIIIICAIeAoAEfsNNj26NHD+BdZxysCCCCAAAIIWAukPAjLukhSIIAAAggggICV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\nIL753a//AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(X1, bins = 70)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bB8CFrHf/7iiy/krbfeMsE2lGX//v3l22+/leuvv17uuusu0ysOPew4lIa/CCCA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\n",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(X1 + X2, bins = 70)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ai9Baxribp/Vw/WuPPOO919wGeeeaZd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\nBBA4LPD/a0rPEPNPUywAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(X1 + X2 + X3, bins = 70)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CHt27eXffv2ybnnnisvvPCCDBs2zARl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\nEgIdOnSQmTNnmg5Ljzz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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(X1 + X2 + X3 + X4, bins = 70) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ЦПТ для равномерного\n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/gif_creator/animation_CPT_1.gif\" width=\"650\"> \n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ЦПТ для $\\chi^2_1$\n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/gif_creator/animation_CPT_2.gif\" width=\"650\"> \n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Доска Гальтона \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_galton.png\" width=\"800\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"https://thumbs.gfycat.com/PleasingMeaslyGalapagossealion-max-1mb.gif\" width=\"400\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ЦПТ на пальцевых пальцах\n",
    "\n",
    "- $Y$ — время прихода Стаса на первую пару "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- На Стаса прыгнул кот и он проснулся пораньше, ускорение на $X_1$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Пока готовил завтрак, убежало молоко, задержка на $X_2$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Быстро приехал автобус, ускорение на $X_3$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Встал в неожиданную пробку, задержка на $X_4$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ЦПТ на пальцевых пальцах\n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_milk.png\" height=\"200\"> \n",
    "</center>\n",
    "\n",
    "- Ни одна из величин не выделяется! \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## ЦПТ и ЗБЧ как скорости\n",
    "\n",
    "В ЗБЧ: \n",
    "\n",
    "$$\n",
    "\\frac{X_1 + \\ldots + X_n - n E(X_1)}{n} \\overset{p}{\\to} 0\n",
    "$$\n",
    "\n",
    "<br>\n",
    "\n",
    "В ЦПТ та же дробь домножается на $\\sqrt{n}$, это замедляет сходимость и мы приходим к более интересному результату: \n",
    "\n",
    "$$\n",
    "\\sqrt{n} \\cdot \\frac{X_1 + \\ldots + X_n - n E(X_1)}{n} \\overset{d}{\\to} N(0, Var(X_1))\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Крайнестан и среднестан \n",
    "\n",
    "- ЦПТ и ЗБЧ работают в среднестане \n",
    "\n",
    "- А что, если какая-то одна случайная величина выбивается? \n",
    "\n",
    "- Тогда мы перемещаемся из среднестана в крайнестан и сталкиваемся с проблемой тяжёлых хвостов \n",
    "\n",
    "- О тяжёлых хвостах мы ещё поговорим, они часто выскакивают в мире финансов \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Фальш в среднестане \n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_EGE_poland.jpg\" width=\"800\"> \n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Фальш на выборах\n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_meduza.png\" width=\"1200\"> \n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Фальш на выборах\n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/intro_vote_yavka.jpg\" width=\"700\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5. Решаем вместе задачки на генерации"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 5.1 Камила, Вика и монетки \n",
    "\n",
    "Две монеты, вероятности орла равны $0.6$ и $0.4$. Камила подбрасывает первую монетку до появления орла. Вика вторую.\n",
    "\n",
    "__а)__ Найдите с помощью симуляций вероятность того, что Вика сделает больше подбрасываний, чем Камила"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__а)__ Найдите с помощью симуляций вероятность того, что Вика сделает больше подбрасываний, чем Камила"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n_obs = 10^6\n",
    "p1 = 0.6\n",
    "p2 = 0.4 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 0\n",
       "3. 0\n",
       "4. 1\n",
       "5. 0\n",
       "6. 0\n",
       "7. 0\n",
       "8. 0\n",
       "9. 2\n",
       "10. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 0 0 0 1 0 0 0 0 2 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# симулируем подбрасывания Вики и Камилы\n",
    "x_kamila = rgeom(n_obs, prob = p1)\n",
    "x_vika = rgeom(n_obs, prob = p2)\n",
    "\n",
    "x_kamila[1:10]  # в векторе стоит число подбрасываний до первого орла"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.473411"
      ],
      "text/latex": [
       "0.473411"
      ],
      "text/markdown": [
       "0.473411"
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      "text/plain": [
       "[1] 0.473411"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(x_vika > x_kamila)/n_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__б)__ Камила сделает больше подбрасываний, чем Вика;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>1</li>\n",
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       "\\begin{enumerate*}\n",
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       "\\end{enumerate*}\n"
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       "1. 0\n",
       "2. 1\n",
       "3. 2\n",
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       "8. 2\n",
       "9. 0\n",
       "10. 0\n",
       "\n",
       "\n"
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      "text/plain": [
       " [1] 0 1 2 0 0 1 0 2 0 0"
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     },
     "metadata": {},
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    }
   ],
   "source": [
    "n_obs = 10^6\n",
    "p1 = 0.6\n",
    "p2 = 0.4 \n",
    "\n",
    "# симулируем подбрасывания Вики и Камилы\n",
    "x_kamila = rgeom(n_obs, prob = p1)\n",
    "x_vika = rgeom(n_obs, prob = p2)\n",
    "\n",
    "x_kamila[1:10]  # в векторе стоит число подбрасываний до первого орла"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.210238"
      ],
      "text/latex": [
       "0.210238"
      ],
      "text/markdown": [
       "0.210238"
      ],
      "text/plain": [
       "[1] 0.210238"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(x_vika < x_kamila)/n_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__в)__ Камила и Вика сделают одинаковое число подбрасываний"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.31644"
      ],
      "text/latex": [
       "0.31644"
      ],
      "text/markdown": [
       "0.31644"
      ],
      "text/plain": [
       "[1] 0.31644"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(x_vika == x_kamila)/n_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__г)__ Верно ли, что в сумме эти три вероятности дают единицу? Логично ли это?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(x_vika > x_kamila)/n_obs + sum(x_vika < x_kamila)/n_obs + sum(x_vika == x_kamila)/n_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.2 Человек и параход\n",
    "\n",
    "Иван Фёдорович Крузенштерн (ШТО?!) случайным образом с возможностью повторов выбирает $10$ натуральных чисел от $1$ до $100$. Пусть $X$ — минимум из этих чисел, а $Y$ — максимум. С помощью симуляций оцените:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__а)__ $P(Y > 3X)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>95</li>\n",
       "\t<li>37</li>\n",
       "\t<li>87</li>\n",
       "\t<li>49</li>\n",
       "\t<li>46</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 95\n",
       "\\item 37\n",
       "\\item 87\n",
       "\\item 49\n",
       "\\item 46\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 95\n",
       "2. 37\n",
       "3. 87\n",
       "4. 49\n",
       "5. 46\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 95 37 87 49 46"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "natural <- sample(1:100, size = 5, replace = TRUE)\n",
    "natural"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "37"
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       "37"
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       "37"
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       "[1] 37"
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    },
    {
     "data": {
      "text/html": [
       "95"
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       "95"
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       "95"
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      "text/plain": [
       "[1] 95"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "min(natural)  # случайная величина X\n",
    "max(natural)  # случайная величина Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__а)__ $P(Y > 3X)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n_obs = 10^6\n",
    "x = rep(0, n_obs)  \n",
    "y = rep(0, n_obs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>13</li>\n",
       "\t<li>10</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\item 13\n",
       "\\item 10\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 3\n",
       "3. 5\n",
       "4. 13\n",
       "5. 10\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  2  3  5 13 10"
      ]
     },
     "metadata": {},
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   ],
   "source": [
    "for(i in 1:n_obs){\n",
    "    natural = sample(1:100, size = 10, replace = TRUE)  # сгенерировали выборку\n",
    "    x[i] = min(natural)                                 # нашли минимум и максимум для неё\n",
    "    y[i] = max(natural)\n",
    "}\n",
    "x[1:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. TRUE\n",
       "2. TRUE\n",
       "3. TRUE\n",
       "4. TRUE\n",
       "5. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] TRUE TRUE TRUE TRUE TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "success = y > 3*x\n",
    "success[1:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.971832"
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       "0.971832"
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       "[1] 0.971832"
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     "metadata": {},
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   ],
   "source": [
    "sum(success) / n_obs "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__б)__ $E(X \\cdot Y)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "884.453621"
      ],
      "text/latex": [
       "884.453621"
      ],
      "text/markdown": [
       "884.453621"
      ],
      "text/plain": [
       "[1] 884.4536"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(x*y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__в)__ $P(Y > 3X \\mid Y < X^2)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. FALSE\n",
       "2. FALSE\n",
       "3. FALSE\n",
       "4. FALSE\n",
       "5. TRUE\n",
       "6. TRUE\n",
       "7. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>7</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\item 7\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. 5\n",
       "2. 6\n",
       "3. 7\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 5 6 7"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z <- c(1,2,3,4,5,6,7)\n",
    "z > 4\n",
    "\n",
    "z[z > 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. FALSE\n",
       "2. FALSE\n",
       "3. FALSE\n",
       "4. TRUE\n",
       "5. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] FALSE FALSE FALSE  TRUE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "usl = y < x^2\n",
    "usl[1:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.928028473824471"
      ],
      "text/latex": [
       "0.928028473824471"
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       "0.928028473824471"
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      "text/plain": [
       "[1] 0.9280285"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "success <- y[usl] > 3*x[usl]\n",
    "sum(success) / sum(usl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__г)__ $E(X \\cdot Y \\mid Y < X^2)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1636.77765428219"
      ],
      "text/latex": [
       "1636.77765428219"
      ],
      "text/markdown": [
       "1636.77765428219"
      ],
      "text/plain": [
       "[1] 1636.778"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(x[usl]*y[usl])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "__д)__ $E \\left( \\frac{X}{X + 2Y} \\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0482978237199387"
      ],
      "text/latex": [
       "0.0482978237199387"
      ],
      "text/markdown": [
       "0.0482978237199387"
      ],
      "text/plain": [
       "[1] 0.04829782"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = x/(x + 2*y)\n",
    "mean(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__е)__ $Corr(X,Y)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0986460764318367"
      ],
      "text/latex": [
       "0.0986460764318367"
      ],
      "text/markdown": [
       "0.0986460764318367"
      ],
      "text/plain": [
       "[1] 0.09864608"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.3 Call me maybe "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Известно, что в пятизначном номере телефона все цифры разные. Какова вероятность того, что при этом условии среди них только одна цифра чётная (номер может начинаться с нуля)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>5</li>\n",
       "\t<li>7</li>\n",
       "\t<li>8</li>\n",
       "\t<li>6</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 5\n",
       "\\item 7\n",
       "\\item 8\n",
       "\\item 6\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 5\n",
       "2. 7\n",
       "3. 8\n",
       "4. 6\n",
       "5. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 5 7 8 6 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# генерируем номер телефона\n",
    "sample(size = 5, 0:9, replace = FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 0\n",
       "3. 0\n",
       "4. 1\n",
       "5. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0 0 0 1 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# проверяем все цифры на чётность \n",
    "sample(size = 5, 0:9, replace = FALSE) %% 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "2"
      ],
      "text/latex": [
       "2"
      ],
      "text/markdown": [
       "2"
      ],
      "text/plain": [
       "[1] 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# смотрим сколько в сумме нечётных цифр\n",
    "sum(sample(size = 5, 0:9, replace = FALSE) %% 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.099513"
      ],
      "text/latex": [
       "0.099513"
      ],
      "text/markdown": [
       "0.099513"
      ],
      "text/plain": [
       "[1] 0.099513"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# и всё это в цикле!\n",
    "n_obs = 10^6\n",
    "\n",
    "m = 0\n",
    "for( i in 1:n_obs){\n",
    "    # если 4 нечётные, значит одна чётная\n",
    "    if(sum(sample(size = 5, 0:9, replace = FALSE) %% 2) == 4){\n",
    "        m = m + 1\n",
    "    }\n",
    "}\n",
    "\n",
    "m/n_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.4 О спорт, ты — мир"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Для  $20$  участников соревнований, среди которых  $8$  российских, в гостинице забронировано  $20$  номеров. Из них  $12$  с видом на море. Участники соревнований наугад получают ключи от номернов. Найдите вероятность того, что номера с видом на море достанутся всем российским спортсменам."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'море'</li>\n",
       "\t<li>'море'</li>\n",
       "\t<li>'море'</li>\n",
       "\t<li>'море'</li>\n",
       "\t<li>'море'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'море'\n",
       "\\item 'море'\n",
       "\\item 'море'\n",
       "\\item 'море'\n",
       "\\item 'море'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'море'\n",
       "2. 'море'\n",
       "3. 'море'\n",
       "4. 'море'\n",
       "5. 'море'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"море\" \"море\" \"море\" \"море\" \"море\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# вектор номеров\n",
    "room = c(rep('море',12),rep('пустошь',8))\n",
    "room[1:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'пустошь'</li>\n",
       "\t<li>'пустошь'</li>\n",
       "\t<li>'море'</li>\n",
       "\t<li>'море'</li>\n",
       "\t<li>'море'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'пустошь'\n",
       "\\item 'пустошь'\n",
       "\\item 'море'\n",
       "\\item 'море'\n",
       "\\item 'море'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'пустошь'\n",
       "2. 'пустошь'\n",
       "3. 'море'\n",
       "4. 'море'\n",
       "5. 'море'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"пустошь\" \"пустошь\" \"море\"    \"море\"    \"море\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample(room)[1:5] # перемешаем номера "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>FALSE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item FALSE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. FALSE\n",
       "2. TRUE\n",
       "3. FALSE\n",
       "4. FALSE\n",
       "5. FALSE\n",
       "6. TRUE\n",
       "7. TRUE\n",
       "8. FALSE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] FALSE  TRUE FALSE FALSE FALSE  TRUE  TRUE FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Будем считать что первые 8 позиций вектора относятся к россиянам\n",
    "sample(room)[1:8] == 'море'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.003901"
      ],
      "text/latex": [
       "0.003901"
      ],
      "text/markdown": [
       "0.003901"
      ],
      "text/plain": [
       "[1] 0.003901"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6\n",
    "\n",
    "# комнаты\n",
    "room = c(rep('море',12),rep('пустошь',8))\n",
    "\n",
    "m = 0\n",
    "for(i in 1:n_obs){\n",
    "    if(sum(sample(room)[1:8] == 'море') == 8){\n",
    "        m = m + 1\n",
    "    }\n",
    "}\n",
    "\n",
    "m/n_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.5 Ещё не успели забыть ЗБЧ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- В начале пары мы смотрели такую картинку, давайте нарисуем её сами!\n",
    "\n",
    "<center>\n",
    "<img src=\"intro_lbn.png\" width=\"800\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Игральная кость. Нам хочется узнать какое среднее значение на ней будет выпадать при увеличении количества бросков."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "2"
      ],
      "text/latex": [
       "2"
      ],
      "text/markdown": [
       "2"
      ],
      "text/plain": [
       "[1] 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>5</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 5\n",
       "\\item 3\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 5\n",
       "2. 3\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 5 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4\n",
       "2. 3\n",
       "3. 4\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4 3 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
       "\t<li>6</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 6\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 6\n",
       "3. 1\n",
       "4. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 6 1 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample(1:6, size = 1, replace = TRUE)\n",
    "\n",
    "sample(1:6, size = 2, replace = TRUE)\n",
    "\n",
    "sample(1:6, size = 3, replace = TRUE)\n",
    "\n",
    "sample(1:6, size = 4, replace = TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4</li>\n",
       "\t<li>6</li>\n",
       "\t<li>3.66666666666667</li>\n",
       "\t<li>3.5</li>\n",
       "\t<li>4.2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4\n",
       "\\item 6\n",
       "\\item 3.66666666666667\n",
       "\\item 3.5\n",
       "\\item 4.2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4\n",
       "2. 6\n",
       "3. 3.66666666666667\n",
       "4. 3.5\n",
       "5. 4.2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4.000000 6.000000 3.666667 3.500000 4.200000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 500\n",
    "kubik = rep(0, n_obs)\n",
    "\n",
    "for(n in 1:n_obs){ # n - количество подбрасываний кубика\n",
    "    \n",
    "    # Сделали выборку \n",
    "    smpl = sample(1:6, size = n, replace = TRUE)\n",
    "    \n",
    "    # Подсчитали среднее значение и запомнили его \n",
    "    kubik[n] = mean(smpl)   \n",
    "}\n",
    "\n",
    "kubik[1:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AQ8Xup+DnguVn/n2QgYASMwPARMwOPY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\nARNoSMAJuCF8d20CJmACJtAvgR/fDyy3p507IgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(1:n_obs, kubik, geom='line', xlab='number of observations', ylab='result')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>n</th><th scope=col>kubik</th><th scope=col>mean</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1  </td><td>4  </td><td>3.5</td></tr>\n",
       "\t<tr><td>2  </td><td>6  </td><td>3.5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " n & kubik & mean\\\\\n",
       "\\hline\n",
       "\t 1   & 4   & 3.5\\\\\n",
       "\t 2   & 6   & 3.5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| n | kubik | mean |\n",
       "|---|---|---|\n",
       "| 1   | 4   | 3.5 |\n",
       "| 2   | 6   | 3.5 |\n",
       "\n"
      ],
      "text/plain": [
       "  n kubik mean\n",
       "1 1 4     3.5 \n",
       "2 2 6     3.5 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = data.frame(n = 1:n_obs, kubik = kubik, mean = rep(3.5,n_obs))\n",
    "head(df,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DEOhlKORJbPgjiadqFnTjziwkTrbcPE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vFvVQUQIlRUAVcEmR1uvkJIFzzz2XcmFp0m3bthE2uW/YsCGdd9559MADDxSJN/Y0\nxhrDr7/+epHyKa0nf/jhhzR69GiveO+8847UF8tZqiiBkiKgCrikSOt1lEAxEsCa5lhuD8uG\nLl26VJbfK8bL5XzWRx99NC1YsMCrB1bBa9WqlayU5AXqgRIoZgKx3Q+4mLlq9kqgRAmsW7dO\nrtetWzc64ogjSvTauXgx/y5KKD/Wf49qbz8X709cyqwKOC53OkfqiV1LsMHB9ddfT0uWLJEd\nbjZu3EhNmjSha6+9VhbdR1WwgxX2QsXuN7Vq1fJqt3btWhlaxDAsdkKBPP7447L3c/PmzWns\n2LH0/vvvi5K69NJLqVq1ajRv3jzZGg92wIsvvpiwU0/yerFQcKNGjaIVK1bIMO/ll18u53oX\n/ucAQ5sTJ04UG2z16tWpdevW1LJlSy8ZdmJ57rnnqEePHvToo4/S6tWrZWcW/4L6XuJ/DhYt\nWiR1zc/Pl2FS7BhkdwNCEuwHa4dOwQ7DxwMHDpTF55PzwnfYdTH8unjxYtq+fbuwuOqqq6hi\nxYpByeXa06ZNI+y+c+qpp1L79u0T0lnmuCfYfxXD4F26dKE999wzIZ2LDRKD8X777SdsUa/6\n9etT5cqVCfwHDRokmzb4M8VGGNjYAQvsQzZt2iT3GJw3b95MNWvWlHuAXYMgWDd65MiRsvsZ\nnq/bb7+dunbtKnlg15wOHTrIVn+SmP+52Id9XpEfdm16+eWXafr06YSdsurUqSPmDVs2e039\njBEBdtxQUQKlhsDUqVOxIazhXW3ks3HjxqZu3bpyfNRRRxlWGFJW3uNTwlgxJJR99uzZEs47\nnHjhrLwNK1XDe8ga3v/TsIKQNIcffrhBOt6Jx7Cylnhcm5Wjdy4PVRpewN1UqVLF4Prt2rUz\nvMG3YaVg5s6d66XDAStUwzuuyB/bjiU98rv55pu9dJMmTZJrsxKTT95AwPAuQF588gHv5GK4\nMSDlxjkoM/L0n3PFFVcYfplLOPfkDG+NaNiZKDkr+c6KzLBtV8rIQ66GGwimXLlyhncCM6yQ\nvXOmTJki+YF/hQoVDO9SZJo2bSphPMztpWMFJCxYeRu2lRtWJsKTFZ/hDeS9dGHYIDGuh/Lz\n5goGbPB3//33y3VfffVVLz8csDKVa3FjTcJx73EeK36DunGDy/AGD8LviSeekDS8baHkD4ZV\nq1aVY3ZcM3iOEMZ7FEs6/AvDPuzzivy4kSBlwfPH2y0a3stXvg8bNgzRKjEkgJagihIoNQTs\nCw1Kj3tMXrl4aFVekDNmzJCwdBVwsiLk3pTkV758ecO9HMmTd0QxULhQSFbwHefedNNNNsiw\nd7AoZCgL7tVIOBQRP5SjtwAAB/pJREFUlG+LFi0M98K8tNwTlfPZRithVgGzzdHw/reGe0Jm\nw4YNXnr/wZw5c0QBdezY0aBsEFyvd+/ekueECRO85NxzlDDu1XlhQQe8DZvhrfsM2z+96M8/\n/1waGQ0aNDDszCXhVgFzb9SsXLnSS3vLLbfIdbgnJ2F9+vSRenMv2EvDIwCS5uGHH5awsGyQ\nGEzBG3VEI4J7soZ3sZF7Ag5+GT58uKTlEQ0JPumkkwzup58nyoUGFhpPfkGjhnu+XlCyAg7L\nPuzzyjs+SWPguuuu866JxiSUMZ51HhL3wvUgPgRUAcfnXudETe0L7Y477kgo78yZM+Vly8PJ\nEp6uAsYLl4devTzRe8WLnodevTAcoJeCcNt7gwKuVKlSSo9y8ODBks72Gnv16iXfbQPBZgoF\ny3tNm7Zt20qQVcBQZC7hYVw5Fz09v6AeUIzo4VkJo4ChjFA31DFZ0AtDnG0oWAU8ZMiQhKRQ\niujtoucM6devn5zHw+oJSoSnbnnnhWWDE6CA0ev13yuE85C/KVu2rIEis4J7w/Zu+YqGCQ/t\nGvZmttHeJ0Y/2NTgfceBSwGHZR/2eUW58Rywp7pZv369VxY8H8l19SL1IPIE1AbMbx2V0kfA\nb9dF6WAXhPDLSj7T/cfDfWLDtOdh/1hIjRo1bJB8woYJgW3UCg/7erZnG8aKQg6590isCAif\n/FIXe7N/egsSseIQ27E9F5+w/7kEc3lRPlt3mx62WDhaYUP6dMTODeah5JTTjj32WAmD7RR2\nXiuwvfsFG9+j7KgvBLZe2J0vuugi6t69u3gSY6P4Nm3aeKelywZ2edTRLzzMTk8//bTYUDt1\n6iQ+ALDhci9YkoE97Oiw++bl5Uk8rgtGsE1jH9h0JF32rueVe+bEDREaOnQo8XA/cY+cYMuH\nrwKeH5V4EtBpSPG876W+1lBafsELFsJNYn9wyrFfcfoj4cgTJDw8mRAclD/bQBPS4It1MILj\nFoR7zFSmTBlxEuIenGwObz952JeaNWsm6ey/wspj4/FZUFBAQddGHK6Pub/pCPKDBOVp65Oc\nZ2FpbUOodu3a4ix3zz33EI7ZhkpQkDjmYVy5XibY8PCyONtB2UPgMMU9Spl2JQH/hEF5s32V\n2LZPWFSjc+fO/0nBpcs+zPN63333ibMcHP3WrFlDYAbva5Qx2Svb1kk/o00g8e0T7bpq7SJE\ngJ1rpDbJCgMvtkyIXxGzTTElS6wSBYGXLYSdu2jhwoV01113pfRu8XJNVvRykuMf8vbPVfUn\nh/e07YX7w//t2JYV5yaLDUvOs7C6+3t87JQmXtfwvIZ3L5Qw2zqpf//+Mjc5U2zgeQ6vZXjF\njx8/nrBICubvQuDdzI57wgQ9YHigW4Hnu/9+2vB/+8w0e1wLjcPTTz9der4oD7zQ2UFPvLbR\naPGPPPxb2TQuOgS0BxydexmrmtgpM3ZY1Vb+rbfesocZ+8Qw5qpVqxLyGzNmjEzbsQoLU5cg\neNn7Zfny5dJb7dmzpz841DHyRE8MS0v6BeXBYht2mpU/7t+OMaUHyhJDuckKCT1GiK2PzQfK\n1C/saSws2FNZgjFtB73OLVu2yHe2lxN7aFO9evXIKu9MsUFPEeWGokdDC8PSVsAEDR22tSco\nX0wTwtSx5B4mGnDs2GZPT/nMNHvcL3buowcffFCuhREdDO9jOhrEspIv+i8+BPiBVlECpYaA\ndWp56aWXEsrEikycfeD5CuEXvjgD8RCpgWMWz301bIOUaSj865XpRTYDTENq1KiR/Sqf8MxF\numQnI+sdzS9ESQdHHzjPcI/IwDGJX/TiPYtz/dNH4KXMCk68dVFGTG0ZN26chGHKEvfaJD/r\nhDV58uSE8gR9gcMT24ClnmxXNmzLNPAwxpQhTKfyex6HccLCNXhurdSbbY8yjQpOZNbDHI5l\nVqwTFuoOT2dWIAaOb5i6g+kz8EyGwJsaLJAfpgnNnz/f9O3bV8Kso1lYNsiPGwApHssIt8J2\nXskb08KsxzbiWCHLfQIXnhNtuEdv4BjGPWHDpgGJsx7rSI/pSnDMAg+cm+wFHZZ92OcV18Q0\nLTwLeG7Ak3vxBp7nmDbFDS0kUYkZAbQoVZRAqSGQzgsNHrsHHXSQvJChBDAHdtmyZfI9eR5w\nURQw5vRiLi+UEa6DF6ZtCPjBQcliri6mvSAd/tgWaniFJS9ZOgoYJ3399deGnZrEMxj5YYoU\nphJhKpRfwipgnAM2UEC2jJhD7G9MII1VwGxrlcaHTcs9Q5Ofn48knrAtU5jYNGgUDRgwwJuz\njYRh2CCdSwFj6hWu459bjfMgaJygfPCiRhp4iqNxZtnMmjXr74T8f8SIEeJVjXRPPfVUigJG\nwjDs03le2SnMsLObx517wVJfNNZU4klgJ1SbH0IVJZCzBGC/hBORtQcWV0Xg1MO9TnEGsjbo\noGthaJPnzsqqUPC+tg5kQWnDhsHpCfWE7RXOR5kQ1AX1QBldwkpXnLcKcx5DnZEfBDbfwupc\nHGySyw57MHwDuHGWHJXwHTZZ2Kzx3BRWXpyQafZwSsMOWwfzZhfwjlaJLwFVwPG991pzJaAE\nlIASyCIBdcLKIny9tBJQAkpACcSXgCrg+N57rbkSUAJKQAlkkYAq4CzC10srASWgBJRAfAmo\nAo7vvdeaKwEloASUQBYJqALOIny9tBJQAkpACcSXgCrg+N57rbkSUAJKQAlkkYAq4CzC10sr\nASWgBJRAfAn8H7cX9YlGnHdrAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://colorscheme.ru/color-converter.html\n",
    "ggplot(df, aes(n)) + \n",
    "  geom_line(aes(y=kubik), color=\"#0aa120\", alpha = 0.6) + \n",
    "  geom_line(aes(y=mean), color=\"blue\",size=1.2) +\n",
    "  xlab('number of observations') + ylab('result') +\n",
    "  ggtitle('Law of large numbers')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5.6 Миша продаёт газеты"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Миша и газетный бизнес\n",
    "\n",
    "__Смешная предыстория, которая не влезла на слайд.__\n",
    "\n",
    "Покупать газету Миша решил по $15$ рублей, а продавать за $30$. Количество потенциальных покупателей - случайная величина с распределением Пуассона. Опытным путём было установлено, что среднее значение этой величины равно $50$. Нераспроданные газеты ничего не стоят. Пусть $n$- количество газет, максимизирующее ожидаемую прибыль Мишы. \n",
    "\n",
    "С помощью компьютера найдите оптимальное значение $n$ и ожидаемую прибыль."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Стохастическая прибыль\n",
    "\n",
    "$$\n",
    "\\Pi = 30 \\cdot X - 15 \\cdot n \\to \\max_{n} \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>51</li>\n",
       "\t<li>40</li>\n",
       "\t<li>35</li>\n",
       "\t<li>62</li>\n",
       "\t<li>53</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 51\n",
       "\\item 40\n",
       "\\item 35\n",
       "\\item 62\n",
       "\\item 53\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 51\n",
       "2. 40\n",
       "3. 35\n",
       "4. 62\n",
       "5. 53\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 51 40 35 62 53"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1230</li>\n",
       "\t<li>900</li>\n",
       "\t<li>750</li>\n",
       "\t<li>1560</li>\n",
       "\t<li>1290</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1230\n",
       "\\item 900\n",
       "\\item 750\n",
       "\\item 1560\n",
       "\\item 1290\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1230\n",
       "2. 900\n",
       "3. 750\n",
       "4. 1560\n",
       "5. 1290\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1230  900  750 1560 1290"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "1199.89653"
      ],
      "text/latex": [
       "1199.89653"
      ],
      "text/markdown": [
       "1199.89653"
      ],
      "text/plain": [
       "[1] 1199.897"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_obs = 10^6  # число наблюдений \n",
    "\n",
    "cost = 15   # издержки на покупку газеты \n",
    "price = 30  # цена, по которой будем продавать газету \n",
    "\n",
    "x = rpois(n_obs, lambda = 50)  # среднее значение совпадает с lambda\n",
    "x[1:5]\n",
    "\n",
    "profit = x*price - 20*cost \n",
    "profit[1:5]\n",
    "\n",
    "# найдём среднюю прибыль \n",
    "mean(profit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "n_obs = 10^6  # число наблюдений \n",
    "\n",
    "profits = rep(0,100) # будем записывать средние прибыли\n",
    "for(s in 1:100){\n",
    "    x = rpois(n_obs, lambda = 50)  # генерируем покупочки \n",
    "    \n",
    "    x[x > s] = s  # нельзя продать лишнее\n",
    "    \n",
    "    profits[s] = mean(x*price - s*cost)  # запоминем среднюю прибыль\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Vxy4H8LTCpVqqTiCMNAEw/fTk+63lN0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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qplot(1:100, profits, geom='line')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "665.65521"
      ],
      "text/latex": [
       "665.65521"
      ],
      "text/markdown": [
       "665.65521"
      ],
      "text/plain": [
       "[1] 665.6552"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "50"
      ],
      "text/latex": [
       "50"
      ],
      "text/markdown": [
       "50"
      ],
      "text/plain": [
       "[1] 50"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max(profits)\n",
    "which.max(profits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "207.004054023229"
      ],
      "text/latex": [
       "207.004054023229"
      ],
      "text/markdown": [
       "207.004054023229"
      ],
      "text/plain": [
       "[1] 207.0041"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sqrt(var(profits))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Дисперсия прибыли"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "n_obs = 10^6  # число наблюдений \n",
    "\n",
    "profits = rep(0,100)    # будем записывать средние прибыли\n",
    "std_error = rep(0,100)  # сюда будем записыват ошибку\n",
    "for(s in 1:100){\n",
    "    x = rpois(n_obs, lambda = 50)  # генерируем покупочки \n",
    "    \n",
    "    x[x > s] = s  # нельзя продать лишнее\n",
    "    profits[s] = mean(x*price - s*cost)         # запоминем среднюю прибыль\n",
    "    std_error[s] = sqrt(var(x*price - s*cost))  # запоминаем дисперсию\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>s</th><th scope=col>profit</th><th scope=col>std_error</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1 </td><td>15</td><td>0 </td></tr>\n",
       "\t<tr><td>2 </td><td>30</td><td>0 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " s & profit & std\\_error\\\\\n",
       "\\hline\n",
       "\t 1  & 15 & 0 \\\\\n",
       "\t 2  & 30 & 0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| s | profit | std_error |\n",
       "|---|---|---|\n",
       "| 1  | 15 | 0  |\n",
       "| 2  | 30 | 0  |\n",
       "\n"
      ],
      "text/plain": [
       "  s profit std_error\n",
       "1 1 15     0        \n",
       "2 2 30     0        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = data.frame(s = 1:100, profit = profits, std_error = std_error)\n",
    "head(df,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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g4BCuDo9DVbSgJdEsBSKIQAk38EYPSG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\ncI0ABbBrKJkRCZAACZAACdgn8P9ZJ3RYdespaQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(df, aes(s)) + \n",
    "  geom_line(aes(y=profit), colour=\"blue\") + \n",
    "  geom_ribbon(aes(ymin = profit - 2*std_error,\n",
    "                  ymax = profit + 2*std_error), alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 5.7 Зёрна \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "6.11287534144001"
      ],
      "text/latex": [
       "6.11287534144001"
      ],
      "text/markdown": [
       "6.11287534144001"
      ],
      "text/plain": [
       "[1] 6.112875"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(42)\n",
    "rnorm(1, mean = 2, sd = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.212804969423"
      ],
      "text/latex": [
       "3.212804969423"
      ],
      "text/markdown": [
       "3.212804969423"
      ],
      "text/plain": [
       "[1] 3.212805"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rnorm(1, mean = 2, sd = 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 6. Случайные величины бывают очень разными"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "picture <- function(x){\n",
    "    df = data.frame(sample = x)\n",
    "\n",
    "    # Размеры картинки \n",
    "    options(repr.plot.width=8, repr.plot.height=3)\n",
    "\n",
    "    binwidth = 1  # ширина бинов\n",
    "    p1 = ggplot(df, aes(x = sample, binwidth = binwidth))+\n",
    "            # Наносим гистограмму \n",
    "            geom_histogram(aes(y=..density..), binwidth = binwidth, colour = \"white\", \n",
    "                                               fill = \"cornflowerblue\", size = 0.1)\n",
    "                                            # цвет линий разделителей, заливка, толщина линий разделителей\n",
    "\n",
    "    p2 = ggplot(df, aes(x = sample, binwidth = binwidth))+\n",
    "            stat_ecdf(color = \"darkred\", size = 1)\n",
    "\n",
    "    # Располагаем графики рядом. Этот код нужен только для юпитерской тетрадки. \n",
    "    pushViewport(viewport(layout = grid.layout(1, 2)))\n",
    "    print(p1, vp = viewport(layout.pos.row = 1, layout.pos.col = 1))\n",
    "    print(p2, vp = viewport(layout.pos.row = 1, layout.pos.col = 2))\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Как бы вы замоделировали подбрасывание монетки? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{equation}\n",
    "\\begin{aligned} \n",
    "& X \\sim Bern(p) \\\\\n",
    "& E(x) = p  \\\\\n",
    "& Var(X) = p \\cdot (1-p)\n",
    "\\end{aligned}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Как бы вы замоделировали число попаданий в баскетбольную корзину?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{equation}\n",
    "\\begin{aligned} \n",
    "& X_i \\sim Bern(p) \\\\\n",
    "& Y = X_1 + \\ldots + X_n \\quad \\Rightarrow \\quad Y \\sim Bin(p,n)\\\\\n",
    "& P(Y = k) = C_n^k \\cdot p^k \\cdot (1-p)^{n-k} \\\\\n",
    "& E(x) = n \\cdot p  \\\\\n",
    "& Var(X) = n \\cdot p \\cdot (1-p)\n",
    "\\end{aligned}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Биномиальное распределение используется для моделирования числа успехов в серии из $n$ испытаний"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LwqQADs1T1D\nuRBAAAEEEEAAAQQQQAABBBwVIAB2lJPMEEAAAQQQQAABBBBAAAEEvCrAKNBe3TOUCwEE0kog\nJ0skJC58pWZkWBnXSIaVOwkBBBBAAAEEEECgdQIunK21rkC8GwEEEEhHgYrqTLnvz1aY6nCc\nmp2VIddekCMdCqvSkYUyI4AAAggggAACnhIgAPbU7qAwCCCQrgIa+O7YVys1tc7WoEMbq6dK\niN4qzqqSGwIIIIAAAggEVYCzqqDueeqNAAIIIIAAAggggAACCARMgAA4YDuc6iKAAAIIIIAA\nAggggAACQRUgAA7qnqfeCCCAAAIIIIAAAggggEDABAiAA7bDqS4CCCCAAAIIIIAAAgggEFQB\nAuCg7nnqjQACCCCAAAIIIIAAAggETIAAOGA7nOoigAACCCCAAAIIIIAAAkEVIAAO6p6n3ggg\ngAACCCCAAAIIIIBAwAQIgAO2w6kuAggggAACCCCAAAIIIBBUgeygVpx6p1bgYGWe7D/sfBmK\n8vWQrnY+Y3JEAAEEEEAAAQQQQACBtBcgAE77XZieFdiyO1PmLD/ieOEHHuV4lmSIAAIIIIAA\nAggggAACPhEgAPbJjkzHalS50FAbColkZKSjBmVGAAEEEEAAAQQQQAABtwXoA+y2MPkjgAAC\nCCCAAAIIIIAAAgh4QoAW4Di7IcNqTszNzY2zVmKLnconsa0ld63MzG+upSRax8zMdGymdbHM\nadhs7aJGerbiu7gPs7Kzre+h+J/prKwss5L+TfSzGD9Xb62RbVno942X66e/GyQEEEAAAQQQ\n8KYAAXCc/aInMgUFBXHWir/YqXzibyk1a9gBcKJWmVl1rhU0Q9Lv5DMdT5hdLXMaBhBuHne5\nOTnW91BO3M+MHQBrcGh/JuO+Kc1W0Dpq3RL9rklF9erq3Pt+S0V92CYCCCCAAAJ+EiAAjrM3\n9UTm8OHWD1ecl5cnBw8ejLO19F3csWNH0RPTROtYU936iwqNaYXE6gjsSnIrX5FQGp4w12mH\na5dSqM69vF0qsoRC7gU9FRUVcjCzKm7RNSjU7xpdv7y8PO766bhCfn6+af0tLS31bPH1u7C4\nuNiz5aNgCCRT4ODmzbLvyy8T3mR2VrbkWZ/zsrL45177N25MOF9WRAABBGwBAmBbgr8IIIAA\nAggggAACjglsfO01+b8TfpmWF3kdQyAjBBDwnACDYHlul1AgBBBAAAEEEEAg/QXW/+f/S2rw\nm2V1FyEhgAAC8QRoAY4nxHIEEEAAAQQQSLqADnjWpUuXetvVPuANza+3oo9maL/+dKxzTuY3\nA/MlY1ccf+k46dGnTzI25co2tNtEUVGRK3l7LVN7DJE2bdp4rWiulMeub4cOHVzJ34uZ6vd0\nSUlJ0otWXZ3YM1YJgJO+a9ggAggggAACCMQTqKmpkV27dtVbTQPBhubXW9EHM/TEuVu3blJV\nVSX79u1LuxpVHqkMlzmvbVv50X/8KTzd2Ivs7CzRvv6HD5c1tkq9+bnFRdL1pJPS8rjQcRt0\nHBUdb6asLPE610NIoxka7NfW1prxKtKo2C0ualvr2NeLG/v375dEA7QWb8wjb9Tg98CBA2Y/\nJ7NIOgaHfn/ESwTA8YRYjgACCKRYYMu+HFm1Pv7o5hlWp5bsrENSU2sNBVeXF7fUPUqy5KQ+\nlcKoxXGpWAEBBFopkGndntz7+8Pj5pJjrafBgp48kxBAAAE3BAiA3VAlTwQQQMBBgc+/qpE3\n/5HYbT3N2ezQY0MyuG/8wLo5ebIuAggggAACCCDgZQEGwfLy3qFsCCCAAAIIIIAAAggggAAC\njgkQADtGSUYIIIAAAggggAACCCCAAAJeFiAA9vLeoWwIIIAAAggggAACCCCAAAKOCRAAO0ZJ\nRggggAACCCCAAAIIIIAAAl4WIAD28t6hbAgggAACCCCAAAIIIIAAAo4JEAA7RklGCCCAAAII\nIIAAAggggAACXhYgAPby3qFsCCCAAAIIIIAAAggggAACjgkQADtGSUYIIIAAAggggAACCCCA\nAAJeFiAA9vLeoWwIIIAAAggggAACCCCAAAKOCRAAO0ZJRggggAACCCCAAAIIIIAAAl4WIAD2\n8t6hbAgggAACCCCAAAIIIIAAAo4JZDuWExn5UiAzK7FDJGTVvq4uJImu70ssKoUAAggggAAC\nCCCAAAKeFkgsuvF0FSicWwIHK3LlyeUi1bUa3sZLh/53hYx4K0qG9d9ZJ3LzQVwoVkAAAQQQ\nQAABBBBAAAFHBQiAHeX0W2YhOVgWkr2ldY5WLNOKkUOhHEfzJDMEEEAAAQQQQAABBBBAIJ4A\nzXDxhFiOAAIIIIAAAggggAACCCDgCwECYF/sRiqBAAIIIIAAAggggAACCCAQT4BboOMJsRwB\nBBBAAAEEEPCpwFcrV8qhr7e6UrvSLVtcyZdMEUAAgdYIEAC3Ro/3IoAAAggggAACaSqwavoM\nWXnf/WlaeoqNAAIItEyAW6Bb5sa7EEAAAQQQQACBtBbY+Ne/Jq382fn5SdsWG0IAAQSaEiAA\nbkqHZQgggAACCCCAgE8F6mpqk1azk355VdK2xYYQQACBpgS4BbopHZYhgAACCCCAAAIBEOh8\n/CC54JGHXalpQceOUty9uyt5kykCCCDQXAEC4OaKsT4CCCCAAAIIIOAzgZzCQuk8aJDPakV1\nEEAAgfoC3AJd34Q5CCCAAAIIIIAAAggggAACPhQgAPbhTqVKCCCAAAIIIIAAAggggAAC9QW4\nBbq+CXMQQAABBBBAAIGUC2z/8EN5+cGH5PCu3VJb6/yAVQc2bUp5HSkAAgggkGwBzwbAW6yH\np6+0Hs7e0Ro4YdiwYVJcXNykTbz1Dx06JG+//bbo39NPP1169+7dZH7ptHBfWZ5UVrtR4iwr\n0yo3MiZPBBDwgEBhXoZsP5grNTV1jpemXWGdFOW68sXkeFnJMFog3u9p9Noi8db38+9vrIXT\n08sn3yp7v/jC6WzJDwEEEAi0gCcD4Llz58rs2bPl7LPPlm3btolOz5gxQzp06NDgzoq3/saN\nG+Waa66R/v37S8+ePeWJJ56Qu+++W84444wG80u3ma9/IvL++hrHiz1yiAbAJAQQ8KtAYX6m\n/OnVGjlc4XwAfM0FOXJ0NwLgdDt24v2extYn3vp+//2N9XB6+tD27U5n2Wh+7fr0aXQZCxBA\nAAE/CXguANYryXPmzJHp06fL4MGDrZaJGpk4caIsWLDA/I3FT2T9e+65Ry6++GK5+eabJSMj\nQ5555hl55JFHZP78+WY6Ns90m66tC1knsCHHix0S5/N0vJBkiAACLRYIWR/x2lq3vj9aXCze\nmCKBRH5PI4uWyPp+//3dv2GDfPr8C1JdVhZJ49jrmsrKcF6FXbpIyTFHh6edfNHWuivuzCm/\ncTJL8kIAAQQ8K+C5AHjVqlXSo0cPE/yqWnZ2towaNUpeeOGFBgPgeOvv3btXPvvsM/ntb38b\nDnZHjx5tWpjXrl0rg5I05P+Bw3Wy+1Cu4yFlZmaG43l69milYAggkDYCmZlZssv6znM65VVl\nSbY1fGNZhQt5W7+I7QqC2+0j3u9p7L6Mt35rf3/3fP65fDx/QexmpaioSMoSDDg1gNy5+mOp\nrTpSLx8nZuz78n/kyMGDTmQVN49+550r5z/8UNz1WAEBBBBAoGkBzwXA263bffQ25cikAfGe\nPXukrq5OMjOjB66Ot/6OHTtMVpqHnUpKSiQ3N1d27doVFQDv27dPHnjgAXs183fEiBGmD3LU\nzBZMrP2qVp54xbrN0OFG1fzcDDm6Z7a0KcxoQamafkt+jnWimVXjeN5a0pysTMfz1dro4ZFl\n/c8NDy1zVlaGlXfTbs1dmmndlZCVneVKmbM1b+tOdjc8cq0oJC8nQ3Ic/hbJsi7qZBtn54/p\nwjzdh+54ZFnHR2G+dUHK4c+4BnvZLn1eCvKyLA/nP+P6GThUmSnP/tX5W6v7dK2V/Nxa+fwr\n5/M+b3CejBla0NyPcL319bcqHVO839Nk//4eYwW66x55NB0pXSlzW6sFuF27dq7k7aVM9TjT\nxo8g1FXds/RHyUr5+fmm3mbC5//Lyckx5/R6Lh6EpPXVpOMZpevvQ3P3kx7Xbdq0sc6JHD4p\nilOQRH0dPnWNU6oEFmvA2rZt26g1FVArdNC6yhrbDzje+vqDnpeXZ/5FZqp57t+/P3KWuaL8\n5z//OWred77zHRk5cmTUvJZM9O9RK7/9aTun418xIYL1vx+d4XBUZlXSikHk1IH5UufCwauB\n5HF9nf/iM5dHrKDPjTJrIHLid/Ic/zDrPrTiG/neMXktObSafI/eIaAHnRseGqge19cdD72Q\n8f0TWx+IxOLoMX3u4AJXPPT4OLa383d56PGhu3HUae58xk8/1p3PeLZV6AFHufQZt/Kus7p+\nOJ3yc62LGIWt/1msqkrPVuR4v6fJ/v0dP+pCp3exq/ll5Vonudbvj9NJu251P/FEOefXt1rH\np/PfA06X16n8NAgOUtJgMCgBYZD2a2Rd9SJHkFJBgfPncfH8Ev399dy3i14l0X6/kcmebuiL\nP976DS3XvPVxArH5devWTZYuXRq56XBLcdTMFkxoq3NNxYEWvDM93tK+ffvmW3nu6GvaWq9G\nl5Udrnd8Nv2uZiy1AqhUJr0yqZ8JvRPC/sylsjzigofeOqmf/cqIfnWO1tGFMjenfPrjqhcQ\nddTdioqK5rzVnXVd8NALmvq9fvjwYefLbDXcWjcGtTppC1anTp1anU+yM2jo99L+Loj9vdSy\nxVu/oeX6vkR/f7e8/jdZpm9wIJUMOEZy4zxNoqWbybD2d6+hQ2X4b6eIvnYyafDbuXNn0ZO6\nAwcOmDvXnMzfi3npcaMnzqWlpV4snuNl0qBXz6H0O628vNzx/L2Yoeu/xR6rtOfOr5Lgo8e0\nnou48fi2poqf6O+v50IQPWnYFPNcOv0S1CvPeuITm+Ktr8sVX79UIn/ANc/u3btHZadfutri\nG5m01dmpL6RkHwSR9XD7tX2Lg9/rqPXzax3t20b0r5/r6Pf66Wfd73XU7xu/HqNuf1c3lX+8\n39PY98Zbv7W/vx2t3/3+554Tu1kTEO7evbve/MZmZFq34mUnoeXF3Glj/UY4mTQA1hSkY15P\nYINU3yD89sZ+JrTOfv6diq2vfY4cpDqrgZfPmZ29VBm7x1sw3a9fP1m3bl1UC9SaNWvq9Qu2\ns463fq9evUyfCs3DTjoolh6Ekf2C7WX8RQABBBBAIIgC8X5PY03ird/a318NXHOtuzZi/+VZ\nLbmx85qaTkbwG2vDNAIIIICAdwU8FwDb/W3nzZtngtQN1iMG9Lbk8ePHhxV1mR3Qxltfb1u9\n4IILzKOV9PYSvfVRnzGsI0vrbUUkBBBAAAEEEJDweBf8/nI0IIAAAgj4WcBzAbDe5jx16lRZ\nvHixCVInT54s48aNixqJedasWbJ69WqzXxJZX58jrH0sLrroIrnkkktMi/CNN97o5/1K3RBA\nAAEEEGiWQCK/p/z+NouUlRFAAAEEPCiQYd2X7vxQmg5VdOfOnaaVVvuDJJLira/9fnVYbu18\nn2hyqg9wF+vxBfrYJb+mjh07mj7aOuq2X5P2Q9cO/fagMH6rp46MrgM16CPHqqur/VY9Ux+t\nn/ZJ8cQAUS4I68AxOvCEU99bLhSx1VnqQF96QdPLA+To74x+56dzivd7Glu3eOs7+fvr99/T\nSFvtA6wDdB45csQMUBi5zK+vdTwWPU/TQb+CkPTCk55D6Wck0edbp7uL33+LY/ePDk6px7Sf\nz69i66yD/+pnONnjdST6++u5QbAiAbt27Ro5Gfd1vPVjH68UN0NWQAABBBBAIIAC8X5PY0ni\nrc/vb6wY0wgggAACqRJIrGk1VaVjuwgggAACCCCAAAIIIIAAAgg4JEAA7BAk2SCAAAIIIIAA\nAggggAACCHhbgADY2/uH0iGAAAIIIIAAAggggAACCDgkQADsECTZIIAAAggggAACCCCAAAII\neFuAANjb+4fSIYAAAggggAACCCCAAAIIOCTg6ccgOVTHVmWjQ9JXVla2Kg99sz6exK+PXtH6\nbdmyxQzfP3DgQNHHNvgx6aMKqqqqxMNPDmsVuz7GZN++fdK3b19zvLYqM4++WR+vofvPr4+y\n0scfbdu2Tbp3724eh+TR3dCqYukjDvSffha9mvTRffrYNFLrBBr7/fX772mkWl1dnXz++efm\nESq9e/eOXOTb1/r50e9qffRTENLhw4flq6++Mo9O00fHBCH5/bc4dh/qY1D37t0r/fr1E32U\nXxCS1lM/w8k+Z07095cAOAhHYRLqOH78eFm1apX84x//MM/oTMIm2YTDAvfcc488/fTTsmDB\nAhk8eLDDuZNdMgSWLFkiv/nNb+SOO+6QK6+8MhmbZBsIIOCigF4EOPnkk2XYsGEyZ84cF7dE\n1qkSWL58uUyaNEluvfVWuf7661NVDLbrosBdd90l8+bNk0WLFskJJ5zg4pbIOlEBboFOVIr1\nEEAAAQQQQAABBBBAAAEE0lqAADitdx+FRwABBBBAAAEEEEAAAQQQSFSAADhRKdZDAAEEEEAA\nAQQQQAABBBBIawH6AKf17vNO4d9//33Zv3+/jBgxQrQDOin9BHSgFR3M7LTTTpN27dqlXwUo\nsWzfvl0+/fRT0cHojjrqKEQQQCDNBWpra+X111+Xjh07yimnnJLmtaH4DQnoAEkff/yxHH30\n0WYQyobWYV56C6xbt84MdHb66adL27Zt07syPik9AbBPdiTVQAABBBBAAAEEEEAAAQQQaFqA\nprqmfViKAAIIIIAAAggggAACCCDgEwECYJ/sSKqBAAIIIIAAAggggAACCCDQtEB204tZikDT\nAocOHZJ33nmn3krnnnuueZB9vQXM8JTAm2++KW3atJEhQ4ZElUv369tvvy36V/us9O7dO2o5\nE94R2Lp1q6xcuVIuu+yyqELp/tNniEamY489lr7BkSC8RsDDAl9++aVs2LAhqoTaF/h73/te\n1Dwm0k+gse9t7fO9evVqWbt2rRnL4dRTT02/ylFiI9DQ+RXnzN45OAiAvbMv0rIkOnDDtGnT\npFOnTlHlHzp0KAFwlIj3JvRH9ve//71cd911UQHwxo0b5ZprrpH+/ftLz5495YknnpC7775b\nzjjjDO9VIuAlOnz4sEyZMkXy8vKiAmA9idJ9qxc3srO//Zq//vrrCYADfsxQ/fQReOGFF+St\nt94yn2O71CeccAIBsI2Rpn+b+t6eOHGiGcxw+PDh8uKLL4o2Jtxyyy1pWtPgFrux8yvOmb1z\nTHx7ZuSdMlGSNBJYv369DBo0SB5//PE0KnWwi1pTUyNz5841/zIyMuph3HPPPXLxxRfLzTff\nLLr8mWeekUceeUTmz59vpuu9gRkpEXjvvffk/vvvlwMHDki/fv2iyvDVV19JVVWVPPnkk1JS\nUhK1jAkEEEgPgS+++MJcoPzxj3+cHgWmlHEFmvre1oBXg+MFCxZIUVGRbN68WcaPHy8/+tGP\nZMCAAXHzZoXUC8Q7v+KcOfX7yC4BfYBtCf62SEA/zHwxt4guZW9aunSpvPLKK6blPvZROXv3\n7pXPPvtMxowZEw52R48eLdu2bTO3ZKWs0Gw4SkBvo7r99tvlwgsvlCuuuCJqmU7o51LvyiD4\nrUfDDATSQuDIkSPmsXT8vqbF7kqokPG+t7W1//zzzzfBr2bYp08fOf7442X58uUJ5c9KqRdo\n6vxKS8c5c+r3kV0CAmBbgr8tEtAPsz7/V2/DvOSSS+S3v/2taN8WkncFzjzzTNOa29AtzTt2\n7DAF79GjR7gCGkTl5uaKPquQ5A2BgoICc3vctddeG3WLs1067Tuotz8//PDDcumll4qup/2R\nSAggkB4C2hWlrq5O3n33XdMl5fLLL5dZs2aJBsak9BSI972tz3GP/O3VWuo0v73ps7+bOr/S\nWnDO7J19SQDsnX2RdiXRq5kaMO3Zs8fcMqsn2foFfsMNN5jbeNKuQgEpsAa0kf1CI6ut+0/7\nk+q/yKTBlF7oIHlDQPdfU627euvkvn375JhjjpHbbrvN9OX+13/91wYHrPNGjSgFAghECuiJ\nsiYNePU3dcSIEfLyyy/LQw89FLkar9NIoKnvbb11Vs+l2rZtG1UjndbvclJ6CDR1fsU5s7f2\nIX2AvbU/0qo0xcXFsnDhQtFRKbWFUNNxxx0nEyZMkNdee83cRptWFaKwZuAy/SGOTTqoUmFh\nYexspj0q8Ic//MG0HnXo0MGUUFv7tVVY+5bpAHUkBBDwtsAFF1xgBrvq3r27KejJJ58sWVlZ\n8vTTT8ukSZPqBUrerg2liyeg+zYzM1Nif391WvsDk9JfgHNmb+1DWoC9tT/SqjQ6QFK3bt3C\nwa8WXkcO7ty5s2kJTqvKUFgjoP1GNdgtLy+PEiktLRX7RCxqAROeFGjXrp3Ywa9dQA18tYWf\nhAAC3hfQu3Biv3Ptbit2VxXv14ISJiqg51PamKCthJFJf3v1PIuU/gKcM3trHxIAe2t/pFVp\nNm3aZFp7dcRZO+kJ9u7du80tl/Y8/qaPQK9evczt0WvWrAkXWgfF0r5osX2TwivwwnMCv/nN\nb2TRokVR5dLHL7APo0iYQMCzAvr51c9xZNLPsJ5ExwbGkevwOn0FtAEh8rdXa6LPA9bHEZLS\nX4BzZm/tQwJgb+2PtCpN3759JT8/3wzMof1DNfidOXOmaXnS/kqk9BPQlkO99W7OnDmmH3dl\nZaXMnj1bRo0aZVr2069GwSzxkCFDzGOutB+h9iF86aWXZN26dfKTn/wkmCDUGoE0Exg2bJjo\nI3O036/eBvvBBx+Y1/pdrGMykPwnoI+7+utf/2qC3lAoZL639XF2P/zhD/1X2QDWiHNmb+10\n+gB7a3+kXWkmT54sd911l4wdO9aUXa9gPvbYY/QXTbs9+W2BJ06cKHfeeadcdNFFZjCsk046\nSW688cZvV+CV5wX0MVaffPKJXH311aaLgt5OqYNg0f/X87uOAiJgBPRuDR38Sn9PZ8yYYbqm\n/OAHP5BbbrkFIZ8K6C3uP/3pT81+z8nJMS2/v/vd70T7jpL8IcA5s3f2Y4Z1lSnkneJQknQV\n0NEL9QtbWxBJ/hDQvkc6MAcDcKTv/iwrKzN9yrp27Rp+rnP61oaSIxA8AW391cfg6PgM9mCT\nwVMIVo211Vd/f3Wfk/wpwDlz6vcrAXDq9wElQAABBBBAAAEEEEAAAQQQSIIAfYCTgMwmEEAA\nAQQQQAABBBBAAAEEUi9AAJz6fUAJEEAAAQQQQAABBBBAAAEEkiBAAJwEZDaBAAIIIIAAAggg\ngAACCCCQegEC4NTvA0qAAAIIIIAAAggggAACCCCQBAEC4CQgswkEEEAAAQQQQAABBBBAAIHU\nCxAAp34fUAIEEEAAAQQQQAABBBBAAIEkCBAAJwGZTSCAQH2B8vJy2bx5s1RWVtZfyBwEEEAA\nAQQQcEWA319XWMk0jQQIgNNoZ1FUBPwk8Oqrr0rfvn3ljTfe8FO1qAsCCCCAAAKeFuD319O7\nh8IlQYAAOAnIbAIBBBBAAAEEEEAAAQQQQCD1AgTAqd8HlAABBBBAAAEEEEAAAQQQQCAJAtlJ\n2AabQACBJAjU1dXJ4sWLZdmyZbJv3z455phj5Ic//KF8//vfj9r67t275dlnn5V169bJ/v37\n5Tvf+Y6MHj06ar0//elP0rFjRxk+fLhZ98MPP5STTjpJfv7zn8tRRx0l77zzjixcuND0373y\nyivlzDPPlIyMDLOd9evXy3PPPSf/9E//JK+//rr85S9/kQ4dOsiPfvQjOeeccyQrKyuqPLET\nNTU1MmfOHFm1apVoP6UhQ4bIddddJ+3atYtdlWkEEEAAAQRSLsDvb8p3AQVAoHkCIRICCPhC\n4KabbgpZQWjohBNOCP34xz8O9ejRw0w//PDD4fq99dZboc6dO4eKi4tD559/fsgKcENWQGrW\ne/LJJ8PrnXrqqSErqA3169cv1L9/f5On9c0SGjRoUOipp54KZWdnh6zA1CzX+ZMmTQq/95VX\nXgnpvAsvvDBUUlISuuqqq8y2dN7kyZPD6y1atMisZ/VFCs/btWtX6Hvf+56ZbwXwoUsuuSTU\nvn37UJ8+fUJr1qwJr8cLBBBAAAEEvCLA769X9gTlQCAxAUlsNdZCAAEvC5SWlppA1mp1DRez\ntrbWBK5du3YNWa2qZv5ZZ50VatOmTWjHjh3h9b766isT0J588snheRoAa8D661//Ojzvd7/7\nnZmn7//73/9u5ldVVYVOOeWUUFFRUXg9OwDWQHvDhg3h+dOmTTPv//Of/2zmNRQAX3311VHr\n6IrWSNGh7t27h6yW7HBevEAAAQQQQMALAvz+emEvUAYEmidAH2DrLJ+EgB8EMjMzxWolle3b\nt5vq6PR///d/y6ZNm8xtx9ZXg9x+++3yn//5n2IFxeEq9+rVS04//XTRW6Mjk97SPHXq1PAs\nvZ1a009/+lOxWmnN65ycHHP7c1lZmezdu9fMs//3z//8z2K1INuTcuutt0qnTp3kpZdeCs+L\nfHHgwAFz6/PQoUNl7Nix4UW9e/cWvc16xYoV8sknn4Tn8wIBBBBAAAEvCPD764W9QBkQSFyA\nPsCJW7EmAp4VsFplxbq9WO6//37p2bOnWK25Yt2CLNYtxGK10Jpya0D7gx/8wPT71SB07dq1\n8vnnn8tHH31kXkcGxfoG6xZqyc/PD9fZatE1r63bkcPz9IXdN9dqcY6ar0F1ZMrNzZWBAwea\n7UXOt19r32EN0q2r6fKTn/zEnm3+fv311+bvF198ISeeeGLUMiYQQAABBBBIlQC/v6mSZ7sI\ntFyAFuCW2/FOBDwlcN9998nSpUtNa+mWLVvk7rvvNi21EyZMEB1YStPcuXPNIFZWH2Gx+vKa\nQaZ0uR0kR1bI6r8bORl+bfX/Db/WFxq0NpSsvrv1ZhcWFsrBgwfrzdcZe/bsMfMLCgpEr6ZH\n/tNW4Msvv1z0RIOEAAIIIICAlwT4/fXS3qAsCMQXiD6Tjb8+ayCAgEcFtAX2ggsuMC2/GpS+\n//77YvXhNaM4/+IXv5Djjz9erD62MnjwYHMbsgaVdtJRoRsLZO114v2Nfb+22sYG1lZ/XtM6\n3VBe1mBbZraOXj1v3ryoVbRu8UaPjnoDEwgggAACCCRJgN/fJEGzGQQcEqAF2CFIskEglQKr\nV68WayAqeeSRR0wx9HZnayArsUZnNtPWoFfm1mNtCdb+tZHBr956rLcW263ETtVj/vz5UVnp\nY430luvTTjstar49oQFwt27dzKOc9DboyPSzn/1MtEVZA2gSAggggAACXhHg99cre4JyIJC4\nAC3AiVuxJgKeFdBW3REjRsi99977/9u7YxRFgigAoLVXMDARwdjEK6ipXsEDGJiYGIkHMDKf\nXLyJlxBjY0NBpn/BwjLo0M72KI2voRMtq7pfC82nqv7PM6XD4TDv6y0yL6ei5FGeFY5EVZG0\nqih3lGvrdrvdXM93sVjk5cbn8znPAkfwXMWx2+1yoB21gw+HQ5rNZnn2dz6f3+w+rm29XqfJ\nZJL3Lq9WqxRLpiOQjr6Wy2X6uv/4Zkc+JECAAAECTxLw/n0StGEIVCggAK4QU1cEXikQs7+x\n1PlvgBmBbK/XS/v9PjUajXzG0uLNZpPG43G6Xq+p2WzmvcKxfGs6naaiTnAqyg1VchuRcXq7\n3ebEXJFMazAYpI+PjxzU3hsgguVIlhUJvfr9fm4We45j6XZRhunez3xOgAABAgReJuD9+zJ6\nAxP4kcCfYt/e7Qw2P+rOjwgQeLVAJJOKUkidTudu0qjT6ZQul0uKEkhVH5GIazQapaLeb15u\nfTwec6AdS7QfOWLZdpRWivt49LePjKMtAQIECBCoQsD7twpFfRD4fQEzwL9vbAQCTxWIWrtx\nfnd8LXn0Xdv//e7fWsCP9BX7geN0ECBAgACBOgh4/9bhKblGAilJguVfQIAAAQIECBAgQIAA\nAQJvISAAfovH7CYJPE+g1WqlyNrcbrefN6iRCBAgQIDAmwt4/775H8DtlxawB7g0lYYECBAg\nQIAAAQIECBAgUGcBM8B1fnqunQABAgQIECBAgAABAgRKCwiAS1NpSIAAAQIECBAgQIAAAQJ1\nFhAA1/npuXYCBAgQIECAAAECBAgQKC0gAC5NpSEBAgQIECBAgAABAgQI1FlAAFznp+faCRAg\nQIAAAQIECBAgQKC0gAC4NJWGBAgQIECAAAECBAgQIFBnAQFwnZ+eaydAgAABAgQIECBAgACB\n0gIC4NJUGhIgQIAAAQIECBAgQIBAnQU+AQ+s1dVXiYj+AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 1000\n",
    "size = 20\n",
    "p = 0.5\n",
    "\n",
    "x <- rbinom(n, size = size, prob = p)\n",
    "picture(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Число людей в очереди "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/poiss_pic.png\" width=\"800\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{equation}\n",
    "\\begin{aligned} \n",
    "& X \\sim Poiss(\\lambda) \\\\\n",
    "& P(X = k) = \\frac{\\lambda^k \\cdot e^{-\\lambda}}{k!} \\\\\n",
    "& E(x) = Var(X) = \\lambda  \\\\\n",
    "\\end{aligned}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AnW1tZmM2bMsHnz5rm/8SW/6KKLTP+8pC4Dzz77bDv11FNt2LBhbvQ777xj48eP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\nNaYxYcIEt7wa11C+jzz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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 1000\n",
    "\n",
    "# Распределение Пуассона, Pois(lambda)\n",
    "lambda =3\n",
    "x <- rpois(n, lambda = lambda)\n",
    "\n",
    "picture(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Распределение Пуассона часто используется для моделирования \"событий-счётчиков\", при этом $\\lambda$ это интенсивность потока событий.\n",
    "\n",
    "* Если у нас ест несколько суммирующихся между собой потоков, их интенсивности суммируются. То есть, если \n",
    "\n",
    "$$\n",
    "X_1, \\ldots, X_k \\sim Poiss(\\lambda_i) \\quad \\Rightarrow \\quad X_1 + \\ldots + X_k \\sim Poiss(\\lambda_1 + \\ldots + \\lambda_k)\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Точное время прихода Стаса на первую пару"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/sem_1/presa_intro/stas_first.png\" width=\"600\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Погрешность весов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cDlAjwC7fIDSPERQAABBBBAAAEEEAhG4NMH/iF52dnmSzT4jUlIkAEzphH8BoPI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\nJv3CX7x4scyePVvatm1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wa/Ti67Xvgj\nIYCAewR+ee99ObBxo6/ALc8+W5qc1s03zwQCCHhLwKURhLcOArVBAAEEEEAAAbuANqHRpxUC\nTcFuH2i+1bWddSFF/wbjUF3lDXS/+hSHk45V1t698vm/HrYVv+vQW4IyNy/KGznocbIu1Nky\ndOmMk45TKAitZjRee09ZnxVeOvf831OhOPZF8yAALirCPAIIIIAAAghUu0BFfnx7KVC0fgB6\n8ce61k2PrxPS3EeHyxGjU1crNenSRY7rfX5Q5bOOlfYr46VUkfegk+tvHScNhL30WaGfEXqs\nnPKeCsU5YB2rYI+TPt0WSCIADkSJbRBAAAEEEECgSgX0h8xhHYomwKRt8nV0Cq8k/ZGemJho\n9v/hpXppW35txpBltLut7vTTu/+VlVOm+IoRa3j3eeWloPt10D5P9HhpfxBeugunwYeXzj1t\n/qPvqSNHjgR9jH0niQMnUlJSxA19GgVDp+8nDeyDPf/0NepRXnJnt67l1Yr1CCCAAAIIIIAA\nAgiUIpC5e7csHjnStvbEq6+WlMaNbcuYQQAB7wkQAHvvmFIjBBBAAAEEEEAAgVIECo2nC2Ze\neZXsX7fet0Wddu2k+/33+eaZQAAB7woQAHv32FIzBBBAAAEEEEAAgSICG+bPl13f/+BbGmU8\nNtn9vnslLinRt4wJBBDwrgABsHePLTVDAAEEEEAAAQQQKCKwfMxY25Iejzwsx/TpbVvGDAII\neFeAANi7x5aaIYAAAggggAACCPgJbP36a/ntiy99SxLr1JGO113rm2cCAQS8L0AA7P1jTA0R\nQAABBBBAAAEEDIHNi74yHaKNHoE1te13oUQZwzKREEAgcgR4x0fOsaamCCCAAAIIIIBARAts\nXrzYrH9Bbq4YA6fKn/71UER7UHkEIlGAADgSjzp1RgABBBBAAAEEIkxgy+IlsunzBb5a1znu\nOIk1xrolIYBAZAkQAEfW8aa2CCCAAAIIIIBAxAnkZGTIvLvvsdW7/aWX2OaZQQCByBAgAI6M\n40wtEUAAAQQQQACBiBX49rVxsn/90XF/azVtKh2vvy5iPag4ApEsQAAcyUefuiOAAAIIIIAA\nAhEgsOHTT221POPBf/D4s02EGQQiR4AAOHKONTVFAAEEEEAAAQQiTmDv2l9l2zfLffVuesYZ\nctxfL/LNM4EAApElQAAcWceb2iKAAAIIIIAAAhEl8Pm/HhYpLPTVueXZPXzTTCCAQOQJEABH\n3jGnxggggAACCCCAQEQIbJz/uWycP99X16iYGDnp2mt880wggEDkCRAAR94xp8YIIIAAAggg\ngEBECCx4bLitnqcM+bvE16xpW8YMAghElgABcGQdb2qLAAIIIIAAAghEhMBvX34pe376yVfX\nlCaNpcttt/rmmUAAgcgUIACOzONOrRFAAAEEEEAAAU8LrP1grq1+Zz38L0lISbEtYwYBBCJP\ngAA48o45NUYAAQQQQAABBDwtkLFrl6yaOMlXx8T0dGl9/vm+eSYQQCByBQiAI/fYU3MEEEAA\nAQQQQMCTAguNtr+F+fkSn5xs1i+tzTESEx/vybpSKQQQCE6AADg4L7ZGAAEEEEAAAQQQcLDA\npoVfyJrZc8wS5hw+bP499ZZbHFxiioYAAlUpQABcldrsCwEEEEAAAQQQQCBsAmtmz5b/Drxc\n8rOzffs48eqrjMefz/PNM4EAApEtQAAc2cef2iOAAAIIIIAAAp4QyDtyRD69/x+2usQm1pDT\n77vXtowZBBCIbAEC4Mg+/tQeAQQQQAABBBBwvUBhQYF8/tDDkrV3r68uCbVqSe/RoySpbl3f\nMiYQQACBWAgQQAABBBBAAAEEEHCrQGFhofy/a6+T9R9/YqvCX9+cIo1OPtm2jBkEEEDAsXeA\nN23aJNOnT5ePPvpIDv/RgUF5hyvf6O1v4sSJcvDgwfI2ZT0CCCCAAAIIIICAywX0see3+l1U\nLPht3K2rNOzc2eW1o/gIIBAOAUcGwJMnT5ZBgwbJ6tWr5a233pKbb75Z9u3bV279X375ZRk3\nblzAAXO5GbIBAggggAACCCCAgGMF1hq9PW/7ZrmtfK16nSv9JrwuUVFRtuXMIIAAAirguEeg\n9c7vhAkTZNSoUdKpUyfJy8uTIUOGyIwZM8y/JR22HTt2yLPPPivLl9s/AEvalmUIIIAAAggg\ngAAC7hfIM3p6XvDIo7aKHHNBH7lw/DjbMmYQQAABfwHHBcBLly6Vxo0bm8GvFjQ2Nlb69Okj\n06ZNKzUAfuqppyQmJkZGjBghd955p3/9mEYAAQQQQACBIAT0QvSiRYskPT1dunfvLsnJyWW+\neuvWrbJw4ULze1i31+9wKx06dEi++uora9b395xzzpG4uDjfPBMIVERg3byPJXP3bt9Lkxs1\nkgteetE3zwQCCCBQkoDjAuBt27ZJkyZNbGXVL9PdxgdcgdHDX3R08ae2H3jgAWnQoIFs3LjR\n9rqiM3uNngFXrVplW9yiRQtJTU21LXPajAb3bvyhoI8e6b+EhISQk5rnQVRByPOtkgyjip/D\nVbLfSu7ErY+ShesctDjDnb+1n1D+1QuL+rkSjvdmKMtZNC/r8z8+Pt4sf9H1zFdeQJsgaVOi\nHj16iAa2Oj969GhJS0srMfOHHnpIlixZIn/6059k/fr18sorr8jjjz8up59+urn9ypUr5Ykn\nnpC6RXrh1fVu/F4rEYGF1SKQsXOnLDJufPinPi+OltgaNfwXMY0AAggUE3BcALx9+3apZXRb\n759SUlLM4PfAgQMlfglr8BtI+u677+Tvf/+7bVNtN3zuuefaljlxpoaLP9D1LkI4UkzM/nBk\nG/Y8Y6Ld2SbJCj7CDhTiHWigl55u/0wJ5S70R3y4zvFQlrOkvBITE0ta7PhlTr9omZOT43jD\nkgoYbBOkn3/+WRYsWCBvv/221K9f38zy0UcfNQNmKwBes2aNdOjQQV566aWSdskyBCos8MXj\nT8j+det9r483fis2/ePCi28hEwgggEAJAo4LgPXHpLb79U/WfFJSkv/ioKdbtWold9xxh+11\njYzHZfQRLScnvUujBtrLtZuSHi8NmgLtxTuYuuldt4L8wmBe4phtCwpcWu5Cd95x1ydHwvUe\n14tz+t7MyspyzPkVSEH0DrC+N90WqOlnod79zcjIMC+KBlLX6thGzzktp9tSsE2QtHPKG264\nwRf8an07G73uzp8/X3RYGv2c1gD4uOOOK5dCty96PrrtO6/cSrJByAR+/fBD+fGdd2z5dbz2\nGts8MwgggEBpAo4LgPUxqQ0bNtjKq8Ma6eNXlX1cr3nz5maP0v6Z79mzJywBmv8+KjutP1SP\nGN386z83Jb1rrT+AwhEAq0lhoeNO34AOT6FLA8lCtwbuRjBy+HB4AlTr6ZRwnOMBnUwV3Ejv\n/GoQ7LZy6918DSwzMzOLXSitIEVYXqbldGMKtgnSaaedJvrPP33yySdy/PHH+3rf1QBYv7u1\nqdJPP/1krhs2bFixpk6bN2+WXr16+Wcl9957rwwePNi2rLwZvajttVSzZk3Rf15LtWvXrnCV\nXrvvfttrz33on3L+Y/bOsGwbVNFMw4YNq2hPVbcbL76ntF+D8vo2qDph9lSWQLDnX9ELqaXl\n7bgIQu/Szp071/xxoz/QNP3www/FvixLqxDLEUAAAQQQQCB4gYo0QfLfi47WoG1+x44day7W\nJy80Tw0KrrjiCjnzzDPlHeOu3dChQ2XKlCm2H6AaJHft2tU/O/POcjAXfvXiSKA/fmw7cuiM\nXkDWOumdcOtJOIcWNahi6QUiveOvT0pUJP36yaeSsetox1cJRrO5M+69p1pvElj9KgRzvlak\n7lX9Gn0qMzc3t6p3G7b9We8pNz5VWRZKZd9TZeVdXev03LNuAAZTBv28DOQJLMcFwHoFWDvR\nmDp1qjkWsN4NnjNnjjz44IO++us6HSJJ2xWREEAAAQQQQKDyApVpgvT666+b39v//ve/fY88\n6x0WbR+sbeStHyTt27eXa665RvRO8UUXXeQrtLYh1g63/JP2+6GdVwaaNI9gtg803+raToOq\nevXqSbYx1I8+CeeVpOeF/kitSNORrL375P277rZRdLrhejl4+LBtWVXP6FOKGoRoswAN7r2S\n9Pzz0ntKP+P0SVN9T4WraVR1HHt9Gk0vVGi9vJL0e0MvjAZ7/un7MJAms47rjlYrO3z4cJk5\nc6Y5/JEOazRgwABzKAbroI4ZM0ZWrFhhzfIXAQQQQAABBCopoD8Mi/4oLK8Jkt7Fe+aZZ0Tv\n/j777LNyxhln+Eqhd1v07q8V/OqK1q1bm0GdPm5NQiBYgU/uf0D2GJ2vWalW06Zyys1DrFn+\nIoAAAgEJOO4OsJZaO9GYNWuW7Nixw/yi1Fvg/knHGywp6ZBGpa0raXuWIYAAAggggMDvAhVp\ngqQXrPWxZ31yS4Nb/6RPcD388MPmsEjNmjUzV2ngu2vXLpo1+UMxHZDAb198IWtnz7Zt22P4\nYxJv3FEmIYAAAsEI2CPLYF5ZBdvq8EZFg98q2C27QAABBBBAIOIErE6otJmR3tldt26d2QRp\n0KBBPgtdp/1yaPrggw/k448/lmuvvda8c6yBsPVPH3Ft2bKlaGeI+tSWPhqqwa8OPaiPi7ph\n+EFfpZmodoE9v/wi710/2FYOvfN7TO/zbcuYQQABBAIRcOQd4EAKzjYIIIAAAgggEDoBqwmS\njuWrga72Fl5SE6QhQ4aYfXBoh1aa9BHooulDY5gabYelzZgee+wx6d+/v7mJ3iV+8cUXA2qj\nVTRP5iNXYOmo0ZLj1863pnGD5Mz/O9o3TOTKUHMEEKiIAAFwRdR4DQIIIIAAAh4UCKYJ0vjx\n48sVaNeunbz55puye/du0Q5oUlNTy30NGyDgL7Dv13Xy28Iv/BdJtzvvkKgizeNsGzCDAAII\nlCFAAFwGDqsQQAABBBCIRAFtghTKpB1skRAIVmDtnA/k/RtvEqNrZd9LT7j6Kjnpb0cfy/et\nYAIBBBAIUMDRbYADrAObIYAAAggggAACCHhIQO/8LnjkUVvwK0bP4h2vvcZDtaQqCCBQHQIE\nwNWhzj4RQAABBBBAAAEEShTIyciQD4YOlYObNx9dbwS/Zxu9PtczxpImIYAAApUR4BHoyujx\nWgQQQAABBBBAAIGQCix9YZTsXPWdLc/+U6dIi7N72JYxgwACCFREgDvAFVHjNQgggAACCCCA\nAAIhF1g5cZJ888oYW769nnma4NcmwgwCCFRGgDvAldHjtQgggAACCCCAAAKVFsjPzZV5d90t\nP737X1te7S6+WE646krbMmYQQACByggQAFdGj9cigAACCCCAAAIIVFrgvWuvlw2ffWbmE2eM\nIZ2bmSn6t9sdt1c6bzJAAAEE/AV4BNpfg2kEEEAAAQQQQACBKhVY99E8X/CrO9bgt0Zabbl8\nzvuSdkzrKi0LO0MAAe8LcAfY+8eYGiKAAAIIIIAAAo4UKDTG+F38/Ehb2Rp37SoXTZkkCcnJ\ntuXMIIAAAqEQIAAOhSJ5IIAAAggggAACCAQlkJeVJYueedbo8XmV73UNOnaUS//7jkRF85Ci\nD4UJBBAIqQABcEg5yQwBBBBAAAEEEECgPIGC/Hz57KF/yQ9vTrNtelz/iwh+bSLMIIBAqAUI\ngEMtSn4IIIAAAggggAACpQrs+eUX+X83D5Xty5fbtklt2VI6XnedbRkzCCCAQKgFCIBDLUp+\nCCCAAAIIIIAAAiUK7PlljUz+c1/J2rPHtr5261Zy0aSJEhMXZ1vODAIIIBBqAQLgUIuSHwII\nIIAAAggggECJAov/82Kx4De9TRu5+N23pWa9eiW+hoUIIIBAKAXoYSCUmuSFAAIIIIAAAggg\nUKLAxs8XyLcTJ/rWRcXESOcbB8sVc+cQ/PpUmEAAgXALcAc43MLkjwACCCCAAAIIRLhAYUGB\nfG3c/fVPJ1x5hfR49BH/RUwjgAACYRcgAA47sfN3EGNcgQ1nCkf+0QyPEM5D5qm8Y4znXMJx\nDvojhSv/fKOXVBICCCDgBYFf534omxct8lUlNrGGnDpsqG+eCQQQQKCqBAiAq0raqfuJipV3\nvoqTbXvzQl7CqKhDEmXkWlAY+iftW9SPM/IlOAj5QfNghrWTY2TSfJEDGQUhr1101F4pNHIt\nDMM53qxerPy1a44QBIf8sJEhAghUscDWZd/IB8Nute31+IsvkdRmzWzLmEEAAQSqQoAAuCqU\nHbwP/fH+8+Y82bwrHMFkOPL8HTMvP0rqpGh4TUKgbIFc4zT8cVO+7D8c+gBYJHzneFaOSFQU\n53jZR5e1CCDgdIGVb0yU+cZ4v4V+T7TUatpEej71hNOLTvkQQMCjAgTAHj2wVAsBBBBAAAEE\nEKhOgay9+2T+Px8Sbf9rpfjkZOn97LMSRVMmi4S/CCBQxQKhfza1iivA7hBAAAEEEEAAAQSc\nJZB35Ih88fjjtuA3Jj5e+o19Rdr0Pt9ZhaU0CCAQUQLcAY6ow01lEUAAAQQQQACB8Ars+eUX\nee+6G2T/+vW2HfWb+Ia0+8uf6dvApsIMAghUtQB3gKtanP0hgAACCCCAAAIeFfjtiy/k3csu\nLxb8Hn/pJdKix1kerTXVQgABNwlwB9hNR4uyIoAAAggggAACDhU4vH27vHf9YMk5fNhWwvon\nnSh/euiftmXMIIAAAtUlQABcXfLsFwEEEEAAAQQQ8IhAXlaW/PfyK23Br7b5Pf3ee+Tkv98k\n0bH85PTIoaYaCLheIOI/jWrUqCGpqamOPpDRRk+JWs7CQh20KLQpN0/zPBDaTKsot+hodw4R\nEx0TU0VCod1NTIw7W0zEuLSn0ShjFO20tNqhPYh/5KbDK+k//VxxU9LPQk1paWmOLnZeXujH\nVXd0hSlcxAvkZGTItAv+LPvW/nrUwviMueTdt6XRKaccXcYUAggg4ACBiA+As7Oz5eDBgw44\nFKUXoVatWnLE6E1R/4U6FUbpKeDOQLKgIPQXBELtW1J+BX5jIZa03qnL8vOPDmPh1DKWVK58\nv+E3Slrv1GWFUij79u2TcARTiYmJEmvcjTl06JBTq19iufRiZVJSUthcStxpBRbGGBe53HZx\noQLVDPtL9BytX79+wPvRCyTBbB9wxtW8ob5fnX4+ff7Ms/bg1zA779FHpOMFFxTTs8Y3T0lJ\nKbbOrQusi3P16tVzaxVKLLdX31P6PaLvK68k6z2l8YJXkvWeCvYzPTc3NyCCiA+AA1JiIwQQ\nQAABBBCoUgG9+LNz586A96k/lILZPuCMq2lDvQCgAVWW8WixUy/U65NpqyZOki+feNKm1LJn\nT2l/w/UlHo9kYxzgfONCsNbLK0mfStGLFLt27QrL03rV5aTnn9bJKykuLk7q1q0rmZmZrrsA\nXNYx0ItJGvjpTT2vpPT0dElISCjxM6SsOgZ6AZoAuCxF1iGAAAIIIIAAAgiUKLDk+ZGy+Lnn\nbetanN1D+k2cYDazsK1gBgEEEHCIAAGwQw4ExUAAAQQQQAABBNwgUGg0Lfnk/gfk+6lv2opr\ndnp1373i1r4ubJVhBgEEPCvgzl5tPHs4qBgCCCCAAAIIIOBsgXl33V0s+E1rc4xcOvNdadip\nk7MLT+kQQCDiBbgDHPGnAAAIIIAAAggggED5AtqJ4wc33yJr3p9t27heh/bSd/w4SW3e3Lac\nGQQQQMCJAgTATjwqlAkBBBBAAAEEEHCQQH5Ojky/sJ/s+u57W6lannuu9PnPKKlROzzDttl2\nxgwCCCAQAgEegQ4BIlkggAACCCCAAAJeFvh+2nRf8BufkmxWtf5JJ0m/CeMJfr184KkbAh4U\nIAD24EGlSggggAACCCCAQKgEDm7eLEv8envOOXRYGnQ8SS4z2vxGG8M1kRBAAAE3CRAAu+lo\nUVYEEEAAAQQQQKAKBXKNMVNnXnGlZO7e7dtr6/PPkys+mCOxiYm+ZUwggAACbhHgsp1bjhTl\nRAABBBBAAAEEqkjg0Jat8u24cfLLe+/J4a3bfHuNjouTM//v/3zzTCCAAAJuEyAAdtsRo7wI\nIIAAAggggECYBNZ+MFe2LF4i302ZLHlZ2cX28ucxr0j6sW2KLWcBAggg4BYBAmC3HCnKiQAC\nCCCAAAIIhFFgzfvvy+ybhpS6hzrt2skxfXqXup4VCCCAgBsECIDdcJQoIwIIIIAAAgggEEaB\n3xYtko/uuKvYHqKio6XFOedIy3POluMvuViioqKKbcMCBBBAwE0CBMBuOlqUFQEEEEAAAQQQ\nCKFA1t598u1rr8myl16Wgrw8W86NTjlZeo8eJbVbtbItZwYBBBBwswABsJuPHmVHAAEEEEAA\nAQQqITD7pr/LZuPur3+KiomRATOmSbPu3f0XM40AAgh4QoBhkDxxGKkEAggggAACCCAQuMDe\nNWvl/RtuLBb8Gs84S88nnyD4DZySLRFAwGUC3AF22QGjuAgggAACCCCAQGUEFj01QpaO/k+x\nLOp1aC99XnpR6rRtW2wdCxBAAAGvCBAAe+VIUg8EEEAAAQQQQKAMgez9+432vuNKDX6v/HCu\naKdXJAQQQMDLAgTAXj661A0BBBBAAAEEIlZAO7VaO+cD2bZ8ufz41tty5OBBKSwosHnEJyfL\nCVdeIV3vuJ3g1ybDDAIIeFWAANirR5Z6IYAAAggggEBEChQWFsp3k6fIspdfkYObNpVq0KjL\nqXLh6+MlqU6dUrdhBQIIIOA1AQJgrx1R6oMAAggggAACES2wcsIbMv+fDxUz0MebrTvAzc48\nQ/7y6lipUbt2se1YgAACCHhZgADYy0eXuiGAAAIIIIBAxAjkHD4sswb9TbYuWVpinZt06yZ6\n17flOedIk25dS9yGhQgggIDXBQiAvX6EqR8CCCCAAAIIeFpAH3leO2eOrBj3erHgN+2Y1vKn\nhx6SxkbAWyM11dMOVA4BBBAIRIAAOBAltkEAAQQQQAABBKpRoCA/XzJ27JCdq76Tgvw82b9+\ng9G+9zfJzzkimxcvKbGtb62mTaX/tGlSq2mTaiw5u0YAAQScJUAA7KzjQWkQQAABBBBAAAFT\nYONXX8miMWNlmxH07l2zRnIzMgKWaXVeLzl3xFOS3LBhwK9hQwQQQCASBAiAI+EoU0cEEEAA\nAQQQcLyAdlC179d1smryZFk9fYZom95gU80GDaTT9dfJqUNvYVijYPHYHgEEIkKAADgiDjOV\nRAABBBBAAAGnCfy2aJEc2LBRdqxYKYd3bJdt33wj2Xv3BVXM2MQaEh0TKw1P7iztLh4g7QYM\nMOZjgsqDjRFAAIFIEiAAjqSjTV0RQAABBBBAoEoE8o4ckR3frpDcrEw5tGWrcWf3VxGjs6o9\nv/wih7fvkHxj/f716wMqS2xiotQ7oYPUbtFS0tseKw07dZSYhBpSs2EDSW3WLKA82AgBBBBA\n4HcBxwbAm4yB2xcZV0bT09Ole/fukpycXOYxC3b7MjNjJQIIIIAAAhEqEOz3aXnbHzp0SL78\n8kvRv92MYXiaN2/uOdns/fvlgPG7pSA317ybu2b2HNmyeHGl63n8hX2l6emnS9vLLpO4pMRK\n50cGCCCAAAIijgyAJxttX8aNGyc9evSQrVu3is6PHj1a0tLSSjxmwW5fYiaVXJibHy2Hj8Tq\nxd2Qp8wCkfzcGMnNiw953nFx0Uae+SHPlwwRQAABBNwnEOz3aXnbrzfucN5www3SunVradKk\niYwdO1Yef/xxOe2009yH80eJ83NyZN1HH0n2/gPmXd0Nn3wq+zdskIK8vErVSe/y1kirLU26\ndpXGXbpIq3POluOM4DfD6Pjq4MGDlcqbFyOAAAIIHBVwXACsV5InTJggo0aNkk6dOkme8YUy\nZMgQmTFjhvn3aNF/nwp2+6KvD9X8gcxYeWl2geSGJZbMDFUxi+XTsbUGwCQEEHCaQHJilKzd\nkSCZ2aH/UImJiZaoKDE+X0N/Ryk+Nkqa1cmRhNjKBQNOOx6RUJ5gv08D2f7JJ5+Ufv36ye23\n326cc1EyceJEGTlypEyfPt2crw7X3MzAv1MPb9sue37+WbavWCHbjceZD23ZIkcOHgi6nW7R\netYyHltObdFcomNjpdmZZ0pLI9hNO+YYiYk/eqE71lhHQgABBBAIvYDjPl2XLl0qjRs3NoNf\nra5+AfTp00emGePYaSBcNAW7fdHXh3I+x/i9dyDDuF3ropRfEIZb1i6qP0VFwKkCGgDP+PyI\n/LYr9AFwOOucXita7v5rtBEAh3Mv5B0OgWC/T8vbfs+ePfLjjz/KP/7xD1+w27dvX/MJr9Wr\nV0uHDh3KrMZuI/BcafSEHGiqWbOmebfUf/u87GzzkWQdK1fTfqPDqSyjXFWVjvvrRdK6d2+p\nkZoqiXXqmO14dd96MYCEAAIIIFA9Ao77ibJt2zbzMSl/Dg2Id+/eLQXG8ADR0fY7lsFs/7Px\nZfrGG2/4Zy0DBw6Utm3b2pZVZOZwXqHExGRKSpK7vtSSEmIkJrrQdeWOjo4yvKPdV27jR0+M\n0Tun284TfU/ExkZLUo2osDzmX5H3XKCvSYiPllijQ1S3mSfXMN6bMe57bxqnieRIkmw+UCPQ\nQxTwdtsORRnDuhyR/LyaUmj8F8pkfKRIw/QoSatZ+Vz1u8qNKZjvU61fedtv377dZNDvcCvV\nMYLAeOMu586dO20B8N69e+WZZ56xNjP/tjUC2p9GvmBb5sQZ8y6u8Uh341NOlkYdO0qU8Rnf\n8MQTpFbTphJv1KGiyQqS1SvVCKC9kuLi4szfc1ovryStk6ZatWp5pUpmPfQ3t5fOPSuGSEhI\nKBZPuPnA6fmn/7ReXknWEzDBnn+Bfv86LgDWL8yiHyApKSnmh+WBA/+/vTMBjqJo+/gTCHeQ\nGwIh3JcIRMAIKFjhFCEgUIhcwRMBETnEEgXk06CCUVFLERWhVJBTqJIyHOIBoiAgCBYQVG6U\n+wyCLyD79r/rnf1mlyXZTWaTmdn/U5XsTG/PTPeve+fpp4+nz123DjiU+Ii7ZMkSn7rRoUMH\nKV68uE9YTk7iClyT5/oVlmvhWASckwQFeQ36EzolRim+1jYmg3x8jqOhmwGNg+535L7scpyI\nHFyIdCu7XW6r77yXFNJ9c7XCFpsdOYAY4iUwyJrXLeq43yZ43+3U36ayJmOKhvOdEh7VFVOs\noNIHud8+5rJaI+pECUWfIn/ZxYeBjAaZf6MMOv3MGd+tfrDO1V8/p6jZX3aSKFWvy9WpI+VV\npzkM26YD+uvzm5SBXyyMBqrRuLUTC6YlMAEr2pOB75x/oW7ME39T+VefQn1yqPUvWP0bnlZE\nqLkzxUelxLpfsxjngSCEEj9ROZVIT08331qKKacT6Im2Qkrkvt0UMBnwgI0CDbZQA94ku0DV\n2LZa4MEbvW0YvXeSoNcJU+nQ4RI2CQNv1GU0LJHu/6jtNcIiYUg30lm6dGnt5CXYnruw5C0H\nN61YsaL+XZ5VHmDDJmFgXrRoUT0TAUZH2CQM6Ub9Rj3H1Np//7V+avh/1NLQ48EvD70hOrz3\nypcvf8Pv7fpFKPoUecgufqDvcR3Kzl+fx8bGXqefD37zrazABRZIufrKaP3fbhIxsZUF58FK\nUfV+qqS2HSqnDN9iAZxxZqr3baZF7QhzmqCLoEcvqjXLFy5cMH/l6GPoV9SBf9T0dLcIRqnQ\n0XPixAk1SyqcnX95Swz1D7Mz3CJ4J8Ghrht/U7CVwtb2y4cKgHahMVsolMcHq39tZwCj0bBf\neVM0C7wfosL69yIjTijxoXBrKycTZkFDKqyGpflhOTzGyxSGQTgafDlMUlCXGUrAaenGyDLS\n7rR0G8ajE+sKKhR4G3kIqoLZKJIT6wqUhNPSbbxTnFrHbVRlAyYlFH2KG2QXH9+jjqGxaTZ4\nodMrV67skwY0TP31c1ml92u1TfKJl9VJhQoVtAHiH6eAmpIcrTp9rJC8/M0YU6CdqI+yYo3f\nr9t+w8a7CfXDOM6KgZO+y8s6H24u0HsQN9Y/N+YJZRWu+heGPnokN+dSs2ZNycjI8BkF3rFj\nx3Xrgo0nhBrfuI6fJEACJEACJEAC/08gVH2aXfyqag0sRjGhww2BUyw01Mzrgo3v/D9huGKq\ncbB/RdQIb6C4Vhm//unjOQmQAAmQgDMJ2M4AxppcyNy5c7WS3Lt3r54WlZKS4iWM7wyFGkx8\n74U8IAESIAESIAESCEggGH0aiv7FtNBOnTrprQ0xhRdTXmfOnKl3dsBoLYUESIAESIAE8oOA\n7QxgTHNOTU2VpUuXaiU5evRo6dWrl9xxxx1ePjNmzJBf1J58kGDiey/kAQmQAAmQAAmQQEAC\nwejTUPUvti/EOq5u3bpJjx499IjwiBEjAj6fgSRAAiRAAiSQFwSi1FoF267WP3bsmKCX2Jiz\nnx2QUOPjfk5YAwyv2FjY7rTF7Vj/hS1/UC5OEkzZC+Sl1O55wBo7jLjAu6rTnItgaxSkG1Mj\nnSRYxwgfAniPOEngSAr1PDMz00nJ1vUb9RyOZgzniHbMAN57cJDmZAlVn2YXH+t+wQUOkIIV\nOPTD+uFgBcytcmoZ7DPDGQ+/UbSB4KwO/NwicOyJdX2XLl1yS5a0nxo4F4RndBs3q0PmfaN1\n9SHfyCYXwNcA2qaYkeI0/ZcVQrRZr1y54ri2X1Z5ggM2dMpiN4FQJFj9azsnWOZMVqpUyXya\n7XGo8bO9ISOQAAmQAAmQQAQSCFWfZhfff3vDCETKLJMACZAACdiEgO2mQNuEC5NBAiRAAiRA\nAiRAAiRAAiRAAiTgMgI0gF1WoMwOCZAACZAACZAACZAACZAACZBAYAI0gANzYSgJkAAJkAAJ\nkAAJkAAJkAAJkIDLCNAAdlmBMjskQAIkQAIkQAIkQAIkQAIkQAKBCdAADsyFoSRAAiRAAiRA\nAiRAAiRAAiRAAi4jYOttkPKCNbYWgOtwOwv2UMSWAfhzkuzdu1ezrV+/vpOSLVFRUXrfSqdt\nO4VthLAFQ5UqVfR2MU6Cju0jwNtp20fs2rVLb+tSrVo1J+HW29Fgezm7v/v8oaJ+o57XqlVL\nb4/g/71dzsG2TJkydkmOY9OB7X9C2dIN23u5aWsdvBOhR7EdSHZetp1UyNiKBu96O29lFirP\nQ4cO6a116tatq7eYC/V6u8Z3228K74f9+/e78jeFbSSdZidkVe8PHjyot4Br0KCBbpdnFdf8\nXbD6N+INYDM0HltLIDk5Wf7880/ZunWrtTfm3QISmDNnjqSmpkpaWpp07949YBwGWkcAiqZh\nw4bSrFkzmTdvnnU35p1uSGDChAmyaNEiWbZsmdSrV++G8fgFCbiBwM6dO6Vnz57Sv39/mTRp\nkhuy5No8DB48WNauXSsbN250XAe0awslQMa2bNki/fr1k4ceekjGjRsXIAaD7EIgJSVF/562\nb98elg5vToG2S0kzHSRAAiRAAiRAAiRAAiRAAiRAAmElQAM4rHh5cxIgARIgARIgARIgARIg\nARIgAbsQoAFsl5JgOkiABEiABEiABEiABEiABEiABMJKgGuAw4o3sm/+448/agcm7dq1i2wQ\neZR7OOHIyMiQxo0bS2xsbB49NbIf89VXX0np0qUlMTExskHkUe7hdOzw4cPSqlUriYmJyaOn\n8jEkkD8EMjMzZcOGDRIfHy9wBEOxLwH4Ojl58qQkJSUJnHxR7Eng7NmzsmnTJqlevTr9SNiz\niLyp2rx5s3Z62b59e4FjK6uFBrDVRHk/EiABEiABEiABEiABEiABEiABWxKw3qS2ZTaZKBIg\nARIgARIgARIgARIgARIggUgnQAM40msA808CJEACJEACJEACJEACJEACEUKg4P8piZC8Mpv5\nQAAbc2MPr5UrV8rRo0f1Wqbo6Oh8SIm7H4k9abEG6euvv5bLly9LXFycuzNsg9z99ddfkp6e\nrtddYx1wyZIlbZAq9ycB6+zmz58vTZo0Ccu6IPcTZA6dRuDixYuyZs0aWbduneBdX7lyZadl\nwdXpxVrtb7/9Vutg6IFSpUq5Or9OzRzbo84ruXDqe64Bdl59cEyKUXEfffRRvYF1QkKCrF+/\nXjuuef/99+Wmm25yTD7snlA0iIYOHSpHjhyR1q1byw8//CBt27aVMWPG2D3pjk3fxIkT5aef\nfpI2bdrIvn375MCBAzJ58mTtnMmxmXJAwj0ej4wdO1Y2btyoO3sKFy7sgFQziSSQcwIrVqyQ\ntLQ07dywePHiAueSycnJ+neQ87vySqsI4P3/yCOPSK1atXTHM/QvdEHLli2tegTvYwEBtkct\ngJjHtwi3vudQXB4XaCQ9bvHixVKlShWZPn26zvalS5ekV69esmDBAhk8eHAkoQhrXhcuXCgX\nLlzQXEuUKKGNsZSUFOnatavUr18/rM+OxJvv3r1b1q5dK4sWLZKKFStqBC+88IK8/fbbNIDD\nXCHwTtm5c2eYn8Lbk4A9CGDE6uOPP9YdnPfdd59OFN4948ePlx49ekidOnXskdAITsUrr7wi\n3bt3l5EjR0pUVJQur2nTpulZKjin2IMA26P2KIdQUhFufc81wKGUBuOGRAC91YMGDfJeU6xY\nMb2VA6aOUqwjgGlxHTt2FBi/ELj3b9SokWCLHor1BM6cOaN7/A3jF09o2rSpnuKPHktKeAhg\npAXGwLBhw8LzAN6VBGxG4PTp03qLNbzfDcG7BkI9ahDJv89Tp04Jtma79957tfGLlGB0HmXD\njrr8K5dAT2Z7NBAV+4blhb6nAWzf8nd8ymD8mqcBQZljnWrDhg0dnzc7ZQBTnzHSbhacHz9+\n3BzEY4sIoE6bO3ZwW6y9vvnmm72NIIsexdv8j8CVK1cEo+yPPfYY17ezVkQMgfLly+ulLPAx\nYAjeNQULFuTsHgNIPn7CrwnErH/LlSsnWJpB/ZuPBRPg0WyPBoBi06C80vc0gG1aAdyWLDhm\ngr81jE5i6hbFGgJXr14VrG3xX1ONc3Q4UMJPAFP6t23bpqfAhf9pkfmEDz/8UE83x1RDCglE\nKoE9e/YIfGgMGDBAKlWqFKkYbJNvdD4XKVJE/5kTBUdYmClEsScBtkftWS5GqvJK33MNsEGc\nnzkmAENr1apV3usxNbRdu3be8/Pnz8uzzz4r+MTamEKFCnm/40HuCGAkoECBAgJD2Cw4N6ZE\nm8N5bC2BWbNmydy5c+Wll17iiIy1aL1327JliyxfvlxPf/YG8oAEXEYAnWiYTmtI8+bNpW7d\nusap3k1h3LhxWrfC6RIl/wmgLeOve5EqOKbElFuK/QiwPWq/MjGnKC/1PQ1gM3ke54jAuXPn\n5IsvvvBe26BBA68BjNHJUaNGaWPsnXfe4fYAXkrWHMDJRtmyZQXbMJgFL/nY2FhzEI8tJADn\nNK+//rqsXr1aXnvtNb0G2MLb81YmAhjxQmNy6tSpOhTvG8iECROkW7du2hO3DuA/EnAwAawZ\nXbZsmTcHZcqU8RrA8PMwadIk6dOnjwwZMsQbhwf5SwBT1GHsYpsqs8EL/cutqvK3bAI9ne3R\nQFTsFZaX+p4GsL3K3pGpqVmzpnz22WfXpf3YsWMyYsQIqV27tp7+jKlCFOsJYPuFHTt2aK/P\nxt3RmOrdu7dxyk+LCaSmpuppz++9957e/sLi2/N2JgLwZm6eTggHM6jv6GhD5w+FBNxAoF+/\nfoI/f8H+snjfwMswnC1R7EOgatWqEh0drd9HiYmJOmEYxUcHqXldsH1SHLkpYXvUGWWfl/qe\nBrAz6oQjU4kRMvSOYvuGjIwMbx6wPhVGM8UaAjB0n3/+ee19Eo6YlixZIljj0qVLF2sewLv4\nEMB0XIz8Pv3003rkHVMXDYH3bUxLp1hHwH/d788//yzp6ekycOBA7WzGuifxTiRgLwLwMjxl\nyhRJSkqSGjVq6E43I4Xx8fHsADJg5NNnqVKlpFOnTjJ79mztBBHG8MyZM6Vz585SoUKFfEoV\nHxuIANujgajYLywv9T0NYPuVvytShFGa9evX67yg59osLVq00NNGzWE8zjkBeCXu27evDB8+\nXK+vjouL09NDY2Jicn5TXnlDAtibDpKWlnZdnJUrV/pMhbsuAgNIgARIIEgC6GzD9Fpsaee/\nrR3WA2O0hJK/BIYOHao91GM5Bma5JSQk6Jlv+ZsqPt1MgO1RMw0eGwSi1L6V3LjSoMFPEnAw\nAYz6Yu0R1iVRSIAESIAESIAE8oYAdC9m/9D5ZN7w5lNIILcEaADnliCvJwESIAESIAESIAES\nIAESIAEScAQB7gPsiGJiIkmABEiABEiABEiABEiABEiABHJLgAZwbgnyehIgARIgARIgARIg\nARIgARIgAUcQoAHsiGJiIkmABEiABEiABEiABEiABEiABHJLgAZwbgnyehIgARIgARIgARIg\nARIgARIgAUcQoAHsiGJiIkmABEiABEiABEiABEiABEiABHJLgAZwbgnyehIgARIgARIgARIg\nARIgARIgAUcQoAHsiGJiIknA+QQuXrwoBw4ckH/++cf5mWEOSIAESIAESMChBKiPHVpwTLZl\nBGgAW4aSNyIBEsiKwPLly6VGjRry3XffZRWN35EACZAACZAACYSRAPVxGOHy1o4gQAPYEcXE\nRJIACZAACZAACZAACZAACZAACeSWAA3g3BLk9SRAAiRAAiRAAiRAAiRAAiRAAo4gEO2IVDKR\nJEAC1xG4du2aLF26VFasWCGnT5+WevXqSZcuXaRNmzY+cU+cOCGffPKJZGRkyJkzZ6R27dqS\nnJzsE++DDz6QsmXLSuvWrXXcLVu2SEJCggwcOFDi4+Nl/fr1smjRIr1+t3///nLnnXdKVFSU\nfs7vv/8uc+bMkccff1y++eYbWbVqlZQpU0a6du0qSUlJUrBgQZ/0+J/8+uuvsnDhQtm1a5dU\nq1ZNp61du3b+0XhOAiRAAiRAArYk4BZ9fPXqVZk9e7Zs3LhRsE64adOmMnjwYClVqpQtuTNR\nJJBjAh4KCZCAIwk8+eSTHmWEeho3buzp3bu3p0qVKvr8jTfe8OZn3bp1ngoVKnhiYmI8HTt2\n9CgD16MMUh3vo48+8sZLTEz0KKPWU7NmTU+tWrX0PdVLxXPLLbd4Zs2a5YmOjvYoRai/R/gT\nTzzhvfbLL7/0IOyee+7xlCtXzvPggw/qZyFs9OjR3niLFy/W8dTaI2/YjBkzPIULF9Z/3bp1\n8zRr1kzHGTt2rDcOD0iABEiABEjAzgTcoI+PHz/uue2227QOVh3qnh49enhKly7tqV69umfH\njh12xs+0kUDIBCTkK3gBCZBAvhM4f/68NmTVqKs3Lf/++682XCtVquRRvbg6/K677vKULFnS\nc/ToUW+8Q4cOaYMWxqYhMIBhsJoNzwkTJugwXL9p0yYd9fLly57mzZt7SpQoYVzqMQxgGNp7\n9+71hr/88sv6+iVLlugwfwNYjRxrw7dt27YeNUrtvW78+PH6utWrV3vDeEACJEACJEACdiTg\nBn0Mrg8//LCPzkaY2rnBU7lyZY+aWYZTCgm4hgDXAKtWP4UEnEigQIEConpl5ciRIzr5OF+z\nZo3s379fTztWbyl57rnnZNmyZaKMYm8Wq1atKi1atBBMjTYLpjSnpqZ6gzCdGtK3b19RvcL6\nuFChQnr6899//y2nTp3SYca/UaNGiRpBNk7lqaeekvLly8vnn3/uDTMfTJ8+XZRBLePGjdPx\njO9wHZ7z7rvvGkH8JAESIAESIAHbEnC6Pj579qye+tyqVSvp2bOnlzOWJWHZ0/fffy/bt2/3\nhvOABJxOgGuAnV6CTH9EElCjsqKmF8urr74qcXFxokZzRU1BFjVlSdQIrWYCg/buu+/W635h\nhO7cuVN2794tW7du1cdmoxgXqCnUUrRoUS9PNaKrj9X0J28YDoy1QGrE2SccRrVZ1NRmadCg\ngX6eOdw4RlqQRqw/njlzphGsP4sXLy6//fabTxhPSIAESIAESMBuBNygj+HLA53majRb+vTp\n44P48OHD+hw6uUmTJj7f8YQEnEqAI8BOLTmmO+IJTJ06VdLT03Xv7MGDB2Xy5Ml6pPaBBx4Q\nOLKAfPrpp9qJlVojLGotr3Zqge8NI9kMUa3fNZ96j9X6X+8xDqAkA4laK3RdMAzZc+fOXReO\ngJMnT0qRIkUE90fvufmvc+fO0rJly4DXMZAESIAESIAE7ETADfoYPIsVK+aji6GXMQp8//33\nCwx9Cgm4hYBvy9YtuWI+SCACCGAEtlOnTnrkF0bp5s2bRa3h1V6cBw0aJI0aNRK1pkduvfVW\nPQ0ZSswQeIW+kSFrxMnu0/969BL7G9Zq/ZAenQ50L+VsS3uafPHFF7UHa3McGPD+hrf5ex6T\nAAmQAAmQgF0IuEEfgyV2k5g7d64PVuQtu90cfC7gCQk4gABHgB1QSEwiCfgT+OWXX0Q5opJp\n06bprzCVWDmyEuWdWZ8rp1d66jEMSaznMRu/mOqEqUzGKLH/vXN6Pn/+fJ9LsY0Cpjnffvvt\nPuHGCbZSgsAYNwvWGSmv1TJy5EhzMI9JgARIgARIwHYE3KCP0SEdGxurt1bENGizDBgwQDDD\nCx3aFBJwCwGOALulJJmPiCKAUd327dvLlClTdM8s9s3FGl/leVkbj1gPDEdVcCaltjvSe/k1\nbNhQ7+f7zDPP6ClOmZmZehQYxrMVsmDBAm1oY+/gPXv2yIgRI/To75gxYwLefsiQIQJHWG++\n+aZgvXGHDh1k27Zteio3DGDlhTrgdQwkARIgARIgAbsQcIM+RlshLS1NUlJStC+RSZMmCZYw\noWMbun3ixIni7w/ELvyZDhLICQEawDmhxmtIwAYEMPqLqc6GgQlDNiEhQTZs2CBly5bVf5jK\n9NZbb0lycrJcu3ZNKlasqA1MTGkaNmyYqH2CRW1vYElu4HF63rx52jEXnGmp7Y20cyso0UAC\nhQuv1cOHD9dTt40R6bp16+r7GE64Al3LMBIgARIgARKwCwGn62NwROc1nFfCwWZSUpJGi6VI\nWErFDmmNg/9cRCBKreML7NHGRZlkVkjAzQTgTApbIdWoUeOGTiqOHTsmV65cEWyBZLXAEVfX\nrl1F7ferp1vv27dPG9qYoh2sYDukP/74Q3uYhjdqq0alg30+45EACZAACZBAbgm4QR+DAZZR\nYatDtCtC0eW55cfrSSCvCHAEOK9I8zkkECYC2GsXf1mJ/5ZHWcXN7XfmvYCDvRd6nTFFm0IC\nJEACJEACTiXgBn0M9lgPjD8KCbiVAJ1gubVkmS8SIAESIAESIAESIAESIAESIAEfAjSAfXDw\nhARIIFQCcXFxAi+R8fHxoV7K+CRAAiRAAiRAAhYRoD62CCRv43oCXAPs+iJmBkmABEiABEiA\nBEiABEiABEiABECAI8CsByRAAiRAAiRAAiRAAiRAAiRAAhFBgAZwRBQzM0kCJEACJEACJEAC\nJEACJEACJEADmHWABEiABEiABEiABEiABEiABEggIgjQAI6IYmYmSYAESIAESIAESIAESIAE\nSIAEaACzDpAACZAACZAACZAACZAACZAACUQEARrAEVHMzCQJkAAJkAAJkAAJkAAJkAAJkAAN\nYNYBEiABEiABEiABEiABEiABEiCBiCBAAzgiipmZJAESIAESIAESIAESIAESIAES+C/jQvUc\njtlT7QAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 1000\n",
    "\n",
    "# Нормальное распределение, N(mu, sigma)\n",
    "mu = 0;  sigma = 1\n",
    "x <- rnorm(n, mean = mu, sd = sigma)\n",
    "picture(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Время до поломки станка, время до смерти, любое время между событиями в потоке\n",
    "\n",
    "<center>\n",
    "<img src=\"http://vremyakryma.ru/wp-content/uploads/2018/11/vremia_daly.jpg\" width=\"500\"> \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{equation}\n",
    "\\begin{aligned} \n",
    "& X \\sim Exp(\\alpha)  &f(x) = \\alpha \\cdot e^{-\\alpha x} \\\\\n",
    "& E(x)= \\frac{1}{\\alpha}  &Var(X) = \\frac{1}{\\alpha^2}\n",
    "\\end{aligned}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3+Iz0wo76SBAwfagN1ZjuYxrWluPg36ReqbskoLyfKj9SJvftw4mMWFX86RU4Zl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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 10000\n",
    "\n",
    "# Экспоненциальное распределение, Exp(alpha)\n",
    "alpha = 0.1\n",
    "\n",
    "x <- rexp(n, rate = alpha)\n",
    "picture(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* У экспоненциального распределения нет памяти, то есть если $X \\sim Exp(\\alpha)$, тогда $P(X > s+t \\mid X \\ge s) = P(X > t)$\n",
    "* Пример: пусть автобусы приходят на остановку случайно, но с некоторой фиксированной средней интенсивностью. Тогда количество времени, уже затраченное пассажиром на ожидание автобуса, не влияет на время, которое ему ещё придётся прождать\n",
    "* Время между потоком пуассоновских событий имеет экспоненциальное распределение\n",
    "* $Exp(\\frac{1}{2}) = \\chi^2_2$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Время, в которое в течение суток родится ребёнок "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HW0dsBAOrXvS1nOUDE7J0/MzgkVLyof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\ndQ1kTI0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Равномерное распределение, U[mn;mx]\n",
    "n = 10000\n",
    "mn=0; mx=24\n",
    "\n",
    "x <- runif(n, min = mn, max = mx)\n",
    "picture(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Взаимосвязи между распределениями \n",
    "\n",
    "http://www.math.wm.edu/~leemis/2008amstat.pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Что мы сделали? \n",
    "\n",
    "- Поняли, что тервер и матстат помогают нам выразить наше невежество\n",
    "- Вспомнили что такое ЗБЧ и ЦПТ и поговорили о том какие вещи они нам разрешают делать\n",
    "- Поговорили о том как в R генерируются случайные величины и решили пару задачек\n",
    "- Обсудили, что распределения бывают разными\n",
    "\n",
    "- - - - - - -\n",
    "- Поделились на команды \n",
    "- Приступили к решению первой домашки\n"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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
}