Prob_distributions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probability distributions, random variables\n",
    "### Dr. Tirthajyoti Sarkar, Fremont, CA 94536\n",
    "\n",
    "---\n",
    "\n",
    "This notebook illustrates the following concepts using simple scripts and functions from `Scipy` and `Numpy` packages.\n",
    "\n",
    "- Random variables\n",
    "- Law of the large number\n",
    "- Expected value\n",
    "- Discrete probability distributions\n",
    "- Concitinuous probability distributions\n",
    "- Moments, variance, and other properties of probability distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Throwing dice many times (illustrating the _Law of large numbers_)\n",
    "When we throw dice a large number of times, the average reaches 3.5 which is the expected value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dice = [x for x in range(1,7)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A fair dice has 6 faces: [1, 2, 3, 4, 5, 6]\n"
     ]
    }
   ],
   "source": [
    "print(\"A fair dice has 6 faces:\",dice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def throw_dice(n=10):\n",
    "    \"\"\"\n",
    "    Throw a (fair) die n number of times and returns the result in an array\n",
    "    \"\"\"\n",
    "    r = []\n",
    "    for _ in range(n):\n",
    "        r.append(random.choice(dice))\n",
    "    return np.array(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "throw_dice(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 3, 1, 5, 1, 4])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "throw_dice(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average of 1 dice throws: 1.0\n",
      "Average of 5 dice throws: 4.8\n",
      "Average of 10 dice throws: 4.3\n",
      "Average of 50 dice throws: 3.48\n",
      "Average of 100 dice throws: 3.25\n",
      "Average of 500 dice throws: 3.56\n",
      "Average of 1000 dice throws: 3.61\n",
      "Average of 5000 dice throws: 3.51\n",
      "Average of 10000 dice throws: 3.51\n"
     ]
    }
   ],
   "source": [
    "for i in [1,5,10,50,100,500,1000,5000,10000]:\n",
    "    print(\"Average of {} dice throws: {}\".format(i,round(throw_dice(i).mean(),2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expected value of a continuous function\n",
    "\n",
    "__Expected value or mean__: the weighted average of the possible values, using their probabilities as their weights; or the continuous analog thereof.\n",
    "\n",
    "Let $X$ be a random variable with a finite number of finite outcomes $x_1$,$x_2$,$x_3$,... occurring with probabilities $p_1$,$p_2$,$p_3$,... respectively. The expectation of $X$ is, then, defined as\n",
    "\n",
    "$$ E[X]=\\sum_{i=1}^{k}x_{i}\\,p_{i}=x_{1}p_{1}+x_{2}p_{2}+\\cdots +x_{k}p_{k} $$\n",
    "\n",
    "Since, all the probabilities $p_1$, $p_2$, $p_3$, add up to 1, $p_1+p_2+p_3+...=1$, it is the **weighted average**.\n",
    "\n",
    "For, continuous probability distributions, with a density function (PDF) of $f(x)$, the expected value is given by,\n",
    "\n",
    "$$ {\\displaystyle \\operatorname {E} [X]=\\int _{\\mathbb {R} }xf(x)\\,dx.}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's calculate the expected value of the function $P(x)=x.e^{-x}$ between $x=0$ and $x=\\infty$\n",
    "\n",
    "We are trying to compute,\n",
    "$$ \\int _{0}^{\\infty}x.P(x).dx = \\int _{0}^{\\infty}x.[x.e^{-x}].dx = \\int _{0}^{\\infty}x^2.e^{-x}.dx$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x):\n",
    "    import numpy as np\n",
    "    return x*np.exp(-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0,10,0.1)\n",
    "y = func(x)\n",
    "plt.plot(x,y,color='k',lw=3)\n",
    "plt.title(\"Function of $x.e^{-x}$\",fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use `scipy.integrate` module\n",
    "We will increase the upper limit of the integral slowly and show that the integral does not change much after a while."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The integral value for upper limit of 1 is : 0.2642411176571154\n",
      "The integral value for upper limit of 2 is : 0.593994150290162\n",
      "The integral value for upper limit of 3 is : 0.8008517265285442\n",
      "The integral value for upper limit of 4 is : 0.9084218055563291\n",
      "The integral value for upper limit of 5 is : 0.9595723180054871\n",
      "The integral value for upper limit of 6 is : 0.9826487347633355\n",
      "The integral value for upper limit of 7 is : 0.9927049442755638\n",
      "The integral value for upper limit of 8 is : 0.9969808363488774\n",
      "The integral value for upper limit of 9 is : 0.9987659019591333\n",
      "The integral value for upper limit of 10 is : 0.9995006007726127\n"
     ]
    }
   ],
   "source": [
    "integral_value=[]\n",
    "for i in range(1,11):\n",
    "    integral=scipy.integrate.quad(func,0,i)[0]\n",
    "    integral_value.append(integral)\n",
    "    print(\"The integral value for upper limit of {} is : {}\".format(i,integral))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1,11),integral_value,color='k',lw=3)\n",
    "plt.title(\"Integral of $x.e^{-x}$\",fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expectation(x):\n",
    "    return x*func(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0,20,0.1)\n",
    "y = expectation(x)\n",
    "plt.plot(x,y,color='k',lw=3)\n",
    "plt.title(\"Function of $x^2.e^{-x}$\",fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The integral value for upper limit of 1 is : 0.16060279414278839\n",
      "The integral value for upper limit of 2 is : 0.6466471676338731\n",
      "The integral value for upper limit of 3 is : 1.1536198377463132\n",
      "The integral value for upper limit of 4 is : 1.5237933888929112\n",
      "The integral value for upper limit of 5 is : 1.7506959610338377\n",
      "The integral value for upper limit of 6 is : 1.8760623911666823\n",
      "The integral value for upper limit of 7 is : 1.9407276722389566\n",
      "The integral value for upper limit of 8 is : 1.972492064511994\n",
      "The integral value for upper limit of 9 is : 1.9875356097872454\n",
      "The integral value for upper limit of 10 is : 1.9944612085689766\n"
     ]
    }
   ],
   "source": [
    "integral_value=[]\n",
    "for i in range(1,11):\n",
    "    integral=scipy.integrate.quad(expectation,0,i)[0]\n",
    "    integral_value.append(integral)\n",
    "    print(\"The integral value for upper limit of {} is : {}\".format(i,integral))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1,11),integral_value,color='k',lw=3)\n",
    "plt.title(\"Integral of $x^2.e^{-x}$\",fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discrete and Continuous Distributions\n",
    "\n",
    "Probability distributions are generally divided into two classes. A __discrete probability distribution__ (applicable to the scenarios where the set of possible outcomes is discrete, such as a coin toss or a roll of dice) can be encoded by a discrete list of the probabilities of the outcomes, known as a [probability mass function](https://en.wikipedia.org/wiki/Probability_mass_function). \n",
    "\n",
    "On the other hand, a __continuous probability distribution__ (applicable to the scenarios where the set of possible outcomes can take on values in a continuous range (e.g. real numbers), such as the temperature on a given day) is typically described by probability density functions (with the probability of any individual outcome actually being 0). Such distributions are generally described with the help of [probability density functions](https://en.wikipedia.org/wiki/Probability_density_function)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some Essential Terminologies\n",
    "\n",
    "* __Mode__: for a discrete random variable, the value with highest probability (the location at which the probability mass function has its peak); for a continuous random variable, a location at which the probability density function has a local peak.\n",
    "* __Support__: the smallest closed set whose complement has probability zero.\n",
    "* __Head__: the range of values where the pmf or pdf is relatively high.\n",
    "* __Tail__: the complement of the head within the support; the large set of values where the pmf or pdf is relatively low.\n",
    "* __Expected value or mean__: the weighted average of the possible values, using their probabilities as their weights; or the continuous analog thereof.\n",
    "* __Median__: the value such that the set of values less than the median, and the set greater than the median, each have probabilities no greater than one-half.\n",
    "* __Variance__: the second moment of the pmf or pdf about the mean; an important measure of the dispersion of the distribution.\n",
    "* __Standard deviation__: the square root of the variance, and hence another measure of dispersion.\n",
    "\n",
    "* __Symmetry__: a property of some distributions in which the portion of the distribution to the left of a specific value is a mirror image of the portion to its right.\n",
    "* __Skewness__: a measure of the extent to which a pmf or pdf \"leans\" to one side of its mean. The third standardized moment of the distribution.\n",
    "* __Kurtosis__: a measure of the \"fatness\" of the tails of a pmf or pdf. The fourth standardized moment of the distribution.\n",
    "\n",
    "![kurtosis](https://anotherbloodybullshitblog.files.wordpress.com/2016/01/normal-not-always-the-norm.gif?w=809)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quick mathematical definitions of mean, variance, skewness, and kurtosis with respect to a PDF $P(x)$\n",
    "\n",
    "$$\\text{1st raw moment } \\mathbf{Mean\\ (1st\\ moment):} \\int x.P(x).dx$$\n",
    "\n",
    "$$\\text{Centralized 2nd moment } \\mathbf{Variance\\ (2nd\\ moment):} \\int (x-\\mu)^2.P(x).dx$$\n",
    "\n",
    "$$\\text{Pearson's 3rd moment (Standardized) }\\mathbf{Skew\\ (3rd\\ moment):} \\int\\left ( \\frac{x-\\mu}{\\sigma} \\right )^3.P(x).dx$$\n",
    "\n",
    "$$\\text{Pearson's 4th moment (Standardized)  }\\mathbf{Kurtosis\\ (4th\\ moment):} \\int\\left ( \\frac{x-\\mu}{\\sigma} \\right )^4.P(x).dx$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bernoulii distribution\n",
    "\n",
    "The Bernoulli distribution, named after Swiss mathematician [Jacob Bernoulli](https://en.wikipedia.org/wiki/Jacob_Bernoulli), is the probability distribution of a random variable which takes the value 1 with probability $p$ and the value 0 with probability $q = 1 − p$ — i.e., the probability distribution of any single experiment that asks a ___yes–no question___; the question results in a boolean-valued outcome, a single bit of information whose value is success/yes/true/one with probability $p$ and failure/no/false/zero with probability $q$. \n",
    "\n",
    "It can be used to represent a coin toss where 1 and 0 would represent \"head\" and \"tail\" (or vice versa), respectively. In particular, unfair coins would have $p ≠ 0.5$.\n",
    "\n",
    "![coin](https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/coin_toss.PNG)\n",
    "\n",
    "The probability mass function $f$ of this distribution, over possible outcomes $k$, is\n",
    "\n",
    "$${\\displaystyle f(k;p)={\\begin{cases}p&{\\text{if }}k=1,\\\\[6pt]1-p&{\\text{if }}k=0.\\end{cases}}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import bernoulli"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random variates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 0, 1, 0, 0, 0])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# p=0.5 i.e. fair coin\n",
    "bernoulli.rvs(p=0.5,size=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loaded coin towards tail, p=0.2 for head"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# p=0.2 i.e. more tails (0) than heads(1)\n",
    "bernoulli.rvs(p=0.2,size=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loaded coin towards head, p=0.8 for head"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# p=0.8 i.e. more heads (1) than tails (0)\n",
    "bernoulli.rvs(p=0.8,size=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note, a single run or even a small number of runs may not produce the expected distribution of 1's and 0's. \n",
    "For example, if you assign $p=0.5$, you may not get half 1's and half 0's every time you evaluate the function. Experiment with $N$ number of trials to see how the probability distribution gradually centers around 0.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ehpqxGO+/f70cm/hzs9tyzJ49eyAiDmzmvlWK/EDgJuDgiLhZ0leA1RHxmeHuM3PmzFi2bFkzeVqmv7+fvr6+jmbolhydzCCJWAD9k8+h74XTNpw/B0Z7DrbSeI/F0N+/XoaasRjvv3+9HJv4c7PbckhqusirfNi5AlgRETfn64uANzazMTMza71RizwiHgOWS5qZbzqUdJrFzMy6QNVvrXwIWJC/sXIf8MH2RTIzs7GoVOQRcTvQ1LkbMzNrL/+y08yscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscJWLXNJmkm6T9L12BjIzs7EZyx75R4C72hXEzMyaU6nIJU0FjgAubG8cMzMbK0XE6AtJi4CzgK2B0yLiyAbLzAXmAkyZMqV34cKFLY46NoODg/T09HQ0QzfkWLLkTnbccSdWrFjRcP6kSZuz7777tW37AwMD9O4OgxOm0vPyhhkG7ofe3t62bX/JkjtZs2btK9enTp263liM199fq3Ys2v33j6TTz81uydAtOWbPnj0QEQc2c99Ri1zSkcDhEXGqpD6GKfJaM2fOjGXLljWTp2X6+/vp6+vraIZuyCGJxZefQ98LpzWePweqvJlvzPZjAfRPbpxhvLY/pD7HeG+/PkO7tz+STj83uyVDt+SQ1HSRVzm1cjBwtKQHgMuAQyRd0szGzMys9UYt8oj454iYGhHTgWOBayPi+LYnMzOzSvw9cjOzwk0cy8IR0Q/0tyWJmZk1xXvkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFc5GbmRXORW5mVjgXuZlZ4VzkZmaFG7XIJU2TtFjSXZKWSvrIeAQzM7NqJlZY5kVgXkTcKmlrYEDSjyPi123OZmZmFYy6Rx4Rj0bErXn6WeAuYNd2BzMzs2oUEdUXlqYD1wP7RMTqunlzgbkAU6ZM6V24cGHrUjZhcHCQnp6ejmYAWLVqFcuXLx92/qRJm7Pvvvu1bfsDAwPM3GMqPS+vaDz/fujt7W3r9nt3h8EJjTOM1/aH1OcY7+3XZ2j39pcsuZM1a9Y2nDd16lRWrVrZ1uffSNsHmDZtGjvuuGPbtl9VN/TF7NmzByLiwGbuW7nIJfUA1wFnRsQVIy07c+bMWLZsWTN5Wqa/v5++vr6OZgA499xzmbfLacPO1xwYy5vpWEli8eXn0PdC4wzjsf1YAP2TG2cYr+0Pqc8x3tuvz9CJ7dfmmP2e0zq2fYBzHz2HefPmtW37VXVDX0hqusgrfWtF0ubA5cCC0UrczMzGV5VvrQj4OnBXRJzX/khmZjYWVfbIDwbeDxwi6fZ8ObzNuczMrKJRv34YETcAGocsZmbWBP+y08yscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscC5yM7PCucjNzArnIjczK5yL3MyscJWKXNJhkpZJulfSJ9sdyszMqhu1yCVtBpwPvBOYBRwnaVa7g5mZWTVV9sj/DLg3Iu6LiDXAZcC72hvLzMyqUkSMvIB0DHBYRJyUr78f+C8R8Y91y80F5uar+wC/an3cMdkBeKLDGaA7cjjDOt2QoxsyQHfk6IYM0B05ZkbE1s3ccWKFZdTgtg3aPyIuAC4AkHRLRBzYTKBW6YYM3ZLDGborRzdk6JYc3ZChW3JIuqXZ+1Y5tbICmFZzfSrwSLMbNDOz1qpS5L8E9pK0u6RJwLHAle2NZWZmVY16aiUiXpT0j8DVwGbANyJi6Sh3u6AV4TZSN2SA7sjhDOt0Q45uyADdkaMbMkB35Gg6w6gfdpqZWXfzLzvNzArnIjczK1zTRT7az/YlvUrSt/P8myVN35igG5HjrZJulfRi/k58JzJ8TNKvJd0p6T8l7dahHCdLWiLpdkk3tOMXulX/OQdJx0gKSW35yleFsThB0uN5LG6XdNJ4Z8jLvDc/N5ZK+larM1TJIenLNeNwj6SnO5DhdZIWS7otv04Ob3WGijl2y6/ROyX1S5rahgzfkLRKUsPf2ij5XznjnZLeOOpKI2LMF9KHnr8FXg9MAu4AZtUtcyrw1Tx9LPDtZrbVghzTgf2Ai4FjOpRhNrBlnj6lg2OxTc300cCPxjtDXm5r4HrgJuDADo3FCcD/bvW2x5hhL+A2YLt8fcdO5Khb/kOkLzSM91hcAJySp2cBD3ToMfkO8IE8fQgwvw053gq8EfjVMPMPB35I+g3PQcDNo62z2T3yKj/bfxfwzTy9CDhUUqMfF22MUXNExAMRcSfwcou3PZYMiyPi9/nqTaTv4ncix+qaq1vR4Idd7c6QfQH4EvBCi7c/1hztVCXD3wPnR8TvACJiVYdy1DoOuLQDGQLYJk+/mvb8VqVKjlnAf+bpxQ3mb7SIuB54aoRF3gVcHMlNwLaSdhlpnc0W+a7A8prrK/JtDZeJiBeBZ4Dtm9zexuRot7FmOJH0btuRHJL+QdJvSUX64fHOIOkAYFpEfK/F2x5Tjuw9+dB1kaRpDea3O8MMYIakGyXdJOmwFmeomgNIpxWA3YFrO5DhDOB4SSuAH5CODFqtSo47gPfk6XcDW0tqdW+NZsy91myRV/nZfqWf9m+k8dhGyzJIOh44EPi3TuWIiPMjYg/gE8Dp45lB0gTgy8C8Fm93TDmyq4DpEbEf8BPWHT2OZ4aJpNMrfaQ94QslbduBHEOOBRZFxEsdyHAccFFETCWdWpifny/jneM04G2SbgPeBjwMvNjiHKMZc681O1BVfrb/yjKSJpIOl0Y6nGhXjnarlEHS24FPA0dHxB86laPGZcBfj3OGrUn/oFq/pAdI5/+ubMMHnqOORUQ8WfM4fA3oHe8MeZnvRsTaiLgfWEYq9vHOMeRYWn9apWqGE4GFABHxc2Ay6R+yGtccEfFIRPzXiDiA9HolIp5pcY7RjL3XmjxZPxG4j3QYNvShwRvqlvkH1v+wc2EbPjQYNUfNshfRng87q4zFAaQPWfZq9fbHmGOvmumjgFs69Xjk5ftpz4edVcZil5rpdwM3dSDDYcA38/QOpMPp7TvxmAAzgQfIPxLswFj8EDghT+9NKq6WZqmYYwdgQp4+E/h8q8cjr3s6w3/YeQTrf9j5i1HXtxFBDgfuyQX16Xzb50l7nJDeUb8D3Av8Anh9mwZktBxvIr3DPQc8CSztQIafACuB2/Plyg6NxVeApTnD4kYv6HZnqFu2nzYUecWxOCuPxR15LP6kAxkEnAf8GlgCHNuJscjXzwDObsf2K47FLODG/HjcDvxlh3IcA/wmL3Mh8Ko2ZLgUeBRYm7vpROBk4OSa58X5OeOSKq8R/0TfzKxw/mWnmVnhXORmZoVzkZuZFc5FbmZWOBe5mVnhXORmZoVzkZuZFe7/AwCsWzAMQJV4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DDn8zsww5/M3MMuTwNzPLkMPfzCxDDn8zsww5/M3MMuTwNzPLkMPfzCxDDn8zsww5/M3MMuTwNzPLkMPfzCxDDn8zsww5/M3MMuTwNzPLkMPfzCxDDn8zsww5/M3MMuTwNzPLkMPfzCxDDn8zsww5/M3MMuTwNzPL0JjhL2m6pJ9LulXSKkmfTsPnSbpJ0t2SviVpyzR8q9S/Jo3vau5bMDOz8arlzP93wL4R8QbgjcD+kvYBvgCcHRHzgSeAJWn6JcATEbEbcHaazszM2siY4R+FodQ7Lb0C2Be4LA1fBrwndR+W+knj95OkhlVsZmYTpogYeyJpC6Af2A04B/gScGM6u0dSJ3B1ROwp6Q5g/4gYSOPuAd4SEY+WLfM44DiAWbNmda9YsaJx76pOQ0NDdHR0ZF9Du9QxODjITtMGxjVP/33Q3d097nX19/fTPW/k8KEpc+l4qXIN9a6rHpPZFtW0wz7RLnW0Qw0Avb29/RGxdz3zTq1looh4EXijpJnAfwF7VJos/VvpLH/EJ0xEnAucC7BgwYLo6emppZSm6uvro9V1tEMN7VLH0qVLOXLOSeOap/ckqOWEZsR8vb3ExSOH900/k56NlWuod131mMy2qKYd9ol2qaMdapiocT3tExEbgD5gH2CmpOEPj7nA+tQ9AHQCpPGvBB5vRLFmZtYYtTztMyud8SNpa+BdwJ3ASuDwNNmxwOWp+4rUTxp/bUzW6ZGZmdWklts+c4Bl6b7/FGBFRFwp6dfApZI+B9wMnJ+mPx9YLmkNxRn/UU2o28zMJmDM8I+I24C9Kgy/F3hzheEbgSMaUp2ZmTWFf+FrZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mb2Ml2ds5E04tXf319xuCS6Ome3umwbp6mtLsDM2svagUHi4pHD+6ZTcTiAFg02tyhrOJ/5m5llyOGfsWqX96Nd4vvy3uyPg2/7ZKza5T1Uv8T35b3ZHwef+ZuZZcjhb2aWIYe/mVmGHP5mZhkaM/wldUpaKelOSask/UMavr2kH0q6O/27XRouSV+WtEbSbZLe1Ow3YWZm41PLmf8LwIkRsQewD3CCpIXAqcA1ETEfuCb1AxwAzE+v44CvNrxqMzObkDHDPyIeiohfpe6ngTuBnYHDgGVpsmXAe1L3YcBFUbgRmClpTsMrNzOzuikiap9Y6gKuB/YEHoiImSXjnoiI7SRdCZwRETek4dcAp0TEL8uWdRzFlQGzZs3qXrFixQTfysQNDQ3R0dGRTQ39/f10z6tSx5S5dLw0MHKe+6C7u7vJlRUGBwfZadrIGkZTb33V2qJaO0xkXfVwW5TUkdlxOpre3t7+iNi7nnlrDn9JHcB1wOcj4juSNlQJ/+8Bp5eF/8kR0V9t2QsWLIjVq1fXU39D9fX10dPTk00Nkkb5kdeZ9Gw8aeQ8i2A8JwwTsXTpUk6cM7KG0dRbX7W2qNYOE1lXPdwWJXVkdpyORlLd4V/T0z6SpgH/CVwcEd9JgweHb+ekfx9JwweAzpLZ5wLr6ynOzMyao5anfQScD9wZEWeVjLoCODZ1HwtcXjL8g+mpn32AJyPioQbWbGZmE1TL3/Z5G/AB4HZJt6RhHwfOAFZIWgI8AByRxl0FHAisAZ4FPtTQis3MbMLGDP90715VRu9XYfoATphgXWZm1kT+ha+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llyOFvZpYhh7+ZWYYc/mZmGXL4m5llaMzwl3SBpEck3VEybHtJP5R0d/p3uzRckr4saY2k2yS9qZnFm5lZfWo5878Q2L9s2KnANRExH7gm9QMcAMxPr+OArzamTDMza6Qxwz8irgceLxt8GLAsdS8D3lMy/KIo3AjMlDSnUcWamVlj1HvPf6eIeAgg/fuqNHxnYF3JdANpmJmZtRFFxNgTSV3AlRGxZ+rfEBEzS8Y/ERHbSfoecHpE3JCGXwOcHBH9FZZ5HMWtIWbNmtW9YsWKBrydiRkaGqKjoyObGvr7++meV6WOKXPpeGlg5Dz3QXd3d5MrKwwODrLTtJE1jKbe+qq1RbV2mMi66uG2KKkjs+N0NL29vf0RsXc989Yb/quBnoh4KN3W6YuIBZL+X+q+pHy60Za/YMGCWL16dT31N1RfXx89PT3Z1CCJuLhKHdPPpGfjSSPnWQS17DONsHTpUk6cM7KG0dRbX7W2qNYOE1lXPdwWJXVkdpyORlLd4V/vbZ8rgGNT97HA5SXDP5ie+tkHeHKs4Dczs8k3dawJJF0C9AA7ShoAPgWcAayQtAR4ADgiTX4VcCCwBngW+FATajYzswkaM/wj4ugqo/arMG0AJ0y0KDMzay7/wtfMLEMOfzOzDDn8zcwy5PA3M8uQw9/MLEMOfzOzDDn8zcwy5PA3M8uQw7/N3H77bUga16urc3aryzabND5GGmPMX/ja5Hr++U1V/9haNVo02JxizNqQj5HG8Jm/mVmGHP5mZhly+JuZZcjhb2aWIYe/mVmGHP5mZhly+JuZZcjhb2aWIYe/mVmGHP5mZhly+JuZZcjhb2aWIYe/mVmGHP5mZhly+JuZZcjhb2aWIYe/mVmGHP5mZhly+JuZZcjhb2aWIYe/mVmGsgv/rs7ZSKr46u/vrzi8q3N2q8s2M2uoqa0uYLKtHRgkLq48rm86Fcdp0WBzizKzttTVOZu1AyOP/zPPPJPe3t6K8+wydyfuX/dws0ubsOzC38ysVtVOFqudKMIfzslidrd9zMzM4W9mlqWmhL+k/SWtlrRG0qnNWIeZmdWv4eEvaQvgHOAAYCFwtKSFjV6PmZnVrxln/m8G1kTEvRHxPHApcNhoMzz33HNVH7+s9vLjl2b2x2K0R9BHe02EIqJB5acFSocD+0fEh1P/B4C3RMTflk13HHBc6t0TuKOhhdRnR+BR1wC0Rx2uYbN2qKMdaoD2qKMdagBYEBEz6pmxGY96Vvo4GvEJExHnAucCSPplROzdhFrGpR3qaIca2qUO19BedbRDDe1SRzvUMFxHvfM247bPANBZ0j8XWN+E9ZiZWZ2aEf6/AOZLmidpS+Ao4IomrMfMzOrU8Ns+EfGCpL8Fvg9sAVwQEavGmO3cRtdRp3aoox1qgPaowzVs1g51tEMN0B51tEMNMIE6Gv6Fr5mZtT//wtfMLEMOfzOzDE1q+I/1Zx8kbSXpW2n8TZK6WlDDOyT9StIL6TcLTVFDHR+T9GtJt0m6RtIuLajheEm3S7pF0g3N+qV2rX8ORNLhkkJSwx+xq6EtFkv6bWqLWyR9uNE11FJHmub9ad9YJembk12DpLNL2uEuSRsaXUONdbxG0kpJN6fj5MAW1LBLOj5vk9QnaW4TarhA0iOSKv4WSoUvpxpvk/SmmhYcEZPyovjy9x5gV2BL4FZgYdk0HwW+lrqPAr7Vghq6gNcDFwGHt7AteoFXpO6PtKgtti3pPhT471a0RZpuBnA9cCOwdwvaYjHw783YH8ZZx3zgZmC71P+qVmyPkun/juKhjla0xbnAR1L3QuD+FtTwbeDY1L0vsLwJbfEO4E3AHVXGHwhcTfEbq32Am2pZ7mSe+dfyZx8OA5al7suA/TTR3zCPs4aIuD8ibgNeauB666ljZUQ8m3pvpPi9xGTX8FRJ7zZU+LHeZNSRfBb4IrCxhTU0Wy11/A1wTkQ8ARARj7SghlJHA5c0uIZa6whg29T9Shr/e6JaalgIXJO6V1YYP2ERcT3w+CiTHAZcFIUbgZmS5oy13MkM/52BdSX9A2lYxWki4gXgSWCHSa5hMoy3jiUUn+yTXoOkEyTdQxG8f9/gGmqqQ9JeQGdEXNmE9ddUQ/K+dFl9maTOCuMno47dgd0l/UTSjZL2b0ENQHHLA5gHXNvgGmqt4zTgGEkDwFUUVyGTXcOtwPtS93uBGZIamVm1qCvXJjP8a/mzDzX9aYgm1zAZaq5D0jHA3sCXWlFDRJwTEa8FTgE+2eAaxqxD0hTgbODEJqy7phqS7wJdEfF64EdsvkKd7DqmUtz66aE46z5P0sxJrmHYUcBlEfFiA9c/njqOBi6MiLkUtz6Wp/1lMms4CXinpJuBdwIPAi80sIZa1JVrkxn+tfzZh99PI2kqxaXcaJc7zahhMtRUh6R3AZ8ADo2I37WihhKXAu9pcA211DGD4g//9Um6n+Ke5hUN/tJ3zLaIiMdKtsHXge4Grr/mOtI0l0fEpoi4D1hN8WEwmTUMO4rm3PKptY4lwAqAiPgZMJ3iD65NWg0RsT4i/ioi9qI4VomIJxtYQy3qy7VGfzkxypcWU4F7KS4Th788eV3ZNCfw8i98V0x2DSXTXkjzvvCtpS32oviyaX4La5hf0n0I8MtW1FE2fR+N/8K3lraYU9L9XuDGFm2T/YFlqXtHisv9HSZ7ewALgPtJPxRtUVtcDSxO3XtQBF7D6qmxhh2BKan788BnmtQeXVT/wvcgXv6F789rWmYzCh3lDRwI3JVC7RNp2Gcozmyh+OT+NrAG+Dmwawtq+DOKT9JngMeAVS1qix8Bg8At6XVFC2r4N2BVWv/KSiEwGXWUTdtHg8O/xrY4PbXFrakt/qRF+4WAs4BfA7cDR7Vie1Dcbz+jGW0wjrZYCPwkbZNbgL9oQQ2HA3enac4DtmpCDZcADwGbUjYtAY4Hji/ZJ85JNd5e6/HhP+9gZpYh/8LXzCxDDn8zsww5/M3MMuTwNzPLkMPfzCxDDn8zsww5/M3MMvT/AVOLPWSSedWOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_trials = [10,20,50,100,200,500,1000,2000,5000] # Number of trials\n",
    "pr=0.5 # Fair coin toss probability\n",
    "av = [] # Empty list to store the average of the random variates\n",
    "\n",
    "# Generate 10 variates every time and take the average. That should be # of 1's i.e. 0.5 for a fair coin.\n",
    "for i in N_trials:\n",
    "    for n in range(1,i+1):\n",
    "        av.append(np.mean(bernoulli.rvs(p=pr,size=10)))\n",
    "    if (i==10):\n",
    "        plt.title(\"Distribution with {} trials of 10 coin tosses\".format(i))\n",
    "        plt.hist(av,bins=10,edgecolor='k',color='orange')\n",
    "        plt.xlim(0.0,1.0)\n",
    "        plt.xticks([0.1*i for i in range(11)])\n",
    "        plt.grid(True)\n",
    "        plt.show()\n",
    "    else:\n",
    "        plt.title(\"Distribution with {} trials of 10 coin tosses\".format(i))\n",
    "        plt.hist(av,bins=25,edgecolor='k',color='orange')\n",
    "        plt.xlim(0.0,1.0)\n",
    "        plt.xticks([0.1*i for i in range(11)])\n",
    "        plt.grid(True)\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean, variance, skew, and kurtosis\n",
    "Use `bernoulli.stats()` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A fair coin is spinning...\n",
      "------------------------------\n",
      "Mean: 0.5\n",
      "Variance: 0.25\n",
      "Skew: 0.0\n",
      "Kurtosis: -2.0\n"
     ]
    }
   ],
   "source": [
    "print(\"A fair coin is spinning...\\n\"+\"-\"*30)\n",
    "pr=0.5 # Fair coin toss probability\n",
    "mean, var, skew, kurt = bernoulli.stats(p=pr, moments='mvsk')\n",
    "print(\"Mean:\",mean)\n",
    "print(\"Variance:\",var)\n",
    "print(\"Skew:\",skew)\n",
    "print(\"Kurtosis:\",kurt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Now a biased coin is spinning...\n",
      "-----------------------------------\n",
      "Mean: 0.7\n",
      "Variance: 0.21000000000000002\n",
      "Skew: -0.8728715609439702\n",
      "Kurtosis: -1.2380952380952361\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nNow a biased coin is spinning...\\n\"+\"-\"*35)\n",
    "pr=0.7 # Biased coin toss probability\n",
    "mean, var, skew, kurt = bernoulli.stats(p=pr, moments='mvsk')\n",
    "print(\"Mean:\",mean)\n",
    "print(\"Variance:\",var)\n",
    "print(\"Skew:\",skew)\n",
    "print(\"Kurtosis:\",kurt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability mass function (PMF) and cumulative distribution function (CDF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability mass function for 0: 0.4\n",
      "Probability mass function for 0.5: 0.0\n",
      "Probability mass function for 1.0: 0.6\n",
      "Probability mass function for 1.2: 0.0\n"
     ]
    }
   ],
   "source": [
    "rv = bernoulli(0.6)\n",
    "x=0\n",
    "print(\"Probability mass function for {}: {}\".format(x,rv.pmf(x)))\n",
    "x=0.5\n",
    "print(\"Probability mass function for {}: {}\".format(x,rv.pmf(x)))\n",
    "x=1.0\n",
    "print(\"Probability mass function for {}: {}\".format(x,rv.pmf(x)))\n",
    "x=1.2\n",
    "print(\"Probability mass function for {}: {}\".format(x,rv.pmf(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CDF for x < 0: 0.0\n",
      "CDF for 0< x <1: 0.4\n",
      "CDF for x >1: 1.0\n"
     ]
    }
   ],
   "source": [
    "print(\"CDF for x < 0:\",rv.cdf(-2))\n",
    "print(\"CDF for 0< x <1:\",rv.cdf(0.75))\n",
    "print(\"CDF for x >1:\",rv.cdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binomial distribution\n",
    "\n",
    "The binomial distribution with parameters $n$ and $p$ is the discrete probability distribution of the **number of successes in a sequence of $n$ independent experiments, each asking a _yes–no question_,** and each with its own boolean-valued outcome: a random variable containing single bit of information: success/yes/true/one (with probability $p$) or failure/no/false/zero (with probability $q = 1 − p$). A single success/failure experiment is also called a _Bernoulli trial_ or _Bernoulli experiment_ and a sequence of outcomes is called a _Bernoulli process_. \n",
    "\n",
    "For a single trial, i.e., n = 1, the binomial distribution is a **Bernoulli distribution**. The binomial distribution is the basis for the popular [binomial test](https://en.wikipedia.org/wiki/Binomial_test) of [statistical significance](https://en.wikipedia.org/wiki/Statistical_significance).\n",
    "\n",
    "The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a __[hypergeometric distribution](https://en.wikipedia.org/wiki/Hypergeometric_distribution)__, not a binomial one. However, for N much larger than n, the binomial distribution remains a good approximation, and is widely used.\n",
    "\n",
    "In general, if the random variable $X$ follows the binomial distribution with parameters n ∈ ℕ and p ∈ [0,1], we write X ~ B(n, p). The probability of getting exactly $k$ successes in $n$ trials is given by the probability mass function:\n",
    "\n",
    "$${\\Pr(k;n,p)=\\Pr(X=k)={n \\choose k}p^{k}(1-p)^{n-k}}$$\n",
    "\n",
    "for k = 0, 1, 2, ..., n, where\n",
    "\n",
    "$${\\displaystyle {\\binom {n}{k}}={\\frac {n!}{k!(n-k)!}}}$$\n",
    "\n",
    "![head_tail](https://wp-media.patheos.com/blogs/sites/308/2018/03/Probability-Tree-Diagram-coin-toss-1.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random variates\n",
    "8 coins are flipped (or 1 coin is flipped 8 times), each with probability of success (1) of 0.25. This trial/experiment is repeated for 10 times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of success for each trial: [3 1 2 1 2 4 3 2 0 1]\n",
      "Average of the success: 1.9\n"
     ]
    }
   ],
   "source": [
    "k=binom.rvs(8,0.25,size=10)\n",
    "print(\"Number of success for each trial:\",k)\n",
    "print(\"Average of the success:\", np.mean(k))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean, variance, skew, and kurtosis\n",
    "\n",
    "$$\\textbf{Mean} = n.p,\\ \\textbf{Variance}= n.p(1 - p), \\textbf{skewness}= \\frac{1-2p}{\\sqrt{n.p(1-p)}}, \\ \\textbf{kurtosis}= \\frac{1-6p(1-p)}{n.p(1-p)}$$\n",
    "\n",
    "Use `binom.stats()` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A fair coin (p=0.5) is spinning 5 times\n",
      "-----------------------------------\n",
      "Mean: 2.5\n",
      "Variance: 1.25\n",
      "Skew: 0.0\n",
      "Kurtosis: -0.4\n"
     ]
    }
   ],
   "source": [
    "print(\"A fair coin (p=0.5) is spinning 5 times\\n\"+\"-\"*35)\n",
    "pr=0.5 # Fair coin toss probability\n",
    "n=5\n",
    "mean, var, skew, kurt = binom.stats(n=n,p=pr, moments='mvsk')\n",
    "print(\"Mean:\",mean)\n",
    "print(\"Variance:\",var)\n",
    "print(\"Skew:\",skew)\n",
    "print(\"Kurtosis:\",kurt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Now a biased coin (p=0.7) is spinning 5 times...\n",
      "---------------------------------------------\n",
      "Mean: 3.5\n",
      "Variance: 1.0500000000000003\n",
      "Skew: -0.39036002917941315\n",
      "Kurtosis: -0.24761904761904757\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nNow a biased coin (p=0.7) is spinning 5 times...\\n\"+\"-\"*45)\n",
    "pr=0.7 # Biased coin toss probability\n",
    "n=5\n",
    "mean, var, skew, kurt = binom.stats(n=n,p=pr, moments='mvsk')\n",
    "print(\"Mean:\",mean)\n",
    "print(\"Variance:\",var)\n",
    "print(\"Skew:\",skew)\n",
    "print(\"Kurtosis:\",kurt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing probability mass function (PMF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=40\n",
    "pr=0.5\n",
    "rv = binom(n,pr)\n",
    "x=np.arange(0,41,1)\n",
    "pmf1 = rv.pmf(x)\n",
    "\n",
    "n=40\n",
    "pr=0.15\n",
    "rv = binom(n,pr)\n",
    "x=np.arange(0,41,1)\n",
    "pmf2 = rv.pmf(x)\n",
    "\n",
    "n=50\n",
    "pr=0.6\n",
    "rv = binom(n,pr)\n",
    "x=np.arange(0,41,1)\n",
    "pmf3 = rv.pmf(x)\n",
    "\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.title(\"Probability mass function: $\\\\binom{n}{k}\\, p^k (1-p)^{n-k}$\\n\",fontsize=20)\n",
    "plt.scatter(x,pmf1)\n",
    "plt.scatter(x,pmf2)\n",
    "plt.scatter(x,pmf3,c='k')\n",
    "plt.legend([\"$n=40, p=0.5$\",\"$n=40, p=0.3$\",\"$n=50, p=0.6$\"],fontsize=15)\n",
    "plt.xlabel(\"Number of successful trials ($k$)\",fontsize=15)\n",
    "plt.ylabel(\"Probability of success\",fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize the cumulative distrubition function (cdf)\n",
    "\n",
    "Cumulative distribution function for binomial distribution can also be represented in terms of the [regularized incomplete beta function](https://en.wikipedia.org/wiki/Regularized_incomplete_beta_function), as follows\n",
    "\n",
    "$${\\displaystyle {\\begin{aligned}F(k;n,p)&=\\Pr(X\\leq k)\\\\&=I_{1-p}(n-k,k+1)\\\\&=(n-k){n \\choose k}\\int _{0}^{1-p}t^{n-k-1}(1-t)^{k}\\,dt.\\end{aligned}}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=40\n",
    "pr=0.5\n",
    "rv = binom(n,pr)\n",
    "x=np.arange(0,41,1)\n",
    "cdf1 = rv.cdf(x)\n",
    "\n",
    "n=40\n",
    "pr=0.3\n",
    "rv = binom(n,pr)\n",
    "x=np.arange(0,41,1)\n",
    "cdf2 = rv.cdf(x)\n",
    "\n",
    "n=50\n",
    "pr=0.6\n",
    "rv = binom(n,pr)\n",
    "x=np.arange(0,41,1)\n",
    "cdf3 = rv.cdf(x)\n",
    "\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.title(\"Cumulative distribution function: $I_{1-p}(n - k, 1 + k)$\\n\",fontsize=20)\n",
    "plt.scatter(x,cdf1)\n",
    "plt.scatter(x,cdf2)\n",
    "plt.scatter(x,cdf3,c='k')\n",
    "plt.legend([\"$n=40, p=0.5$\",\"$n=40, p=0.3$\",\"$n=50, p=0.6$\"],fontsize=15)\n",
    "plt.xlabel(\"Number of successful trials\",fontsize=15)\n",
    "plt.ylabel(\"Cumulative probability of success\",fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interval that contains a specific percentage of distribution\n",
    "Use `binom.interval` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interval that contains 25 percent of distribution with an experiment with 40 trials and 0.3 success probability  is: (11.0, 13.0)\n"
     ]
    }
   ],
   "source": [
    "n=40\n",
    "pr=0.3\n",
    "percent=25\n",
    "interval = binom.interval(percent/100,n,pr,loc=0)\n",
    "print(\"Interval that contains {} percent of distribution with an experiment with {} trials and {} success probability  is: {}\"\n",
    "      .format(percent,n,pr,interval))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson Distribution\n",
    "\n",
    "The Poisson distribution (named after French mathematician Siméon Denis Poisson), is a discrete probability distribution that **expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.** The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.\n",
    "\n",
    "For instance, an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day. If receiving any particular piece of mail does not affect the arrival times of future pieces of mail, i.e., if pieces of mail from a wide range of sources arrive independently of one another, then a reasonable assumption is that the number of pieces of mail received in a day obeys a Poisson distribution. Other examples, that may follow a Poisson distribution, include\n",
    "\n",
    "* number of phone calls received by a call center per hour \n",
    "* number of decay events per second from a radioactive source\n",
    "* The number of meteors greater than 1 meter diameter that strike Earth in a year\n",
    "* The number of patients arriving in an emergency room between 10 and 11 pm\n",
    "\n",
    "**Poisson distribution is a limiting case of a Binomial Distribution where the number of trials is sufficiently bigger than the number of successes one is asking about i.e. $n>>1>>p$**\n",
    "\n",
    "An event can occur 0, 1, 2, … times in an interval. The average number of events in an interval is designated $\\lambda$. This is the event rate, also called the rate parameter. The probability of observing k events in an interval is given by the equation\n",
    "\n",
    "${P(k{\\text{ events in interval}})=e^{-\\lambda }{\\frac {\\lambda ^{k}}{k!}}}$\n",
    "\n",
    "where,\n",
    "\n",
    "${\\lambda}$ is the average number of events per interval\n",
    "\n",
    "e is the number 2.71828... (Euler's number) the base of the natural logarithms\n",
    "\n",
    "k takes values 0, 1, 2, …\n",
    "k! = k × (k − 1) × (k − 2) × … × 2 × 1 is the factorial of k."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "la=0.5\n",
    "rv = poisson(la)\n",
    "x=np.arange(0,11,1)\n",
    "pmf1 = rv.pmf(x)\n",
    "\n",
    "la=1\n",
    "rv = poisson(la)\n",
    "x=np.arange(0,11,1)\n",
    "pmf2 = rv.pmf(x)\n",
    "\n",
    "la=5\n",
    "rv = poisson(la)\n",
    "x=np.arange(0,11,1)\n",
    "pmf3 = rv.pmf(x)\n",
    "\n",
    "plt.figure(figsize=(9,6))\n",
    "plt.title(\"Probability mass function: $e^{-\\lambda}{(\\lambda^k/k!)}$\\n\",fontsize=20)\n",
    "plt.scatter(x,pmf1,s=100)\n",
    "plt.scatter(x,pmf2,s=100)\n",
    "plt.scatter(x,pmf3,c='k',s=100)\n",
    "plt.legend([\"$\\lambda=0.5$\",\"$\\lambda=1$\",\"$\\lambda=5$\"],fontsize=15)\n",
    "plt.xlabel(\"Number of occurences ($k$)\",fontsize=15)\n",
    "plt.ylabel(\"$Pr(X=k)$\",fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the cumulative distribution function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "la=0.5\n",
    "rv = poisson(la)\n",
    "x=np.arange(0,11,1)\n",
    "cdf1 = rv.cdf(x)\n",
    "\n",
    "la=2\n",
    "rv = poisson(la)\n",
    "x=np.arange(0,11,1)\n",
    "cdf2 = rv.cdf(x)\n",
    "\n",
    "la=5\n",
    "rv = poisson(la)\n",
    "x=np.arange(0,11,1)\n",
    "cdf3 = rv.cdf(x)\n",
    "\n",
    "plt.figure(figsize=(9,6))\n",
    "plt.title(\"Cumulative distribution function\\n\",fontsize=20)\n",
    "plt.scatter(x,cdf1,s=100)\n",
    "plt.scatter(x,cdf2,s=100)\n",
    "plt.scatter(x,cdf3,c='k',s=100)\n",
    "plt.legend([\"$\\lambda=0.5$\",\"$\\lambda=2$\",\"$\\lambda=5$\"],fontsize=15)\n",
    "plt.xlabel(\"Number of occurences ($k$)\",fontsize=15)\n",
    "plt.ylabel(\"Cumulative distribution function\",fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moments - mean, variance, skew, and kurtosis\n",
    "Various moments of a Poisson distributed random variable $X$ are as follows:\n",
    "\n",
    "$$ \\textbf{Mean}=\\lambda,\\ \\textbf{Variance}=\\lambda,\\ \\textbf{skewness}=\\frac {1}{\\sqrt{\\lambda}},\\ \\textbf{kurtosis}=\\frac{1}{\\lambda}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Geometric distribution\n",
    "\n",
    "The geometric distribution is either of two discrete probability distributions:\n",
    "- The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...}\n",
    "- The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... }\n",
    "\n",
    "Which of these one calls \"the\" geometric distribution is a matter of convention and convenience.\n",
    "\n",
    "These two different geometric distributions should not be confused with each other. Often, the name shifted geometric distribution is adopted for the former one (distribution of the number $X$); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly.\n",
    "\n",
    "The geometric distribution gives the probability that the first occurrence of success requires $k$ independent trials, each with success probability $p$. If the probability of success on each trial is $p$, then the probability that the $k^{th}$ trial (out of $k$ trials) is the first success is\n",
    "\n",
    "${\\Pr(X=k)=(1-p)^{k-1}\\,p\\,}$\n",
    "\n",
    "for $k = 1, 2, 3, ....$\n",
    "\n",
    "The above form of the geometric distribution is used for modeling the number of trials up to and including the first success. By contrast, the following form of the geometric distribution is used for modeling the number of failures until the first success:\n",
    "\n",
    "${\\Pr(Y=k)=(1-p)^{k}\\,p\\,}$\n",
    "\n",
    "for $k = 0, 1, 2, 3, ....$\n",
    "\n",
    "In either case, the sequence of probabilities is a geometric sequence.\n",
    "\n",
    "The geometric distribution is an appropriate model if the following assumptions are true.\n",
    "- The phenomenon being modelled is a sequence of independent trials.\n",
    "- There are only two possible outcomes for each trial, often designated success or failure.\n",
    "- The probability of success, p, is the same for every trial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import geom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random variates\n",
    "It is difficult to get a success with low probability, so it takes more trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2  8  3 14  2 10  7 17 20  3]\n"
     ]
    }
   ],
   "source": [
    "r=geom.rvs(p=0.1,size=10)\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is easier to get the first success with higher probability, so it takes less number of trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 1 2 4 1 3 2 1 3 2]\n"
     ]
    }
   ],
   "source": [
    "r=geom.rvs(p=0.5,size=10)\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing probability mass function (PMF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p=0.1\n",
    "rv = geom(p)\n",
    "x=np.arange(1,11,1)\n",
    "pmf1 = rv.pmf(x)\n",
    "\n",
    "p=0.25\n",
    "rv = geom(p)\n",
    "x=np.arange(1,11,1)\n",
    "pmf2 = rv.pmf(x)\n",
    "\n",
    "p=0.75\n",
    "rv = geom(p)\n",
    "x=np.arange(1,11,1)\n",
    "pmf3 = rv.pmf(x)\n",
    "\n",
    "plt.figure(figsize=(9,6))\n",
    "plt.title(\"Probability mass function: $(1-p)^{k-1}p$\\n\",fontsize=20)\n",
    "plt.scatter(x,pmf1,s=100)\n",
    "plt.scatter(x,pmf2,s=100)\n",
    "plt.scatter(x,pmf3,c='k',s=100)\n",
    "plt.plot(x,pmf1)\n",
    "plt.plot(x,pmf2)\n",
    "plt.plot(x,pmf3,c='k')\n",
    "plt.legend([\"$p=0.1$\",\"$p=0.25$\",\"$p=0.75$\"],fontsize=15)\n",
    "plt.xlabel(\"Number of trials till first success ($k$)\",fontsize=15)\n",
    "plt.ylabel(\"$Pr(X=x)$\",fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing cumulative distribution function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p=0.1\n",
    "rv = geom(p)\n",
    "x=np.arange(1,11,1)\n",
    "cdf1 = rv.cdf(x)\n",
    "\n",
    "p=0.25\n",
    "rv = geom(p)\n",
    "x=np.arange(1,11,1)\n",
    "cdf2 = rv.cdf(x)\n",
    "\n",
    "p=0.75\n",
    "rv = geom(p)\n",
    "x=np.arange(1,11,1)\n",
    "cdf3 = rv.cdf(x)\n",
    "\n",
    "plt.figure(figsize=(9,6))\n",
    "plt.title(\"Cumulative distribution function: $1-(1-p)^k$\\n\",fontsize=20)\n",
    "plt.scatter(x,cdf1,s=100)\n",
    "plt.scatter(x,cdf2,s=100)\n",
    "plt.scatter(x,cdf3,c='k',s=100)\n",
    "plt.plot(x,cdf1)\n",
    "plt.plot(x,cdf2)\n",
    "plt.plot(x,cdf3,c='k')\n",
    "plt.legend([\"$p=0.1$\",\"$p=0.25$\",\"$p=0.75$\"],fontsize=15)\n",
    "plt.xlabel(\"Number of trials till first success ($k$)\",fontsize=15)\n",
    "plt.ylabel(\"$Pr(X\\leq x)$\",fontsize=15)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expected value (mean), variance, skewness, kurtosis\n",
    "Various moments of a geometrically distributed random variable $X$ are as follows:\n",
    "\n",
    "$$ \\textbf{Mean}=\\frac {1}{p},\\ \\textbf{Variance}=\\frac {1-p}{p^2},\\ \\textbf{skewness}=\\frac {2-p}{\\sqrt{1-p}},\\ \\textbf{kurtosis}=6+\\frac{p^2}{1-p}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Uniform (continuous) distribution\n",
    "\n",
    "This is the distribution of the likelihood of uniformly randomly selecting an item out of a finite collection.\n",
    "\n",
    "We are mostly familiar with the discontinuous version of this distribution. For example, in case of throwing a fair dice, the probability distribution of a single throw is given by: \n",
    "\n",
    "$$ \\left \\{ \\frac{1}{6},\\ \\frac{1}{6}, \\ \\frac{1}{6},\\ \\frac{1}{6},\\ \\frac{1}{6},\\ \\frac{1}{6} \\right \\} $$\n",
    "\n",
    "![dice](https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/dice.PNG)\n",
    "\n",
    "For the continuous case, the PDF looks deceptively simple, but the concept is subtle,\n",
    "\n",
    "$$ f(x)={\\begin{cases}{\\frac {1}{b-a}}&\\mathrm {for} \\ a\\leq x\\leq b,\\\\[8pt]0&\\mathrm {for} \\ x<a\\ \\mathrm {or} \\ x>b\\end{cases}} $$\n",
    "\n",
    "![uniform](https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/uniform_dist.PNG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import uniform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random variates (default between 0 and 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.49229275, 0.06090477, 0.30486429, 0.36542636, 0.78165005])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "uniform.rvs(size=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Change the `loc` and `scale` parameters to move the range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.51829242, -0.84691311, -7.73647821, -3.66167998, -1.11062837])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Random floats between -10 and 0\n",
    "uniform.rvs(loc=-10,scale=10,size=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.68295239, -1.30280798,  0.29132953, -5.6221547 ,  6.13996204])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Random floats between -10 and +10\n",
    "uniform.rvs(loc=-10,scale=20,size=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normal (Gaussian) distribution\n",
    "\n",
    "In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.\n",
    "\n",
    "The normal distribution is useful because of the **[central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem)**. In its most general form, under some conditions (which include finite variance), it states that **averages of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal**, that is, they become normally distributed when the number of observations is sufficiently large. \n",
    "\n",
    "Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.\n",
    "\n",
    "### PDF and CDF\n",
    "\n",
    "The probability density function (PDF) is given by,\n",
    "$$ f(x\\mid \\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}} $$\n",
    "where,\n",
    "- $\\mu$ is the mean or expectation of the distribution (and also its median and mode),\n",
    "- $\\sigma$ is the standard deviation, and $\\sigma^2$ is the variance.\n",
    "\n",
    "Cumulative distribution function (CDF) is given by,\n",
    "$$\\frac{1}{2}\\left [ 1+\\text{erf} \\left ( \\frac{x-\\mu}{\\sigma\\sqrt{2}}\\right ) \\right ]$$\n",
    "\n",
    "![normal](https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/normal.PNG)\n",
    "\n",
    "Scipy Stats page: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probability Density')"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2t2ZyZLfm/Pvig+J+yqp2jWvz+iWH0KdNAy57eSrPfbko7EgiEjIVcCKSMNydW9+aydMTF3LmwFSeOXd/aldPjNGSGtWpzr9+cyDH9WzB6Pdm89gnC8KOJCIhUgEnIgnB3bn7/Tn867ul/O6IjtxzSm+qJSfWj7iaKck8dfb+nDqgLQ+Nn8+zX2SFHUlEQpIYf5qKSJX30Pj5/P3LRVxwSAduGtq90ozvVtaSk4z7T+1Ddk4uf/pgDjWrJ3PuQe3DjiUiFUwFnIjEvSc/y+TxTzM5I70dfzyxZ8IWb3tVS07ikTP6sSsYnLhWSjKn7d827FgiUoES6/6CiFQ5z325iAfHzWNEv9bcM7IPSUmJXbztlZKcxBNnDeCwLk254bXpvDt9ZdiRRKQCqYATkbg1NmMZo9+bzZBeLfjLr/YjuYoUb3vVTElmzLnppLdvzDWvTuPTuWvCjiQiFUQFnIjEpa8XrueWN37ksC5NeezM/gnXYaGkalVP5u8XpNOjVX2ufPkH5qzaEnYkEakAVfMnnojEtax127j0pamkNa3Dk2cPqPRTY5W3ejVT+Nv56dSrmcJv/pnB2q2aO1Uk0amAE5G4smnHbi76ZwbJScbfzz+A+jVTwo5UKbSoX5O/nZ/Oxu27ufiFKWTvyQ07koiUIxVwIhI39uTmcelLU1nx006eOXd/UpvUDjtSpdK7TQMePqMf05Zt4vrXZuDuYUcSkXKiAk5E4oK7c9tbM/kmawP3ndqHAzo0DjtSpTS0d0tuHNqdd6ev5FHN1iCSsDQOnIjEhb9/uYhXJi/j8iM7MXKAxjwryiVHdCRz7TYembCATs3qctJ+rcOOJCJlTFfgRKTSm7x4I/d+OJchvVpw3bHdwo5T6ZkZ94zsTXr7Rtz4+gwy124LO5KIlDEVcCJSqW3YtosrX/6Bdo1q8eCv9qsyA/XuqxrVknnirAHUSknmsn9NYedudWoQSSQq4ESk0srLc37/6jQ27tjNk2cPUI/TGLVsUJNHRvVjwdpt3Pb2zLDjiEgZCr2AM7OhZjbPzDLN7KYCtl9iZj+a2TQz+9LMegbrO5jZzmD9NDP7a8WnF5Hy9ORnmUxasJ47TupFr9YNwo4Tlw7r0oyrjurCa1OWMzZjWdhxRKSMhNqJwcySgSeBY4HlwGQze8fdZ0c1e9nd/xq0Hw48BAwNti10934VmVlEKsbXC9fz8IT5nNyvNWcObBd2nLh21dFdyFiykdvemknftg3o3rJ+2JFEZB+V+AqcmV1jZmXdb38gkOnuWe6+G3gFGBHdwN2j54WpA2hgI5EEt3ZrNlf9exppTevwp1P6YKbn3vZFcpLxyBn9aVArhcv+NZVtu3LCjiQi+yiWW6h/AZab2QtmdmgZnb8NEH1Nf3mw7mfM7HIzWwg8AFwVtSnNzH4ws8/N7LCCTmBmF5tZhpllrFu3roxii0h5yctzfv/KNLbt2sPT5+xPnRoa7agsNKtXg8fP7M/i9du59c0fw44jIvsolgLuBmApcA7wRfBc2hVmti8PphT0Z/UvrrC5+5Pu3gm4Ebg1WL0KSHX3/sC1wMtm9ov7Au4+xt3T3T29WbNm+xBVRCrCc18t4uuFG7hzeC+6tqgXdpyEcmDHJlxzTFfemraSd6avDDuOiOyDEhdw7v5nd+8OHAWMBToDjwIrzew5MzuwFOdfDkQ/3NIWKOqnyivAyUGeXe6+Ifh4CrAQ6FqKDCJSScxbvZUHPprHsT1bcHq6nnsrD5cO7kT/1Ibc+uaPrN6sSe9F4lXMvVDdfaK7n0mk2LqRyC3QC4Cvg96gl5hZ3RIebjLQxczSzKw6MAp4J7qBmXWJWjwBWBCsbxZ0gsDMOgJdgKxY/z0iUjnsysnl969Oo36tatw7Us+9lZdqyUk8fHo/9uQ61782nbw8PVYsEo9KPYyIu2+Iuio3hMiVsz5EepWuMrMnzKzIP6HdPQe4AhgHzAHGuvssMxsd9DgFuMLMZpnZNCK3Ss8P1h8OzDCz6cBrwCXuvrG0/x4RCdcjExYwZ9UW7hvZl6Z1a4QdJ6F1aFqHW0/swaQF63nx2yVhxxGRUjD30v/1ZWZpwG+BXwMtgN3AB8B+QBqwDTjZ3T/d96j7Lj093TMyMsKOISL5TF68kdOf+YZRB7Tj3pF9w45TJbg7Fz4/ma8XbuD9qw6jc/OS3jgRkYpiZlPcPb2gbTFfgTOzZDM7xcw+InI78yZgF5HOBanuPpLI83GjgFzgwVInF5GEtzV7D9e8Oo12jWpz6wk9w45TZZgZ95/Wl9rVk7nm1Wnsyc0LO5KIxCCWceBSzewuIj1RXyMy+O7HRMZtS3P3e9x9LYBHjAXGAL3KPraIJIq73pvNyk07eej0/TRkSAVrXq8m947sw48rNvP4JwvCjiMiMYjlp2UWkYJvA5Ex4Z5290XF7PMTUL2U2UQkwU2ct5axGcu5bHAn0juU9TjhUhJDe7di5IA2PDlxIcf1aknvNpqyTCQexHILNYNIB4I27n5DCYo33P0+dw99vlURqXy27crhD2/OpFOzOlx9TJfid5Byc/uJvWhcpzo3vj6DHN1KFYkLsYwDd5C7vxhMeSUisk/+PG4eKzfv5P5T+1KjWnLYcaq0BrVTGD28F7NWbuHZScX+bS4ilUAsz8BlmdmVxbS53Mw0FpuIFClj8Ub++c1izj+4g26dVhLD+rRiaK+WPDxhPlnrtoUdR0SKEcvtzQ5Ao2LaNATalzqNiCS87D253Pj6DFo3qMX1Q7qFHUeijB7Ri5rVkrjp9R81wK9IJVfWz6fVJTIWnIhIgZ74NJOF67bzp1N6q9dpJdO8fk1uPbEn3y/eyL++Xxp2HBEpQpE/Pc0sNd+qhgWsA0gGUoHT0HRWIlKI2Su38NfPFzJyQBsGd2sedhwpwK/2b8s701Zy/4dzObp7c1o3rBV2JBEpQHFX4BYDi4IXwNVRy9GvTOBToBPwbHkEFZH4lpObx42vz6BBrRRu04C9lZaZcc8pfcjNc259ayb7MluPiJSf4u5fvAA4YMB5wAxgWgHtcomMD/eJu39cpglFJCG8+O0SflyxmcfO7E+jOhoesjJLbVKb647ryt3vz+GjmasZ1qdV2JFEJJ8iCzh3v2Dvx2Z2HvCmu48u71AikljWbMnmLx/P57AuTTmpr4qBeHDBIR14feoK7nx3Nod1bUZdPa8oUqnEMg5ckoo3ESmNu9+fw+7cPO4a0RszCzuOlEC15CTuPrk3q7dk8+iE+WHHEZF8NEuCiJSrSQvW8e70lVx6RCc6NK0TdhyJwf7tG3HmwHY899Vi5qzaEnYcEYlS6DVxM3uOyPNvt7j7mmC5JNzdLyqTdCIS13bl5PLHt2fRoUltLh3cKew4Ugo3DOnOuFlruPWtmfzndweTlKQrqCKVQVEPNVxApIC7H1gTLJeEAyrgRIRnPs9i0frtvHDhQGqmaLqseNSoTnVuGtadG16bwWtTlnP6Ae3CjiQiFF3ApQXvK/Iti4gUa8mG7TzxWSYn9GnF4V2bhR1H9sFpA9ryn4xl3PvhHI7t2UK9iEUqgUKfgXP3JcErJ99ysa+Kiy8ilZG7c/s7s0hJMm47UWO+xbukJOOuk3uzJTuH+z+aG3YcEUGdGESkHHw8ew0T563jmmO70rJBzbDjSBno3rI+Fw1K45XJy/hh6U9hxxGp8kpcwJlZfzO7zMwaRK2rY2b/NLNNZrbSzK4un5giEi+y9+Ry13uz6dqiLhcc0iHsOFKGrjq6C83r1eCOd2ZpsnuRkMVyBe5G4A/uvjlq3b3AucFxmgAPmdlxZZhPROLMs19ksfynndx+Ui+qJesifyKpW6MaNw3rzvTlm3lt6vKw44hUabH8dE0HJu5dMLMU4Hzge6A5kU4O64GryjCfiMSRlZt28tTEhQzr3ZJDOzcNO46Ug5P7tWFAakMe+GgeW7L3hB1HpMqKpYBrDiyLWk4H6gHPuHu2u68E3gb6lmE+EYkj9344lzx3bjm+R9hRpJwkJRl3DO/Fhu27ePyTBWHHEamyYingnJ8POzIoWPd51Lp1QEzjBZjZUDObZ2aZZnZTAdsvMbMfzWyamX1pZj2jtt0c7DfPzIbEcl4RKVvfL9rIu9NX8rsjOtGuce2w40g56tu2Iafv345/fLWYzLXbwo4jUiXFUsAtBQ6KWh4BLHf3rKh1rYESd08ys2TgSWAY0BM4M7pAC7zs7n3cvR/wAPBQsG9PYBTQCxgKPBUcT0QqWG5eZNiQ1g1qcukRmnGhKrh+aDdqpSQz+r3ZuKtDg0hFi6WAGwscYmavmdlLwMHAa/na9AYWxnDMgUCmu2e5+27gFSKF4X+5e/QEfHWIXPUjaPeKu+9y90VAZnA8Ealg//5+KXNWbeGWE3pQq7r+jqoKmtatwdXHdOGL+ev4ZM7asOOIVDmxFHAPA98AI4GzgOnA6L0bgyti+/PzW6rFacPPn6tbHqz7GTO73MwWErkCd1Us+4pI+dq0Yzd/+XgeB6Y15oQ+rcKOIxXo/EM60Ll5Xe56fza7cnLDjiNSpZS4gHP3be5+KJFOCn2B9HxDiuwATgGejuH8Bc2K/Itr8e7+pLt3IjKUya2x7GtmF5tZhpllrFu3LoZoIlISj36ygM0793D7Sb0w00TnVUlKchJ/PLEnSzbs4PmvFocdR6RKiXmQJnefGbzy8q1f7O5vu/uKwvYtwHIgembktsDKItq/Apwcy77uPsbd0909vVkzzccoUpYWrtvGi98s4YwDUunZun7YcSQEh3dtxlHdm/PEp5ms37Yr7DgiVUbYo2xOBrqYWZqZVSfSKeGd6AZm1iVq8QRgb7/1d4BRZlbDzNKALkTGpBORCnLvB3OomZLMtcd2DTuKhOiW43uwY08uD4+fH3YUkSqjWvFN/icopq4m0lmgEVDQ08oe3O4slrvnmNkVwLjgWM+5+ywzGw1kuPs7wBVmdgywh0gP1/ODfWeZ2VhgNpADXO7ueghDpIJ8lbmeCXPWcsPQbjSrVyPsOBKizs3rcs6Bqbz47RLOP6QDXVvUCzuSSMKzknb/NrODgQlALSIF05rg/RfcPa2sApal9PR0z8jICDuGSNzLzXNOeGwS23blMOHaI6iZop6nVd1P23dzxIOf0S+1ES9cqAEBRMqCmU1x9/SCtsVyC/VeoAZwCVDb3du5e1pBr7IILSKV138yljF39VZuGtZdxZsA0KhOda46OjKsyGfzNKyISHmLpYA7AHgt6BRQ4JU3EUl823bl8OeP57N/+0YaNkR+5ryDO9ChSW3+9P4ccnLzit9BREotlgJuN5HZGESkCnt6YqS34W0n9tSwIfIz1aslcfPxPchcu41/f69fFyLlKZYC7mugf3kFEZHKb/lPO3h20iJO7teafu0ahh1HKqHjerbgoI6NeWj8fDbv3BN2HJGEFUsBdwuRqbTOLa8wIlK5PThuHgbcMLR72FGkkjIzbjuxJ5t27uGpzzLDjiOSsGIZRmQE8CnwvJn9BpgCbCqgnbv7XWURTkQqjxnLN/H2tJVcfmQnWjesFXYcqcR6tW7AyP5t+cfXizn34Pa0bVQ77EgiCSeWAu6OqI8PC14FcUAFnEgCcXfu+WAOTepU55IjSjTMo1Rx/zekK+/NWMmfx83jkVF6+kakrMVSwB1ZbilEpFL7dO5avs3ayOgRvahXMyXsOBIHWjWoxUWD0nhq4kIuGtSRPm0bhB1JJKGUuIBz98/LM4iIVE45uXnc++FcOjatw5kDU8OOI3HkksGdeGXyMu75YA4v//ZA9VoWKUNhz4UqIpXc2IzlZK7dxg1Du5OSrB8ZUnL1a6Zw9dFd+CZrgwb3FSljMf80NrO+Znafmb1tZhOi1ncws9PNrFHZRhSRsGzflcND4+eT3r4RQ3q1CDuOxKGzDkwlrWkd7vlgrgb3FSlDMRVwwSTzU4EbgJP4+XNxScC/gXPKLJ2IhGrMF1ms37aLP5zQQ7e/pFRSkpO4cWh3MtduY2zG8rDjiCSMEhdwZjYKuBUYD/QjMjfqf7l7FpABDC/LgCISjrVbshnzRRYn9G1F/1RdWJfSG9KrBentG/HQ+Pls36WZGEXKQixX4K4CMoER7j6DyNRa+c0BupRFMCuGuJwAACAASURBVBEJ18MT5pOTl8eNQzRor+wbM+OWE3qwftsuxnyRFXYckYQQSwHXBxjn7gUVbnutBPSgjEicy1y7lVcnL+Ocg9qT2kSDsMq+G5DaiOP7tOTZSVms3ZoddhyRuBdLAWdAcU+gtgD0P1Mkzt3/0TzqVK/GlUfpgrqUneuHdGd3Th6PfbIg7CgicS+WAm4BcEhhG80sGRgEzNrXUCISnozFGxk/ew2XDO5E4zrVw44jCSQtGEvw398vI2vdtrDjiMS1WAq4scAAM7uukO03A52Bl/c5lYiEYu+UWS3q1+DCQ9PCjiMJ6Kqju1CzWhIPjpsXdhSRuBZLAfcIMB14wMy+A4YBmNmfg+U7gW+BMWWeUkQqxLhZa5i6dBPXHNOVWtWTw44jCahZvRr89vCOfDhzNVOX/hR2HJG4VeICzt13Ehn37UVgADCQyHNx1wL7Ay8BQ91dfcRF4lBObh4PjJtL5+Z1OW3/tmHHkQT228M60rRude77YC7uHnYckbgU00C+7r7Z3S8g0llhGJFBe08CWrn7+e6+tewjikhFeDVjGVnrtnPDkG5U05RZUo7q1KjG1Ud34fvFG/lkjqbYEimNUv2UdveN7j7O3V929/fdfV1ZBxORirNjdw6PTFhAevtGHNtTIwFJ+Rs1MDLF1v0faYotkdKIdSqtumZ2hJmdZmanmtnhZlanvMKJSMX426RFrNu6i5uP764ps6RCpCQncf2QbixYu43Xp2qKLZFYlaiAM7OuZvYGsBH4FHiVSK/Uz4CNZvYfM+tcfjFFpLxs2LaLZz5fyJBeLdi/feOw40gVMqx3S/q1a8jD4xeQvSc37DgicaXYAs7MBhLpXXoyUA1YAXwPTA4+TgFOBb41swGxBjCzoWY2z8wyzeymArZfa2azzWyGmX1iZu2jtuWa2bTg9U6s5xYRePzTTHbuyeV6TZklFczMuGlYd1Zvyeb5rxeHHUckrhRZwJlZCpFepw2BF4BO7p7q7ge7+0Hunkpk7tOXgMbAS2ZWraQnDwb/fZJIh4iewJlm1jNfsx+AdHfvC7wGPBC1bae79wtew0t6XhGJWLphB//6bglnHNCOzs3rhh1HqqCDOjbhyG7NeOqzTDbtKGqmRhGJVtwVuBFECrTH3P0Cd1+Uv4G7L3T384AngG5EeqWW1EAg092zgjlWXwnOGX38z9x9R7D4LaDxDUTKyF/GzyM5ybj66K5hR5Eq7Iah3dm6K4enJy4MO4pI3CiugBsObANuK8Gx/gDsIHKrtaTaAMuilpcH6wpzEfBh1HJNM8sws2/NrMDzmtnFQZuMdevUWVZkr5krNvP2tJVceGgaLRvUDDuOVGE9WtXnlP5t+MfXi1m5aWfYcUTiQnEFXD9gUknGdwvafBHsU1IFdXcrcFRHMzsHSAcejFqd6u7pwFnAI2bWqYBcY9w93d3TmzVrFkM0kcT2wLh5NKydwu+O+MV/G5EKd+2xXcHh4fHzw44iEheKK+BaA7FMWDePoq+g5bccaBe13BZYmb+RmR1D5ArfcHfftXe9u68M3rOAiUD/GM4tUmV9lbmeL+av44ojO9OgVkrYcURo26g25x3cntenLmf+Go0JL1Kc4gq4+sCWGI63BagXQ/vJQBczSzOz6sAo4Ge9Sc2sP/AMkeJtbdT6RmZWI/i4KXAoMDuGc4tUSe7O/R/NpXWDmpxzUPvidxCpIJcf2Zk61avxwEea6F6kOMUVcNWAWIbI9mCfkjWOzJt6BTAOmAOMdfdZZjbazPb2Kn0QqAv8J99wIT2ADDObTmQ8uvvcXQWcSDE++HE1M5Zv5trjulEzRRPWS+XRqE51LhnciQlz1jB58caw44hUaiUpthqaWWoJj9cw1gDu/gHwQb51f4z6+JhC9vsa6BPr+USqsj25eTw4bi7dWtTjlP6xPO0gUjEuPDSNF75ZzL0fzOH1Sw/RzCAihShJAXd18BKROPfK5GUs3rCD5y5IJzlJvxil8qlVPZnfH9OVm9/4kfGz13Bcr5ZhRxKplIor4JZSSK9QEYkv23fl8OiEBQxMa8yR3ZqHHUekUL/avy3PTsrigXHzOKp7c6olxzRtt0iVUGQB5+4dKiiHiJSzv3+5iPXbdjHmvP11W0oqtWrJSdwwpDuXvDSF16cu54wDSvoUj0jVoT9rRKqAvRPWD+3VkgGpjcKOI1KsIb1a0D9VE92LFEYFnEgVsHfC+v8b0i3sKCIlYmbcNFQT3YsURgWcSILThPUSrw7s2ISjujfXRPciBVABJ5LgNGG9xLMbhnbTRPciBVABJ5LANGG9xLvuLeszsn9bTXQvko8KOJEEdv9HczVhvcS9a4+LXD1+SBPdi/yXCjiRBPXlgvVMWrCeywdrwnqJb20a1uL8g9vzxtTlzFutie5FIIYCzsz0G0AkTuTlOfd9NIc2DWtx7sGasF7i32WDO1OnRjXu/2hu2FFEKoVYrsCtMLP7zaxzuaURkTLx7oyVzFyxheuO66oJ6yUhNKpTncsGd+bTuWv5NmtD2HFEQhdLAZcEXA/MM7PxZnaqmZVkLlURqUC7cnL588fz6NGqPif304T1kjh+fWgHWjWoyb0fzsVdszxK1RZLAdcaOAeYBBwNjAWWmdmfzCytPMKJSOz+9e1Slm3cyU3DupOkCeslgdRMSeaaY7syfdkmPvhxddhxREJV4gLO3Xe7+8vuPhjoDjxCZC7Vm4EFZvaBmY0wM3WMEAnJluw9PP7pAg7t3ITDuzQNO45ImTt1QFu6tajHg+Pmsic3L+w4IqEpVbHl7vPd/TqgDf+7KjcUeANYamZ3mFnrsospIiXxzOcL+WnHHm4a2kMT1ktCSk4ybhzWjcUbdvDK90vDjiMSmn26Wubuu4H3gTeBlYARudX6R2CRmT1iZjX2OaWIFGv15mz+/uUihu/Xmj5tG4QdR6TcHNmtOQemNebRTxawbVdO2HFEQlHqAs7MDjKzfxAp3B4G6gCPAf2AC4F5wJVEbrWKSDl79JP55OY512vCeklwZsbNx/dg/bbdPPtFVthxREIRUwFnZvXM7DIzmw58BZwPzAEuBlq7++/dfYa7Pw/0Bz4FTivjzCKSz4I1W3l18jLOPrA97RrXDjuOSLnr164hJ/RpxbOTsli7JTvsOCIVLpaBfP9G5Grb40AX4EXgIHdPd/e/u/vPJqlz91xgItC47OKKSEHu+3AudapX46qju4QdRaTCXD+kG7tz8nh4woKwo4hUuFiuwF0IrAZuANq6+wXu/n0x+0wERpcym4iUwDcLN/DJ3LVcemQnGtepHnYckQrToWkdzjmoPa9OXkrmWk2xJVVLLAXcMHfv4u5/cfeNJdnB3b9y9ztLmU1EipGX59z74RxaN6jJhYdqOEapeq46ugt1qlfjvg81xZZULbEUcC3MrG9RDcyst5mdt4+ZRKSE3p2xkhnLN3Pdcd00ZZZUSY3rVOfSIzsxYY6m2JKqJZYC7nng5GLajAD+EUsAMxtqZvPMLNPMbipg+7VmNtvMZpjZJ2bWPmrb+Wa2IHidH8t5ReLdrpxcHhw3j56t6nNKf02ZJVXXhYem0apBTe75YA55eZpiS6qGsp41IRko8f8eM0sGngSGAT2BM82sZ75mPwDp7t4XeA14INi3MXA7cCAwELjdzBrt879AJE68+M0Slv+0k1uO76Eps6RKq5mSzHXHdWPG8s289+OqsOOIVIiyLuC6Aj/F0H4gkOnuWcGgwK8QuYr3X+7+mbvvCBa/BdoGHw8Bxrv7Rnf/CRhPZDYIkYS3ecceHv80k8O7NmOQpswS4ZT+bejRqj4PfDSXXTm5YccRKXfVitpoZs/lW3WymXUooGkykAocRmRmhpJqAyyLWl5O5IpaYS4CPixiX91Hkirhic8WsCV7DzcP6x52FJFKITnJuOX47pz79+958Zsl/OawjmFHEilXRRZwwAVRHzuRWRb6FdLWge+Aa2I4f0H3fQq8BWtm5wDpwBGx7GtmFxMZaJjU1NQYoolUTss27uCfXy/htAFt6dGqfthxRCqNw7o047AuTXn800xO278tDWtrWB1JXMXdQk0LXh2JFEyPRK2LfqUC9d39EHePZV6T5UC7qOW2RAYL/hkzOwb4AzDc3XfFsq+7jwkGG05v1qxZDNFEKqf7P5pLUhJcd5ymzBLJ75bje7AlO/KIgUgiK7KAc/clwWsxcCfwVtS66Ndyd99eivNPBrqYWZqZVQdGAe9ENzCz/sAzRIq3tVGbxgHHmVmjoPPCccE6kYQ1ZclPvDdjFRcf3omWDWqGHUek0unRqj5npLfjhW8Ws2h9aX4ticSHEndicPc73f2Lsjy5u+cAVxApvOYAY919lpmNNrPhQbMHgbrAf8xsmpm9E+y7EbiLSBE4GRhd0gGGReKRu3P3+7NpXq8Gvztcz/eIFOba47qSkpzEfR/OCTuKSLkp9Bk4M9v7wNgKd8+NWi6Wuy+Noe0HwAf51v0x6uNjitj3OSB/RwuRhPTejFX8sHQTD5zWlzo1int8VaTqal6vJpce0Ym/jJ/Pd1kbOLBjk7AjiZS5oq7ALQYWAZ3yLRf3iuUZOBEpgew9udz34Vx6tKrPqQPaFr+DSBX3m8M60qpBTe5+X4P7SmIq6s/4F4j06tycb1lEKtg/vlrMik07eeC0viRr0F6RYtWqnswNQ7txzavTeWvaCkbqDx9JMIUWcO5+QVHLIlIx1m/bxVOfZXJMj+Yc2lmD9oqU1Ij92vCPrxbz4Lh5DOvdilrVNV+wJI6ynolBRMrYIxPms2NPLjcN6xF2FJG4kpRk/OH4HqzanM3fJunpHkksKuBEKrEFa7by8ndLOefAVDo3rxt2HJG4c2DHJgzt1ZKnP1/I2i3ZYccRKTNF9UItbe9Od/eLSrmviATcndHvzaZujWpcfUzXsOOIxK2bhnXnk7lreGDcPP78q/3CjiNSJorqxHBBKY/pROYsFZF98MmctUxasJ4/ntiTxnU0JZBIaXVoWocLB6XxzOdZnHtQe/Zr1zDsSCL7rKgCLq3CUojIz+zOyePu92fTqVkdzj24fdhxROLeFUd25vUpKxj93mxeu+RgzNSbW+JbUb1Ql1RkEBH5n+e/XsTiDTt4/tcHkJKsR1VF9lW9mincMKQbN7w+g3emr2REvzZhRxLZJ/rNIFLJrNu6i8c/yeTIbs0Y3K152HFEEsZp+7eld5v63PfhXHbszgk7jsg+KbSAM7PU4JWcb7nYV8XFF0k8f/l4Hjv35HLriT3DjiKSUJKSjNtP6sWqzdk887mGFZH4VtQzcIuJdEjoAcyPWi6OF3NcESnEzBWbeTVjGRcemkanZho2RKSsHdChMSf2bcVfP1/I6Qe0o03DWmFHEikVTaUlUkm4O6PfnU2j2tW56uguYccRSVg3H9+D8bPXcN+Hc3n8zP5hxxEpFU2lJVJJvP/jKr5fvJE/ndKbBrVSwo4jkrDaNKzF747oxGOfLODcg9ozMK1x2JFEYqZODCKVwPZdOfzp/Tn0aFWfUQfoMVKR8nbJER1p3aAmt78zi5zcvLDjiMSsVAWcmbUzs+Fmdm7w3q6sg4lUJU9+lsmqzdncNaIXyUkan0qkvNWuXo1bT+zJnFVbePn7pWHHEYlZTAWcmXUxs/FEOjS8CTwfvC82s/Fmpvl+RGKUtW4bz07KYuSANqR30K0ckYoyrHdLBnVuyp/HzWPDtl1hxxGJSYkLODPrDHwNHA1kEenU8EDwnhWs/zJoJyIl4O7c+e5salZL5qZh3cOOI1KlmBl3DO/Jjt25PPDRvLDjiMQklitw9wJNgKuBbu7+a3e/2d1/DXQDrgGaAveUfUyRxDR+9ho+n7+O3x/bleb1aoYdR6TK6dy8HhcOSuPVjGVMW7Yp7DgiJRZLAXc08IG7P+7uP3vi093z3P1R4EPgmLIMKJKosvfkMvq92XRtUZfzNN+pSGiuOroLzevV4I9vzyQ3T6NlSXyIpYCrDkwrps00QOMfiJTA0xMXsvynndw5vLfmOxUJUd0a1fjDCT2YsXwzYzOWhR1HpERi+a0xHSju+bbOwIzSxxGpGpZu2MHTny/kpP1ac3CnJmHHEanyhu/XmoFpjXngo7ls2rE77DgixYqlgLsHGGlmwwraaGYnAKcAfyqLYCKJKtJxYRbVkow/HN8j7DgiQqRDw+gRvdiSncMD49ShQSq/QmdiMLPzClj9IfCemX0CfAGsAVoARwBHAe8S6cggIoUYN2sNn8xdy60n9KBlA3VcEKksuresz68P6cDfvlzEqQPasn/7RmFHEimUuRf8wKaZ5fHLuU9LMsKou3tyiQOYDQUeBZKBv7n7ffm2Hw48AvQFRrn7a1HbcoEfg8Wl7j68qHOlp6d7RkZGSaOJlLltu3I49qHPaVi7Ou9ecSjV9OybSKWy9/9og1opvHflIP0flVCZ2RR3Ty9oW1GT2f+6nPL8l5klA08CxwLLgclm9o67z45qthS4APi/Ag6x0937lXdOkbLy8Pj5rN6SzZNnD9AvBpFKqG6Natx+Ui8ueWkK//hqMb89vGPYkUQKVNRk9v+sgPMPBDLdPQvAzF4BRgD/LeDcfXGwTZPVSVybuWIz//hqEWcOTGVAqm7NiFRWQ3q14JgezXl4wnyO79uKNg1rhR1J5BfCvgTQBojus708WFdSNc0sw8y+NbOTC2pgZhcHbTLWrVu3L1lFSi03z/nDWzNpXKc6Nw7RjAsilVlkhoZeuMOd78wKO45IgcIu4Ap6pi6WURRTg3vDZwGPmFmnXxzMfYy7p7t7erNmzUqbU2SfvPz9UqYv28StJ/SkQW0NlShS2bVtVJvfH9OFj2evYfzsNWHHEfmFWCezr2Nm15vZBDObY2ZZBbwWxnDI5UC7qOW2wMqS7uzuK4P3LGAi0D+Gc4tUiLVbs3ngo7kc0qkJI/q1DjuOiJTQhYPS6NaiHre/PZPtu3LCjiPyM7FMZt8Q+A64H0gnMv9pIyLDiHQIXtVjOSYwGehiZmlmVh0YBbxTwjyNzKxG8HFT4FCinp0TqSzuem8Ou/bkcdfJvTErSUduEakMUpKTuGdkb1ZuzuaRCfPDjiPyM7EUW7cCPYGLiBRuAA8DdYFDgKnAQqDEI5O6ew5wBTAOmAOMdfdZZjbazIYDmNkBZrYc+BXwjJntfSChB5BhZtOBz4D78vVeFQndJ3PW8O70lVx2ZCc6NasbdhwRidH+7Rtz1oGp/P3LRUzXZPdSiRQ6DtwvGprNB1a6++BgOQ+4w91HB8vNiYzJNsbdbyufuPtG48BJRdqavYfjHv6C+jVTePfKQVSvFvYjpyJSGluy93DsQ5/TqHZ13rlC/5el4hQ1Dlws34XtiFxl2ysPqLF3wd3XEpmpYVRpQookmvs/msvqLdncd2of/cAXiWP1a6Zw98l9mLt6K898Hstj3iLlJ5bfKjuA3KjlzUDLfG3WENswICIJ6busDbz07VIuPDSN/hrzTSTuHduzBSf2bcXjn2aSuXZr2HFEYirglvHzHqOzgcOD2RT2GgSsLotgIvEqe08uN7/xI+0a1+K647qGHUdEysgdw3tRu0YyN77+I3l5sYx4JVL2YingPgeOsP91o3sV6AS8b2aXm9l/gIOAD8o4o0hceeyTBWSt3869p/SldvWiZqsTkXjStG4N/nhiT6Ys+YkXv10Sdhyp4mL57fJPIsOEtCVyNe6vwFHAycBxQZuviPRWFamSZq7YzDNfZPGr/dsyqEvTsOOISBk7pX8b3pq2kvs/msvRPZrTtlHtsCNJFVXiK3DuPtXdL3X3ZcFyjruPBA4AzgQOBo5wd/WzlippT24eN74+g8Z1qnPrCT3DjiMi5cDMuOeU3gDc/MaPlHQkB5Gyts9d49x9iru/6u7fubsmnJcq64lPM5m1cgt3n9xb02WJJLC2jWpz87DuTFqwnn9/v6z4HUTKQakKODNLMbO+ZnZY8K7fVlKl/bh8M098lsnI/m0Y0it/52wRSTRnH9ieQZ2bcvf7s1m6YUfYcaQKinUu1CZm9iywCfiByPyjPwCbzOzZYEorkSole08u146dRrO6Nbj9pF5hxxGRCpCUZNx/Wl+Szbj+tenqlSoVLpa5UFsQmQv1ImA38AUwNnjfHaz/NmgnUmU8PH4+C9Zu475T++jWqUgV0qZhLW47qSffLdrI818vDjuOVDGxXIG7B+gIPAK0d/cj3f1Mdz8SaA88Gmz/U9nHFKmcMhZvZMykLM4cmMrgbs3DjiMiFexX+7fl6O7Nuf+juSxcty3sOFKFxFLAnQhMcvdr3X1L9AZ33+Lu1xAZRuSksgwoUlnt2J3Ddf+ZTpuGtfjDCT3CjiMiITAz7h3Zh5opyVw3djo5uerLJxUjlgKuHvBlMW0mAXVLH0ckftz/4VyWbNjBn3+1H3VraMBekaqqef2a3HVyb6Yt28QzX2SFHUeqiFgKuLlAq2LatALmlT6OSHz4bN5a/vnNEn59aAcO6tgk7DgiErKT+rbihD6teGTCfH5cvjnsOFIFxFLAPQqcYWZ9C9poZv2A04k8IyeSsNZt3cX1/5lOtxb1uHFo97DjiEglYGb86ZTeNKlTg6tf+YEdu3PCjiQJrtACzswOj34Bi4DxwPdmNsbMzjGzY4P3Z4FvgY+BxRWSXCQE7s71r01nS3YOj53Zn5opyWFHEpFKomHt6jx8Rj8WbdjO6Hdnhx1HElxRD+5MBAoa2MaA3xAZNiR6HcAIYDig32qSkJ7/ejET563jzuG96NayXthxRKSSObhTEy49ohNPTVzI4V2bcXyf4p48Eimdogq40RRcwIlUSXNXb+HeD+dyVPfmnHdw+7DjiEgldc2xXfkqcz03vT6Dfu0a0rphrbAjSQKyqjQRb3p6umdkZIQdQ+JQ9p5chj/xJRu37+Gj3x9G07o1wo4kIpXY4vXbOf6xSfRp04CXf3sQyUlW/E4i+ZjZFHdPL2jbPk9mL1IV3PPBHOav2cZfTt9PxZuIFKtD0zqMHtGb7xZt5K+fLww7jiSgUg1eZWaDgP5AQ2AzMNXdixsjTiQufTRzFS98s4SLBqVxRNdmYccRkThx6oA2TJy3lofGz2dgWmMO6NA47EiSQGIq4MxsAPAS0G3vKoLn5MxsHnCeu+sepSSMxeu3c/1/ZrBf2wbcMLRb8TuIiATMjHtG9mHmis1c8fJUPrjqMJroCr6UkVgms+8MfAp0JzJl1l3ApcH7l8H68WbWpRxyilS47D25XPavqSQlGU+ePYAa1dS5WkRiU79mCk+ePYCfduzh969OIzev6jx3LuUrlmfgbiMyTdYZ7n64u9/h7s8E70cQGcS3HnBrLAHMbKiZzTOzTDO7qYDth5vZVDPLMbPT8m0738wWBK/zYzmvSHHufHc2s1dt4eEz9qNto9phxxGRONWrdQNGD+/FpAXrefzTBWHHkQQRSwF3DPCWu/+noI3u/hrwdtCuRMwsGXgSGAb0BM40s575mi0FLgBezrdvY+B24EBgIHC7mTUq6blFivLmD8v59/dLuXRwJ47q3iLsOCIS5844oB0j+7fh0U8W8OWC9WHHkQQQSwHXlMh8qEWZG7QrqYFAprtnuftu4BUigwH/l7svdvcZQF6+fYcA4919o7v/RGSWiKExnFukQPPXbOWWN2ZyYFpjrju2a9hxRCQBmBl3n9KbLs3rcvUrP7B6c3bYkSTOxVLArSNylawo3YFY/rRoAyyLWl4erCvvfUUKtH1XDpf9ayp1aiTz+Jn9qZaskXZEpGzUrl6Np84ewM49uVz576nsyc1/XUKk5GL57fQpMNzMRhW00cxOJXL1bEIMxyxoZMOSPuFZon3N7GIzyzCzjHXr1sUQTaqavDzn2rHTyFq3jcdG9ad5/ZphRxKRBNO5eT3uHdmHyYt/4u73NF+qlF4sw4iMJlKg/cvMLgc+A1YBLYHBwCBgK3B3DMdcDrSLWm4LrIxh38H59p2Yv5G7jwHGQGQmhhiySRXz+KeZjJu1hltP6MEhnWN5EkBEpORG9GvDzBWbeXbSInq0qs+ogalhR5I4VOICzt0zzewY4AXg0ODl/O9K2DzgfHePpYvNZKCLmaUBK4BRwFkl3HcccE9Ux4XjgJtjOLfIf308azUPT5jPyAFtuGhQWthxRCTB3Ti0O3NXb+W2t2fSpUVd9m+vQX4lNjE94OPuk929B5GrbVcBfwzeD3P3Hu7+fYzHywGuIFKMzQHGuvssMxttZsMBzOwAM1sO/Ap4xsxmBftuJDIG3eTgNTpYJxKT+Wu2cs2r09ivbQPuOaUPZpqzUETKV7XkJJ44cwBtGtbidy9OZdXmnWFHkjhT4snszexwYIu7TyvfSOVHk9lLfpt27GbEk1+xY3cu714xiJYN9NybiFScBWu2cvKTX9GpeV3G/u5gaqZowHD5n7KazP4z4OKyiSQSvpzcPK789w+s3LSTv54zQMWbiFS4Li3q8fAZ/ZixfDM3v/EjJb2oIhJLAbce0DVeSQjuzl3vzWbSgvXcNaK3nj8RkdAc16sl1x7blTd/WMFTExeGHUfiRCy9UCcCh5RTDpEK9fcvF/HPb5bw28PS1ANMREJ35VGdWbhuGw+Om0fbRrUY0U/DmkrRYrkCdyvQzczuMrOU/2/vzuOrqu/8j78+SSAJhCRAwhIISyBsQZYKqIjLr6KgVRCrFms7jHWfMtaxOm11Wrexi+PUsVYda8W6UZeqbergUqpOBUQIlFUWgbAl7EkuCdlzP78/clWGRQIkObnJ+/l43EfuPefc5JPvI8l553zP9/ttqoJEmtpbK3fwwJw1XDi8Bz+6cGjQ5YiIYGY8ePkIxvXvwh2vruDjTfuCLklauOMZxDALGEj99CG7gOXATg6fPNfd/drGLLKxaBCDLNlSzDefWkhORjKzrz9dNwyLSItSUl7NZU8sYF9ZNa/dPJ6B3ZKCQfDV9gAAFD1JREFULkkC9GWDGI4nwDV0zQ939xZ5VlSAa9s27z3AZU8soFNCHK/fPJ6uSfFBlyQicphtReVMe3w+ie1jef3mM0nvpL9VbVVjjULt38BH1klVK9IEig5U84/PLMLd+d014xTeRKTFyuzSgd/OGMue0ique3Yx5dW1QZckLVCDA5y7b2nooykLFjleZVW1XPPMIgpDlTz1D2Pon9Yx6JJERL7UqMxUfjV9NCsKQtz8wlKqa7XwvfxfDQpwZtbHzL5uZpeZWeax3yHSMlTW1HHds4tZVbifx775Fcb003QhIhIdLsjpwc+mncL/rt/Dv7y8jLqw5oiTLxxzGhEzewi4lS/WPHUze9jd72jSykROUk1dmJmzl/JxfhEPXzmK84d1D7okEZHjMn1cH0ora3lgzho6JcTxs8u03J/U+9IAZ2bfBG6jfqTpWupD3GDgNjNb6u6/b/oSRY5fOOzc/upy5q7Zzf1Tc7h0tOZUEpHodP3ZWeyvrOHR9zbQKSGOOy8aqhAnx+xCvRaoBSa6e467DwMmAeHIPpEWx925O3c1f1pWyB2TBvPtM/oFXZKIyEm57fxBzDijL099mM9j728IuhxpAY7VhToC+KO7v//ZBnefa2Z/As5tysJEToS78/O31/L8wi3ceE4W/3TugKBLEhE5aWbG3ZfkUFpZy0PvriexfRzXTugfdFkSoGMFuM7AuiNsXwtc2vjliJw4d+enc9bw1If5fOv0Pvxw8hB1M4hIqxETU79aQ0VNHfe/+QnhsHP92Zq5q606VhdqDFBzhO01fDGoQSRw7s59b37CUx/m84/j+3H/1OEKbyLS6sTFxvCrq0bztVN68sCcNTzxwcagS5KANGQxe41blhbN3bkndzXPfrSF75zZnx9frBt8RaT1ahcbwyPTRxETY/zi7bXUhcPM/Gp20GVJM2tIgLvHzO450g4zqzvCZnf3hnxekZMWDjs/yV3FCwu3cv1Z/TU6S0TahLjYGB6+ciSxBg+9u566MHxvokJcW9KQoHW8Z0OdPaVZ1NaFueuNVbyct42bzhnADyYPVngTkTYjLjaG/7yy/krcw3PXU1Vbxx2T9HewrfjSAOfux7NWqkizqaypY+bsvzN3zS5uOS+bf5mYrT9aItLmxMYY/3H5SOLjYnj8g43sK6vmgWnDiYvV6bu1U1enRJ1QeQ3XPbeYvC3F3Dslhxnj+wVdkohIYGJjjJ9OO4W0pHgefW8DReXVPHrVaBLaxQZdmjQhRXSJKjtDlVz55Ecs21bCo1eNVngTEaF+nrjvXzCYe6fkMHfNLr799MeEyo80iYS0FgpwEjU27C7j608soKCkgt9dM46LR2QEXZKISIsyY3w/Hr1qNMu3hbjyyY/YGaoMuiRpIgpwEhUWbNjL159YQFVtHS/dcDpnDkwLuiQRkRbp4hEZ/O6asRSUVDDt8fmsKggFXZI0AQU4afGeX7iFb89aRPfkeF6/+UyG90oJuiQRkRZt/MA0XrnxDAy4/L8XMGfljqBLkkYWeIAzs8lmts7MNpjZD4+wP97MXo7s/9jM+kW29zOzCjNbFnn8d3PXLk2rpi7Mj/+4ih//cRXnDErntZvH06drh6DLEhGJCsMykvnTzAnkZKTwTy8u5ZG5n+Kuuflbi0BHoZpZLPAYcD6wHVhsZrnu/slBh10LFLv7QDObDvwC+EZk30Z3H9WsRUuzKCmv5ruzlzJ/wz5uPDuLf508hNgYTRMiInI80jvFM/v60/jR6yt5eO561u8u5aHLR5LYXiNUo13Q04iMAza4+yYAM3sJmAocHOCmAvdEnv8B+LVpwq9WbXVhiO++uJTCkkoeumIkl5/aO+iSRESiVnxcLP95xUiG9OjEz95ay+a9B3j86q/Qt2vHoEuTkxB0F2ovYNtBr7dHth3xGHevBUJA18i+/mb2dzP7XzM760hfwMxuMLM8M8vbs2dP41Yvjcrdmf3xVqY9voCKmjp+f8NpCm8iIo3AzLjh7AE8PWMM24sruPhX83h7le6Li2ZBB7gjXUk7tIP+aMfsAPq4+2jgNmC2mSUfdqD7b9x9jLuPSU9PP+mCpWkcqKrl1peXcecbKzmtfxfm3HIWp/btEnRZIiKtyleHdOfNf55AVrckbnphKff+eTXVteGgy5ITEHSA2w5kHvS6N1B4tGPMLA5IAYrcvcrd9wG4+xJgIzCoySuWRrduZylTfj2PPy8v5PvnD+LZa8bRNSk+6LJERFqlzC4dePXGM7jmzH48M38zVzz5EduLy4MuS45T0AFuMZBtZv3NrD0wHcg95JhcYEbk+eXAe+7uZpYeGQSBmWUB2cCmZqpbGkE47Pxufj5TH5tHqKKWF649jX8+L5sYDVYQEWlS7eNiuPuSHJ64+its2l3GRY98yB//XqBRqlEk0EEM7l5rZjOBd4BYYJa7rzaz+4A8d88FngaeN7MNQBH1IQ/gbOA+M6sF6oCb3L2o+b8LOREFJRXc8epyFmzcx7mD03nw6yPolpwQdFkiIm3Khaf0ZFhGMre9spxbX17Gu5/s5N8vPYUuHdsHXZocg7WltD1mzBjPy8sLuow2zd15bWkB9+auJuzOv108jOljM9HAYhGR4NSFnd/8bRO//Ms6UhLb8/PLTmHisO5Bl9XmmdkSdx9zpH1Bd6FKG7JrfyU3Pr+E219dztCeybz1vbO5alwfhTcRkYDFxhg3nzuA3JkTSEtqz3XP5XHHq8spKa8OujQ5iqDngZM2oC7svLBwCw+9s46qujB3XjSEaydkaWJeEZEWZmjPZHJnTuC/5q7nyb9t4r21u/m3i4dy6ahe+me7hVEXqjSpVQUh7nxjJSu2hzgrO437pw6nX5omjxQRaelWF4a4841VLN9WwvgBXbn/0uEMSE8Kuqw25cu6UBXgpEmEKmp4+C/ree6jzXTpGM9PLhnGJSN66j84EZEoUhd2Zi/ayoNvr6WqJsxN5w7g5nMGaCmuZqIAF6EA1/Rq6sK8uHALj/z1U0oqavjWaX25fdJgUhLbBV2aiIicoN2llfz7m2vIXV5Iz5QEbr9gMNNG99K0T01MAS5CAa7puDvvfrKLn7+1lvy9Bzgjqyt3fW0ow3ulBF2aiIg0koWb9vHTOWtYsT1ETkYyd31tKOMHpAVdVqulABehANc0lmwp5sG31/JxfhED0jty50VD+eqQbuouFRFphcJh588rCnnw7XUUlFQwcWg3vn/BYIb2PGw1SzlJCnARCnCNK29zEY/89VM+/HQvXTu259bzB3HV2EziYjU7jYhIa1dZU8cz8zfz+PsbKK2qZXJOD245L5thGQpyjUUBLkIBrnEs3lzEI3M/Zd6G+uB24zlZfOv0vnRor1lpRETamlB5DU/Pz+eZefmUVtUyKac7t5yXTU6GbqE5WQpwEQpwJ64u7Px1zS5+Oy+fRflFpCW158azB3D16X0U3EREhFB5DbPm5zNrfj6llbWcOzid6yZkcebArrql5gQpwEUowB2/A1W1/GHJdmbNz2fLvnJ6pSZyzZn9uPq0vhpGLiIihwlV1PDsgs0899Fm9pZVM6RHJ74zoT9TR2UQH6fzxvFQgItQgGu4DbvLeGnRVl7J28b+ylpG90nluglZTMrprnvcRETkmCpr6shdXsisefms3VlKWlI83xyXyZVjM+nduUPQ5UUFBbgIBbgvV1Fdx5yVO3hp8VYWby4mLsaYlNOD70zoz6l9OwddnoiIRCF3Z/6Gfcyan8/763YDcFZ2OtPHZjJxaHfax+miwNEowEUowB0uHHYWby4id3khucsLKa2spX9aR6aPzeSyr/QmvVN80CWKiEgrUVBSwSuLt/Fq3jYKQ5V07dieS0f3YsrIDEb0TtG9codQgItQgKvn7qwq2E/u8gLeXLGDHaFKEtvFMimnO9PH9eG0/l30SyQiIk2mLuz87dM9vLRoK++v3UN1XZh+XTtwycgMpozMILt7p6BLbBEU4CLacoCrrQuzZEsxc9fs4i+f7GLzvnLaxRpnZ6czZVQGE4d2p2O8RpOKiEjzCpXX8M7qnfxpeQEfbdxH2GFQ9yTOH9ad84f1YESvlDa7ZJcCXERbC3Ch8hrmb9zL3DW7eH/tborLa2gXa5wxII0Lh/fgwuE9SO3QPugyRUREgPo1V/9nxQ7eXrWTxZuLCDt06xTPeUO7c96Qbpw+oCtJbehigwJcRGsPcFW1dSzZUsz8DXuZ9+leVhaECDukdmjHVwd3Y+Kw7pyVnUanBC0sLyIiLVvxgWo+WL+buZ/s5oN1uzlQXUdcjDG6TyoTBqYzIbsrI3untuqZERTgIlpbgNtfWcPSLcXkbS4mb0sRy7aVUFkTJjbGGJ2ZypkD05iQncbozNb9Ay4iIq1bVW0deZuLmRe5QLGqMIQ7JMXHMbpPKmP7dWFM386M6pPaqiaXV4CLiOYAV10bZt3OUlYUlLCqIMTft5awblcp7hAbYwzrmcyYfp0ZPyCN07O66CqbiIi0WsUHqlmwcR8LNu5lyZbi/3M+zMlIZmTvVE7pncKI3ikMTE+K2osYCnAR0RLg9pVVsW5nKWt3lrJuZylrdu5n7Y5SquvCQH2X6Cm9Uji1b2fG9uvCqMxUDUAQEZE2K1RRw9KtxeRtLmLJlmJWFeynrKoWgIR2MQzrmczQnskM6dGJwT2SGdyjEymJLf9ChwJcREsKcLV1YbYXV5C/9wAb95SRv/cAm/Yc4NPdZewtq/r8uM4d2jGkRzIjeqfU/zfRK5XMLoma5kNEROQowmEnf98BVm4PsWJ7iJUFJazdWUppZe3nx/RMSWBgtyT6p3UkK60jWen1zzNSE4ltIaNeFeAimjPAVdXWsStURWGogp2hSrYXl7OtqIJtxeVsKy6nsKSSuvAXbZ+S2I6s9I4MSE+K/IdQ/0hPildYExEROUnuzo5Q5UE9XPvZFLl48tnVOoB2sUav1EQyu3Sof3TuQK/OifRMSaBnSgLdkxNo10xdsl8W4ALvdzOzycAjQCzwW3f/+SH744HngFOBfcA33H1zZN+PgGuBOuAWd3+nGUs/jLsz7fEFbCsqZ9+B6sP2pyXFk9klkdGZnZkyMpG+XTqSlV6f+jt3aKegJiIi0kTMjIzURDJSE/l/Q7p9vt3d2VNWxaY99WFua1H9hZZtReWsWrmD4vKaQz5P/fl8ZO8UfjtjbHN/G58LNMCZWSzwGHA+sB1YbGa57v7JQYddCxS7+0Azmw78AviGmQ0DpgM5QAYw18wGuXtd834XXzAzstI7MrRnMj1TEuiRkkBGSmL9x9SEVjUyRkREpDUwM7p1SqBbpwROz+p62P6yqloKSyrYEapkZ6iCwpJKdoYq6RAfG0C1Xwg6UYwDNrj7JgAzewmYChwc4KYC90Se/wH4tdVfqpoKvOTuVUC+mW2IfL6Pmqn2I/rllaOC/PIiIiLSiJLi4xjUvRODWtjyXkGPq+0FbDvo9fbItiMe4+61QAjo2sD3ioiIiLQ6QV+BO9JNX4eOqjjaMQ15L2Z2A3BD5GWZma07rgpPTBqwtxm+Tluh9mx8atPGpfZsfGrTxqc2bVzN0Z59j7Yj6AC3Hcg86HVvoPAox2w3szggBShq4Htx998Av2nEmo/JzPKONmpEjp/as/GpTRuX2rPxqU0bn9q0cQXdnkF3oS4Gss2sv5m1p35QQu4hx+QCMyLPLwfe8/q5T3KB6WYWb2b9gWxgUTPVLSIiIhKYQK/AuXutmc0E3qF+GpFZ7r7azO4D8tw9F3gaeD4ySKGI+pBH5LhXqB/wUAt8N8gRqCIiIiLNJeguVNx9DjDnkG0/Oeh5JXDFUd77APBAkxZ4Ypq1y7YNUHs2PrVp41J7Nj61aeNTmzauQNuzTa3EICIiItIaBH0PnIiIiIgcJwW4JmJm95vZCjNbZmbvmllG0DVFMzP7DzNbG2nTN8wsNeiaop2ZXWFmq80sbGYamXaCzGyyma0zsw1m9sOg64l2ZjbLzHab2aqga2kNzCzTzN43szWR3/fvBV1TtDOzBDNbZGbLI216byB1qAu1aZhZsrvvjzy/BRjm7jcFXFbUMrMLqB+BXGtmvwBw9x8EXFZUM7OhQBh4Erjd3fMCLinqRJYDXM9BywECVx2yHKAcBzM7GygDnnP34UHXE+3MrCfQ092XmlknYAlwqX5GT1xkNaiO7l5mZu2AecD33H1hc9ahK3BN5LPwFtGRI0wyLA3n7u9GVuIAWEj9vH9yEtx9jbs3x8TWrdnnywG6ezXw2XKAcoLc/W/UzzggjcDdd7j70sjzUmANWrXopHi9ssjLdpFHs5/jFeCakJk9YGbbgKuBnxzreGmw7wBvBV2ECFrST6KImfUDRgMfB1tJ9DOzWDNbBuwG/uLuzd6mCnAnwczmmtmqIzymArj7Xe6eCbwIzAy22pbvWO0ZOeYu6uf9ezG4SqNHQ9pUTkqDlvQTCZqZJQGvAbce0kMkJ8Dd69x9FPW9QePMrNm7+wOfBy6aufvEBh46G/gf4O4mLCfqHas9zWwGcDFwnuvmzQY5jp9ROTENWtJPJEiR+7ReA15099eDrqc1cfcSM/sAmAw068AbXYFrImaWfdDLKcDaoGppDcxsMvADYIq7lwddj0hEQ5YDFAlM5Ib7p4E17v7LoOtpDcws/bOZEMwsEZhIAOd4jUJtImb2GjCY+lF+W4Cb3L0g2KqiV2QptXhgX2TTQo3qPTlmNg14FEgHSoBl7j4p2Kqij5ldBPwXXywH2BJXh4kaZvZ74FwgDdgF3O3uTwdaVBQzswnAh8BK6s9HAHdGVkGSE2BmI4Bnqf+djwFecff7mr0OBTgRERGR6KIuVBEREZEoowAnIiIiEmUU4ERERESijAKciIiISJRRgBMRERGJMgpwIiIiIlFGAU5EREQkyijAiYiIiESZ/w+m287fMwxKvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-3, 3, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5));\n",
    "ax.plot(x, pdf_normal_distribution);\n",
    "ax.set_ylim(0);\n",
    "ax.set_title('Normal Distribution', size = 20);\n",
    "ax.set_ylabel('Probability Density', size = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Derive the familiar 68-95-99.7 rule from the basic definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )# Integrate PDF from -1 to 1\n",
    "\n",
    "def integrate_normal(num_sigma):\n",
    "    result, _ = scipy.integrate.quad(normalProbabilityDensity, -num_sigma, num_sigma, limit = 1000)\n",
    "    return round(result,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The percentage of data present within 1 standard deviation: 0.683\n",
      "The percentage of data present within 2 standard deviations: 0.954\n",
      "The percentage of data present within 3 standard deviations: 0.997\n"
     ]
    }
   ],
   "source": [
    "print(\"The percentage of data present within 1 standard deviation:\",integrate_normal(1))\n",
    "print(\"The percentage of data present within 2 standard deviations:\",integrate_normal(2))\n",
    "print(\"The percentage of data present within 3 standard deviations:\",integrate_normal(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random variable generation using `Numpy.random` module\n",
    "Numpy offers an amazing module called `Numpy.random`, which has all the important probability distributions built-in for generation. We will check it out for,\n",
    "\n",
    "- Normal\n",
    "- Uniform\n",
    "- Binomial\n",
    "- Chi-square\n",
    "- Poisson\n",
    "- F-distribution and Student's t-distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate normally distributed numbers with various mean and std.dev\n",
    "In `numpy.random.normal` method, the `loc` argument is the mean, adnd the `scale` argument is the std.dev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "a1 = np.random.normal(loc=0,scale=np.sqrt(0.2),size=100000)\n",
    "a2 = np.random.normal(loc=0,scale=1.0,size=100000)\n",
    "a3 = np.random.normal(loc=0,scale=np.sqrt(5),size=100000)\n",
    "a4 = np.random.normal(loc=-2,scale=np.sqrt(0.5),size=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.hist(a1,density=True,bins=100,color='blue',alpha=0.5)\n",
    "plt.hist(a2,density=True,bins=100,color='red',alpha=0.5)\n",
    "plt.hist(a3,density=True,bins=100,color='orange',alpha=0.5)\n",
    "plt.hist(a4,density=True,bins=100,color='green',alpha=0.5)\n",
    "plt.xlim(-7,7)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate dice throws and average them to show the emergence of Normality as per the Central Limit Theorem\n",
    "We can use either `np.random.uniform` or `np.random.randint` to generate dice throws uniformly randomly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.82410209, 6.98933133, 6.02069315, 5.56135199, 6.37788852,\n",
       "       2.74708621, 1.42448256, 4.42000875, 6.2479585 , 3.84727738])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.uniform(low=1.0,high=7.0,size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dice_throws(num_sample):\n",
    "    int_throws = np.vectorize(int)\n",
    "    throws = int_throws(np.random.uniform(low=1.0,high=7.0,size=num_sample))\n",
    "    return throws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 2, 6, 1, 5])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice_throws(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 5, 4, 1, 1])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(1,7,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def average_throws(num_throws=5,num_experiment=100):\n",
    "    averages = []\n",
    "    for i in range(num_experiment):\n",
    "        a = dice_throws(num_throws)\n",
    "        av = a.mean()\n",
    "        averages.append(av)\n",
    "    return np.array(averages)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in [50,100,500,1000,5000,10000,50000,100000]:\n",
    "    plt.hist(average_throws(num_throws=20,num_experiment=i),bins=25,edgecolor='k',color='orange')\n",
    "    plt.title(f\"Averaging with 20 throws and repeating it for {i} times\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chi-square ($\\chi^2$) distribution as a sum of squared Normally distributed variables\n",
    "\n",
    "In probability theory and statistics, the **chi-square distribution (also chi-squared or χ2-distribution) with _k_ degrees of freedom is the distribution of a sum of the squares of _k_ independent standard normal random variables**. \n",
    "\n",
    "The chi-square distribution is a special case of the [gamma distribution](https://en.wikipedia.org/wiki/Gamma_distribution) and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing or in construction of confidence intervals.\n",
    "\n",
    "The probability density function (pdf) of the chi-square distribution is\n",
    "\n",
    "$$ f(x;\\,k)={\\begin{cases}{\\dfrac {x^{{\\frac {k}{2}}-1}e^{-{\\frac {x}{2}}}}{2^{\\frac {k}{2}}\\Gamma \\left({\\frac {k}{2}}\\right)}},&x>0;\\\\0,&{\\text{otherwise}}.\\end{cases}} $$\n",
    "\n",
    "where $\\Gamma({k/2})$ denotes the gamma function, which has closed-form values for integer $k$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.92081201, 1.15089252, 2.2436439 , 2.17530209, 3.92828797,\n",
       "       1.14588668, 0.361803  , 2.92001566, 3.40380868, 1.25404746])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.chisquare(df=3,size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_normal(k,num_experiments=100):\n",
    "    dist = []\n",
    "    for i in range(num_experiments):\n",
    "        total = 0\n",
    "        for i in range(k):\n",
    "            total+=(float(np.random.normal()))**2\n",
    "        dist.append(total)\n",
    "    return np.array(dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a1 = np.random.chisquare(df=5,size=1000)\n",
    "plt.hist(a1,bins=25,edgecolor='k',color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a2 = sum_normal(k=5,num_experiments=1000)\n",
    "plt.hist(a2,bins=25,edgecolor='k',color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## F-distribution as a ratio of two scaled Chi-squared distributions\n",
    "In probability theory and statistics, the F-distribution, also known as **Snedecor's F distribution** or the **Fisher–Snedecor distribution** (after [Ronald Fisher](https://en.wikipedia.org/wiki/Ronald_Fisher) and [George W. Snedecor](https://en.wikipedia.org/wiki/George_W._Snedecor)) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.\n",
    "\n",
    "Then the probability density function (pdf) for X is given by\n",
    "\n",
    "$$ {\\begin{aligned}f(x;d_{1},d_{2})&={\\frac {\\sqrt {\\frac {(d_{1}\\,x)^{d_{1}}\\,\\,d_{2}^{d_{2}}}{(d_{1}\\,x+d_{2})^{d_{1}+d_{2}}}}}{x\\,\\mathrm {B} \\!\\left({\\frac {d_{1}}{2}},{\\frac {d_{2}}{2}}\\right)}}\\\\&={\\frac {1}{\\mathrm {B} \\!\\left({\\frac {d_{1}}{2}},{\\frac {d_{2}}{2}}\\right)}}\\left({\\frac {d_{1}}{d_{2}}}\\right)^{\\frac {d_{1}}{2}}x^{{\\frac {d_{1}}{2}}-1}\\left(1+{\\frac {d_{1}}{d_{2}}}\\,x\\right)^{-{\\frac {d_{1}+d_{2}}{2}}}\\end{aligned}} $$\n",
    "\n",
    "Here $\\mathrm {B}$ is the beta function. In many applications, the parameters $d_1$ and $d_2$ are positive integers, but the distribution is well-defined for positive real values of these parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.37384911, 0.77104827, 0.2431134 , 1.02307076, 1.02080626,\n",
       "       0.49639599, 0.55050777, 0.04846961, 0.74689589, 0.61597569])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.f(dfnum=5,dfden=25,size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a1 = np.random.f(dfnum=5,dfden=25,size=1000)\n",
    "plt.hist(a1,bins=25,edgecolor='k',color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a2 = sum_normal(k=5,num_experiments=1000)\n",
    "a3 = sum_normal(k=25,num_experiments=1000)\n",
    "a4 = a2/a3\n",
    "\n",
    "plt.hist(a4,bins=25,edgecolor='k',color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Student's t-distribution\n",
    "\n",
    "In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when **estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown**. It was developed by [William Sealy Gosset](https://en.wikipedia.org/wiki/William_Sealy_Gosset) under the pseudonym Student.\n",
    "\n",
    "The t-distribution plays a role in a number of widely used statistical analyses, including Student's t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. The Student's t-distribution also arises in the Bayesian analysis of data from a normal family.\n",
    "\n",
    "Student's t-distribution has the probability density function given by,\n",
    "$$ f(t)={\\frac {\\Gamma ({\\frac {\\nu +1}{2}})}{{\\sqrt {\\nu \\pi }}\\,\\Gamma ({\\frac {\\nu }{2}})}}\\left(1+{\\frac {t^{2}}{\\nu }}\\right)^{\\!-{\\frac {\\nu +1}{2}},\\!} $$\n",
    "\n",
    "where $\\nu$ is the number of degrees of freedom and $\\Gamma$ is the gamma function. \n",
    "\n",
    "![t_dist_538](https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/t_dist_538.PNG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a1=np.random.standard_t(10,size=10000)\n",
    "plt.hist(a1,bins=50,edgecolor='k',color='orange',density=True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}