Module3-Statistics/M3A_Distributions_Sampling_Expectations_and_SummaryStatistics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Introduction to Basic Probability and Statistics - Distributions, Sampling, and Expectations \n",
    "<html>\n",
    "    <summary></summary>\n",
    "         <div> <p></p> </div>\n",
    "         <div style=\"font-size: 20px; width: 800px;\"> \n",
    "              <h1>\n",
    "               <left>Intro to Basic Probability and Statistics: Distributions, Sampling, and Expectations.</left>\n",
    "              </h1>\n",
    "              <p><left>============================================================================</left> </p>\n",
    "<pre>Course: BIOM 421, Spring 2024\n",
    "Instructor: Brian Munsky\n",
    "Authors: Huy Vo, Ania Baetica, Brian Munsky\n",
    "Contact Info: munsky@colostate.edu\n",
    "</pre>\n",
    "         </div>\n",
    "    </p>\n",
    "\n",
    "</html>\n",
    "\n",
    "<details>\n",
    "  <summary>Copyright info</summary>\n",
    "\n",
    "```\n",
    "Copyright 2024 Brian Munsky\n",
    "\n",
    "Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:\n",
    "\n",
    "1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.\n",
    "\n",
    "2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.\n",
    "\n",
    "3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.\n",
    "\n",
    "THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n",
    "```\n",
    "<details>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](figures/image0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import sympy as sym\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.random as rng\n",
    "import scipy.stats as stats\n",
    "# Uncomment the following the first time if you do not have seaborn installed:\n",
    "#!pip install seaborn\n",
    "import seaborn as sns\n",
    "from typing import Union # for code annotation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random Numbers\n",
    "![alt text](figures/image.png)\n",
    "\n",
    "A random variable is a quantity $X$ whose precise value is _uncertain_. For example, the number of cells in the next microscope field of view you image or the height of the first person you see on the street tomorrow are random variables.\n",
    "\n",
    "If $X$ can only take integer values $0,1,2,\\ldots$ we say that $X$ is a __discrete random variable__. If $X$ can take the whole range of real values in $\\mathbb{R}$, we say that $X$ is a __continuous random variable__. There are random variables that can behave discretely in some domain and continuously in others, but for the purpose of the summer school we will only focus on these two types."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probability Distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability Mass Functions and Probability Density Functions\n",
    "![alt text](figures/image-1.png)\n",
    "\n",
    "When $X$ is discrete, the __probability mass function__ (PMF) of $X$ gives us the probability for it to take on each possible specific value $n=0,1,2,\\ldots$:\n",
    "$$\n",
    "p_{X}(n) = \\mathrm{Pr}\\left(X = n\\right).\n",
    "$$\n",
    "\n",
    "When $X$ is continuous, we are interested in the __probability density function__ (PDF) of $X$, defined as a function $f_X(x)$ taking nonnegative values such that\n",
    "$$\n",
    "\\int_a^b{f_X(x)\\mathrm{dx}} = \\mathrm{Pr}(a \\leq X \\leq b).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cumulative Probability Distribution\n",
    "![alt text](figures/image-2.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common Discrete Distrbutions\n",
    "There are several discrete distributions that we will encounter in this class.  The most important are Bernoulli, Binomial, and Poisson."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bernoulli Distribution\n",
    "![alt text](figures/image-4.png)\n",
    "The Bernoulli distribution is used to model a binary reponse $Y$ that, without loss of generality, we assume to be either $0$ or $1$. Its probability mass function is given by\n",
    "$$\n",
    "\\mathrm{Ber}\\left(y\\vert \\theta\\right)\n",
    ":=\n",
    "\\begin{cases}\n",
    "1-\\theta \\;\\;\\text{if }y=0\\\\\n",
    "\\theta \\;\\;\\text{if }y=1\n",
    "\\end{cases}\n",
    "$$\n",
    "where $\\theta$ is the parameter of the distribution. This parameter has the clear interpretation as the probability for $Y$ to take value $1$. You can use this distribution to model a _single occurrence_ of a trial that has binary outcomes, such as a single coin flip.\n",
    "\n",
    "The Bernoulli distribution is important for understanding binary classification (e.g., in machine learning).\n",
    "\n",
    "* What is the mean of a Bernoulli random variable?\n",
    "\n",
    "* What is its standard deviation?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1UAAAHHCAYAAABXznKnAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABLQElEQVR4nO3de1xUdeL/8fcAMmgJXhC8hEhq3igzsERTMxUvZVrtV8ryFm4RmV8lK8nWlK2ofoXYGqjrha9d/PKttHWLVaet1CK3FbHL6lqZBdogoRuYGiic3x+us46gzjgMB+T1fDzO4+F85lzekzw8vfmcOcdiGIYhAAAAAMBF8TE7AAAAAAA0ZJQqAAAAAPAApQoAAAAAPECpAgAAAAAPUKoAAAAAwAOUKgAAAADwAKUKAAAAADxAqQIAAAAAD1CqAAAAAMADlCoAAAAA8AClCgAAAAA8QKkCAAAAAA9QqgAAAADAA5QqAAAAAPAApQoAAAAAPECpAgAAAAAPUKoAAAAAwAOUKgAAAADwAKUKAAAAADxAqQIAAAAAD1CqAAAAAMADlCoAAAAA8AClCgCAM2zZskVjxoxR+/btZbFY9M4771xwm82bNysqKkoBAQG68sortWTJEu8HBQDUG6aXqoyMDEVERCggIEBRUVHaunXrOdedMmWKLBZLtaVXr151mBgAcCk7evSoevfurcWLF7u0/r59+zR69GgNHDhQ+fn5euKJJzRjxgy9/fbbXk4KAKgvLIZhGGYdPDs7WxMnTlRGRoYGDBigpUuXavny5dq1a5c6duxYbf3S0lIdP37c8frkyZPq3bu3Hn74Yc2fP78OkwMAGgOLxaJ169Zp3Lhx51zn8ccf1/r167V7927HWEJCgj7//HN9+umndZASgLcZhqHjJyrNjoGL1LSJrywWi1ePYWqpuuGGG3TdddcpMzPTMdajRw+NGzdOqampF9z+nXfe0R133KF9+/YpPDzcm1EBAI2QK6Vq0KBB6tOnjxYtWuQYW7duncaPH69jx46pSZMm1bYpLy9XeXm547VhGKqoqFBwcLDXT/wA3GMYhn6z5FPl/fAvs6PgIu1KGaFm/n5ePYZ3934eFRUVysvL05w5c5zGY2NjlZub69I+VqxYoWHDhp23UHHiAi7C0QKpvMTsFGiIrMHSZdWvNLiUFRUVKTQ01GksNDRUJ0+eVElJidq1a1dtm9TUVC1YsKDaeGlpqQIDA72WFYD7jp+opFDhgkwrVSUlJaqsrKzxRFRUVHTB7e12u/7yl7/ojTfeOO96nLgANx0tkP7cTar61ewkaIh8AqQxexpdsTr7l3SnLwI51y/vkpOTlZSU5HhdVlamsLAw7wUEUCu2PzlMzfx9zY4BNzVt4v2/M9NK1Wk1nYhcmUHKyspSixYtzntJhsSJC3BbeQmFChev6tdTP0ONqFS1bdu22i8Di4uL5efnp9atW9e4jdVqldVqrYt4AGpRM39fr19GhobJtJ+K4OBg+fr61ngiOnv26myGYWjlypWaOHGi/P39z7suJy4AgDfFxMToz3/+s9PYpk2bFB0dXeP3qQAAlx7Tbqnu7++vqKgo2Ww2p3Gbzab+/fufd9vNmzfr22+/VXx8vDcjAgAaoV9++UU7d+7Uzp07JZ26ZfrOnTtVUFAg6dQVEJMmTXKsn5CQoB9++EFJSUnavXu3Vq5cqRUrVmj27NlmxAcAmMDU+cukpCRNnDhR0dHRiomJ0bJly1RQUKCEhARJp05cBw4c0OrVq522W7FihW644QZFRkaaERsAcAnbvn27hgwZ4nh9+hLyyZMnKysrS3a73VGwJCkiIkI5OTmaNWuWXnnlFbVv314vv/yy7rzzzjrPDgAwh6mlKi4uTocOHVJKSorsdrsiIyOVk5PjuJvf2Scu6dQNJt5++22nW9cCAFBbbrrpJp3vaSNZWVnVxgYPHqwdO3Z4MRUAoD4z/Zt2iYmJSkxMrPG9mk5cQUFBOnbsmJdTAQAAAIBrTPtOFQAAAABcCihVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAcoVQAAAADgAUoVAAAAAHiAUgUAAAAAHqBUAQAAAIAHKFUAAAAA4AFKFQAAAAB4gFIFAAAAAB6gVAEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAcoVQAAAADgAUoVAAAAAHiAUgUAAAAAHqBUAQAAAIAHKFUAAAAA4AFKFQAAAAB4gFIFAAAAAB6gVAEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAcoVQAAAADgAUoVAAAAAHiAUgUAAAAAHqBUAQAAAIAHKFUAAAAA4AFKFQAAAAB4gFIFAAAAAB6gVAEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAdML1UZGRmKiIhQQECAoqKitHXr1vOuX15errlz5yo8PFxWq1WdO3fWypUr6ygtAAAAADjzM/Pg2dnZmjlzpjIyMjRgwAAtXbpUo0aN0q5du9SxY8catxk/frwOHjyoFStWqEuXLiouLtbJkyfrODkAAAAAnGJqqUpLS1N8fLymTZsmSUpPT9fGjRuVmZmp1NTUautv2LBBmzdv1nfffadWrVpJkjp16lSXkQEAAADAiWmX/1VUVCgvL0+xsbFO47GxscrNza1xm/Xr1ys6OlovvPCCOnTooKuuukqzZ8/W8ePHz3mc8vJylZWVOS0AAAAAUFtMm6kqKSlRZWWlQkNDncZDQ0NVVFRU4zbfffedPv74YwUEBGjdunUqKSlRYmKiDh8+fM7vVaWmpmrBggW1nh8AAAAApHpwowqLxeL02jCMamOnVVVVyWKx6PXXX9f111+v0aNHKy0tTVlZWeecrUpOTlZpaaljKSwsrPXPAAAAAKDxMm2mKjg4WL6+vtVmpYqLi6vNXp3Wrl07dejQQUFBQY6xHj16yDAM7d+/X127dq22jdVqldVqrd3wAAAAAPBvps1U+fv7KyoqSjabzWncZrOpf//+NW4zYMAA/fjjj/rll18cY19//bV8fHx0xRVXeDUvAAAAANTE1Mv/kpKStHz5cq1cuVK7d+/WrFmzVFBQoISEBEmnLt2bNGmSY/0JEyaodevWmjp1qnbt2qUtW7bo0Ucf1X333aemTZua9TEAAAAANGKm3lI9Li5Ohw4dUkpKiux2uyIjI5WTk6Pw8HBJkt1uV0FBgWP9yy+/XDabTQ8//LCio6PVunVrjR8/Xk8//bRZHwEAAABAI2dqqZKkxMREJSYm1vheVlZWtbHu3btXu2QQAAAAAMxi+t3/AAAAAKAho1QBAAAAgAcoVQAAAADgAUoVAAAAAHiAUgUAAAAAHqBUAQAAAIAHKFUAAJwlIyNDERERCggIUFRUlLZu3Xre9V9//XX17t1bzZo1U7t27TR16lQdOnSojtICAMxGqQIA4AzZ2dmaOXOm5s6dq/z8fA0cOFCjRo1yehj9mT7++GNNmjRJ8fHx+sc//qE333xTf//73zVt2rQ6Tg4AMAulCgCAM6SlpSk+Pl7Tpk1Tjx49lJ6errCwMGVmZta4/rZt29SpUyfNmDFDERERuvHGG/XAAw9o+/btdZwcAGAWShUAAP9WUVGhvLw8xcbGOo3HxsYqNze3xm369++v/fv3KycnR4Zh6ODBg3rrrbd0yy23nPM45eXlKisrc1oAAA0XpQoAgH8rKSlRZWWlQkNDncZDQ0NVVFRU4zb9+/fX66+/rri4OPn7+6tt27Zq0aKF/vCHP5zzOKmpqQoKCnIsYWFhtfo5AAB1i1IFAMBZLBaL02vDMKqNnbZr1y7NmDFD8+bNU15enjZs2KB9+/YpISHhnPtPTk5WaWmpYyksLKzV/ACAuuVndgAAAOqL4OBg+fr6VpuVKi4urjZ7dVpqaqoGDBigRx99VJJ0zTXX6LLLLtPAgQP19NNPq127dtW2sVqtslqttf8BAACmYKYKAIB/8/f3V1RUlGw2m9O4zWZT//79a9zm2LFj8vFxPp36+vpKOjXDBQC49FGqAAA4Q1JSkpYvX66VK1dq9+7dmjVrlgoKChyX8yUnJ2vSpEmO9ceMGaO1a9cqMzNT3333nT755BPNmDFD119/vdq3b2/WxwAA1CEu/wMA4AxxcXE6dOiQUlJSZLfbFRkZqZycHIWHh0uS7Ha70zOrpkyZoiNHjmjx4sV65JFH1KJFC9188816/vnnzfoIAIA6ZjEa2bUJZWVlCgoKUmlpqQIDA82OA9Q/h3dIG6LMToGGbGSe1Oo6s1M0KJybgPrrWMVJ9Zy3UZK0K2WEmvkzJ4HquPwPAAAAADxAqQIAAAAAD1CqAAAAAMADlCoAAAAA8AClCgAAAAA8QKkCAAAAAA9QqgAAAADAA5QqAAAAAPAApQoAAAAAPECpAgAAAAAPUKoAAAAAwAOUKgAAAADwAKUKAAAAADxAqQIAAAAAD1CqAAAAAMADlCoAAAAA8AClCgAAAAA8QKkCAAAAAA9QqgAAAADAA5QqAAAAAPAApQoA0ODt27fP7AgAgEaMUgUAaPC6dOmiIUOG6LXXXtOvv/5qdhwAQCNDqQIANHiff/65+vTpo0ceeURt27bVAw88oM8++8zsWACARoJSBQBo8CIjI5WWlqYDBw5o1apVKioq0o033qhevXopLS1NP/30k9kRAQCXMEoVAOCS4efnp9tvv13/93//p+eff1579+7V7NmzdcUVV2jSpEmy2+1mRwQAXIJML1UZGRmKiIhQQECAoqKitHXr1nOu+9FHH8lisVRb/vnPf9ZhYgBAfbV9+3YlJiaqXbt2SktL0+zZs7V371598MEHOnDggMaOHWt2RADAJcjPzINnZ2dr5syZysjI0IABA7R06VKNGjVKu3btUseOHc+53Z49exQYGOh43aZNm7qICwCop9LS0rRq1Srt2bNHo0eP1urVqzV69Gj5+Jz63WFERISWLl2q7t27m5wUAHApMnWmKi0tTfHx8Zo2bZp69Oih9PR0hYWFKTMz87zbhYSEqG3bto7F19e3jhIDAOqjzMxMTZgwQQUFBXrnnXd06623OgrVaR07dtSKFStMSggAuJSZVqoqKiqUl5en2NhYp/HY2Fjl5uaed9s+ffqoXbt2Gjp0qD788MPzrlteXq6ysjKnBQBwabHZbHr88cfVtm1bp3HDMFRQUCBJ8vf31+TJk82IBwC4xJlWqkpKSlRZWanQ0FCn8dDQUBUVFdW4Tbt27bRs2TK9/fbbWrt2rbp166ahQ4dqy5Yt5zxOamqqgoKCHEtYWFitfg4AgPk6d+6skpKSauOHDx9WRESECYkAAI2Jqd+pkiSLxeL02jCMamOndevWTd26dXO8jomJUWFhoV588UUNGjSoxm2Sk5OVlJTkeF1WVkaxAoBLjGEYNY7/8ssvCggIqOM0AIDGxrRSFRwcLF9f32qzUsXFxdVmr86nX79+eu211875vtVqldVqveicAID66/QvzSwWi+bNm6dmzZo53qusrNTf/vY3XXvttSalAwA0FqaVKn9/f0VFRclms+n22293jNtsNrdueZufn6927dp5IyIAoJ7Lz8+XdGqm6ssvv5S/v7/jPX9/f/Xu3VuzZ882Kx4AoJEw9fK/pKQkTZw4UdHR0YqJidGyZctUUFCghIQESacu3Ttw4IBWr14tSUpPT1enTp3Uq1cvVVRU6LXXXtPbb7+tt99+28yPAQAwyembFU2dOlWLFi1yetwGAAB1xdRSFRcXp0OHDiklJUV2u12RkZHKyclReHi4JMlutzvu2iSdumPg7NmzdeDAATVt2lS9evXSe++9p9GjR5v1EQAA9cCqVavMjgAAaMQsxrm+3XuJKisrU1BQkEpLS/mNJlCTwzukDVFmp0BDNjJPanWd1w9zxx13KCsrS4GBgbrjjjvOu+7atWu9nscTnJuA+utYxUn1nLdRkrQrZYSa+Zt+nzfUQ/xUAAAapKCgIMfdYoOCgkxOAwBozChVAIAG6cxL/rj8DwBgJtMe/gsAAAAAlwJmqgAADVKfPn3O+bD4s+3YscPLaQAAjRmlCgDQII0bN87sCAAASKJUAQAaqKeeesrsCAAASOI7VQAAAADgEbdnqgoLC2WxWHTFFVdIkj777DO98cYb6tmzp+6///5aDwgAQE1atWqlr7/+WsHBwWrZsuV5v191+PDhOkwGAGhs3C5VEyZM0P3336+JEyeqqKhIw4cPV69evfTaa6+pqKhI8+bN80ZOAACcLFy4UM2bN5ckpaenmxsGANCouV2qvvrqK11//fWSpP/7v/9TZGSkPvnkE23atEkJCQmUKgBAnZg8eXKNfwYAoK65XapOnDghq9UqSXr//fd12223SZK6d+8uu91eu+kAAHBRZWWl1q1bp927d8tisahHjx4aO3as/Py4JxMAwLvcPtP06tVLS5Ys0S233CKbzabf//73kqQff/xRrVu3rvWAAABcyFdffaWxY8eqqKhI3bp1kyR9/fXXatOmjdavX6+rr77a5IQAgEuZ23f/e/7557V06VLddNNNuvvuu9W7d29J0vr16x2XBQIAUJemTZumXr16af/+/dqxY4d27NihwsJCXXPNNdxECQDgdW7PVN10000qKSlRWVmZWrZs6Ri///771axZs1oNBwCAKz7//HNt377d6bzUsmVLPfPMM+rbt6+JyQAAjYHbM1XHjx9XeXm548T1ww8/KD09XXv27FFISEitBwQA4EK6deumgwcPVhsvLi5Wly5dTEgEAGhM3C5VY8eO1erVqyVJP//8s2644Qa99NJLGjdunDIzM2s9IAAANSkrK3Mszz77rGbMmKG33npL+/fv1/79+/XWW29p5syZev75582OCgC4xLl9+d+OHTu0cOFCSdJbb72l0NBQ5efn6+2339a8efP04IMP1npIAADO1qJFC6cH/hqGofHjxzvGDMOQJI0ZM0aVlZWmZAQANA5ul6pjx445Hra4adMm3XHHHfLx8VG/fv30ww8/1HpAAABq8uGHH5odAQAASRdRqrp06aJ33nlHt99+uzZu3KhZs2ZJOnXdemBgYK0HBACgJoMHDzY7AgAAki6iVM2bN08TJkzQrFmzNHToUMXExEg6NWvVp0+fWg8IAICrjh07poKCAlVUVDiNX3PNNSYlAgA0Bm6Xqt/85je68cYbZbfbHc+okqShQ4fq9ttvr9VwAAC44qefftLUqVP1l7/8pcb3+U4VAMCb3L77nyS1bdtWffr0kY/Pfza//vrr1b1791oLBgCAq2bOnKl//etf2rZtm5o2baoNGzbof/7nf9S1a1etX7/e7HgAgEuc2zNVkvT3v/9db775Zo2XWKxdu7ZWggEA4KoPPvhAf/rTn9S3b1/5+PgoPDxcw4cPV2BgoFJTU3XLLbeYHREAcAlze6bqf//3fzVgwADt2rVL69at04kTJ7Rr1y598MEHCgoK8kZGAADO6+jRo44H0Ldq1Uo//fSTJOnqq6/Wjh073N5fRkaGIiIiFBAQoKioKG3duvW865eXl2vu3LkKDw+X1WpV586dtXLlSvc/CACgQXK7VD377LNauHCh3n33Xfn7+2vRokXavXu3xo8fr44dO3ojIwAA59WtWzft2bNHknTttddq6dKlOnDggJYsWaJ27dq5ta/s7GzNnDlTc+fOVX5+vgYOHKhRo0apoKDgnNuMHz9ef/3rX7VixQrt2bNHa9as4ZJ4AGhE3L78b+/evY7LKKxWq44ePSqLxaJZs2bp5ptv1oIFC2o9JAAA5zNz5kzZ7XZJ0lNPPaURI0bo9ddfl7+/v7KystzaV1pamuLj4zVt2jRJUnp6ujZu3KjMzEylpqZWW3/Dhg3avHmzvvvuO7Vq1UqS1KlTJ48+DwCgYXF7pqpVq1Y6cuSIJKlDhw766quvJEk///yzjh07VrvpAABwwT333KMpU6ZIkvr06aPvv/9ef//731VYWKi4uDiX91NRUaG8vDzFxsY6jcfGxio3N7fGbdavX6/o6Gi98MIL6tChg6666irNnj1bx48fP+dxysvLVVZW5rQAABout2eqBg4cKJvNpquvvlrjx4/Xf//3f+uDDz6QzWbT0KFDvZERAACXGYahpk2b6rrrrnN725KSElVWVio0NNRpPDQ0VEVFRTVu89133+njjz9WQECA1q1bp5KSEiUmJurw4cPn/F5VamoqV3YAwCXE7ZmqxYsX66677pIkJScna/bs2Tp48KDuuOMOrVixotYDAgDgihUrVigyMlIBAQEKCAhQZGSkli9fflH7slgsTq8Nw6g2dlpVVZUsFotef/11XX/99Ro9erTS0tKUlZV1ztmq5ORklZaWOpbCwsKLygkAqB/cnqk6fb24JPn4+Oixxx7TY489VquhAABwx+9+9zstXLhQDz/8sGJiYiRJn376qWbNmqXvv/9eTz/9tEv7CQ4Olq+vb7VZqeLi4mqzV6e1a9dOHTp0cLoDbo8ePWQYhvbv36+uXbtW28Zqtcpqtbr68QAA9dxFPfwXAID6JDMzU3/84x+Vmpqq2267TbfddptSU1O1bNkyLVmyxOX9+Pv7KyoqSjabzWncZrOpf//+NW4zYMAA/fjjj/rll18cY19//bV8fHx0xRVXXNwHAgA0KC6XKl9fX5cWAADqWmVlpaKjo6uNR0VF6eTJk27tKykpScuXL9fKlSu1e/duzZo1SwUFBUpISJB06tK9SZMmOdafMGGCWrduralTp2rXrl3asmWLHn30Ud13331q2rSpZx8MANAguHz5n2EYCg8P1+TJk9WnTx9vZgIAwC333nuvMjMzlZaW5jS+bNky3XPPPW7tKy4uTocOHVJKSorsdrsiIyOVk5Oj8PBwSZLdbnd6ZtXll18um82mhx9+WNHR0WrdurXGjx/v8iWHAICGz+VS9be//U0rV67UokWLFBERofvuu0/33HOPWrZs6c18AADUKCkpyfFni8Wi5cuXa9OmTerXr58kadu2bSosLHSaVXJVYmKiEhMTa3yvpudede/evdolgwCAxsPlUtW3b1/17dtXCxcu1FtvvaVVq1bp8ccf15gxYxQfH6/hw4d7MycAAE7y8/OdXkdFRUk69ZB6SWrTpo3atGmjf/zjH3WeDQDQuLh997+AgADde++9uvfee7Vv3z7Fx8dr5MiR+umnn5zuDAgAgDd9+OGHZkcAAEDSRZQqSdq/f7+ysrIcz+B49NFHFRgYWNvZAABw2/79+2WxWNShQwezowAAGgmX7/5XUVGh7OxsxcbGqmvXrtqxY4fS09NVWFio5557Tn5+F9XPAADwWFVVlVJSUhQUFKTw8HB17NhRLVq00O9//3tVVVWZHQ8AcIlzuQm1a9dOzZs31+TJk5WRkaGQkBBJcnouhyRmrAAAdW7u3LlasWKFnnvuOQ0YMECGYeiTTz7R/Pnz9euvv+qZZ54xOyIA4BJmMQzDcGVFH5//TGpZLJZq7xuGIYvFosrKytpL5wVlZWUKCgpSaWkpBRCoyeEd0oYos1OgIRuZJ7W6rk4P2b59ey1ZskS33Xab0/if/vQnJSYm6sCBA3Wax12cm4D661jFSfWct1GStCtlhJr5c3UWqnP5p4IvBAMA6qvDhw+re/fu1ca7d++uw4cPm5AIANCYuFyqBg8e7JUAGRkZ+n//7//JbrerV69eSk9P18CBAy+43SeffKLBgwcrMjJSO3fu9Eo2AEDD0Lt3by1evFgvv/yy0/jixYvVu3dvk1IBABoLU+cvs7OzNXPmTGVkZGjAgAFaunSpRo0apV27dqljx47n3K60tFSTJk3S0KFDdfDgwTpMDACoj1544QXdcsstev/99xUTEyOLxaLc3FwVFhYqJyfH7HgAgEucy3f/84a0tDTFx8dr2rRp6tGjh9LT0xUWFqbMzMzzbvfAAw9owoQJiomJqaOkAID6bPDgwfr66691++236+eff9bhw4d1xx13aM+ePS5d/QAAgCdMm6mqqKhQXl6e5syZ4zQeGxur3Nzcc263atUq7d27V6+99pqefvrpCx6nvLxc5eXljtdlZWUXHxoAUO+cOHFCsbGxWrp0KXf5AwCYwrSZqpKSElVWVio0NNRpPDQ0VEVFRTVu880332jOnDl6/fXXXX4uVmpqqoKCghxLWFiYx9kBAPVHkyZN9NVXX9V4Z1oAAOqC26UqKytLx44dq7UAZ58ET9+a/WyVlZWaMGGCFixYoKuuusrl/ScnJ6u0tNSxFBYWepwZAFC/TJo0SStWrDA7BgCgkXL78r/k5GTNmDFD//Vf/6X4+Hj179//og4cHBwsX1/farNSxcXF1WavJOnIkSPavn278vPzNX36dElSVVWVDMOQn5+fNm3apJtvvrnadlarVVar9aIyAgAahoqKCi1fvlw2m03R0dG67LLLnN5PS0szKRkAoDFwu1Tt379f7733nrKysjRkyBBFRERo6tSpmjx5stq2bevyfvz9/RUVFSWbzabbb7/dMW6z2TR27Nhq6wcGBurLL790GsvIyNAHH3ygt956SxEREe5+FADAJeKrr77SddedeuDw119/7fQelwUCALzN7VLl6+ur2267TbfddpuKi4v12muvKSsrS7/73e80cuRIxcfHa8yYMfLxufCVhUlJSZo4caKio6MVExOjZcuWqaCgQAkJCZJOzYodOHBAq1evlo+PjyIjI522DwkJUUBAQLVxAEDjwgPqAQBm8ujufyEhIRowYID27Nmjr7/+Wl9++aWmTJmiFi1aaNWqVbrpppvOu31cXJwOHTqklJQU2e12RUZGKicnR+Hh4ZIku92ugoICTyICAC5xb775pt555x2dOHFCw4YN0/333292JABAI3NRd/87ePCgXnzxRfXq1Us33XSTysrK9O6772rfvn368ccfdccdd2jy5Mku7SsxMVHff/+9ysvLlZeXp0GDBjney8rK0kcffXTObefPn6+dO3dezEcAAFwCli1bpri4OG3fvl179uzRgw8+qOTkZLNjAQAaGbdL1ZgxYxQWFqasrCz99re/1YEDB7RmzRoNGzZMktS0aVM98sgj3GUPAOB1f/jDHzR37lzt2bNHn3/+uVasWKHFixebHQsA0Mi4XapCQkK0efNmffXVV5o5c6ZatWpVbZ127dpp3759tRIQAIBz+e677zR16lTH64kTJ6q8vPyczzsEAMAb3C5VgwcPdtxh6UwVFRVavXq1pFN3Wjr9vSgAALzl+PHjuvzyyx2vfX19ZbVaa/V5igAAXIjbN6qYOnWqRo4cqZCQEKfxI0eOaOrUqZo0aVKthQMA4EKWL1/uVKxOnjyprKwsBQcHO8ZmzJhhRjQAQCPhdqkyDKPGZ37s379fQUFBtRIKAABXdOzYUX/84x+dxtq2batXX33V8dpisVCqAABe5XKp6tOnjywWiywWi4YOHSo/v/9sWllZqX379mnkyJFeCQkAQE2+//57syMAAOB6qRo3bpwkaefOnRoxYoTTpRb+/v7q1KmT7rzzzloPCAAAAAD1mcul6qmnnpIkderUSXFxcQoICPBaKAAAAABoKNz+TpWrD/UFAAAAgMbApVLVqlUrff311woODlbLli1rvFHFaYcPH661cAAAAABQ37lUqhYuXKjmzZs7/ny+UgUAAAAAjYlLperMS/6mTJnirSwAAFy0vXv3atWqVdq7d68WLVqkkJAQbdiwQWFhYerVq5fZ8QAAlzAfV1YqKytzeQEAoK5t3rxZV199tf72t79p7dq1+uWXXyRJX3zxheNGSwAAeItLM1UtWrS44CV/px8KXFlZWSvBAABw1Zw5c/T0008rKSnJcbm6JA0ZMkSLFi0yMRkAoDFwqVR9+OGH3s4BAMBF+/LLL/XGG29UG2/Tpo0OHTpkQiIAQGPiUqkaPHiwt3MAAHDRWrRoIbvdroiICKfx/Px8dejQwaRUAIDGwqVS9cUXXygyMlI+Pj764osvzrvuNddcUyvBAABw1YQJE/T444/rzTfflMViUVVVlT755BPNnj1bkyZNMjseAOAS51Kpuvbaa1VUVKSQkBBde+21slgsMgyj2np8pwoAYIZnnnlGU6ZMUYcOHWQYhnr27KnKykpNmDBBTz75pNnxAACXOJdK1b59+9SmTRvHnwEAqE+aNGmi119/XSkpKcrPz1dVVZX69Omjrl27mh0NANAIuFSqwsPDa/wzAAD1webNmzV48GB17txZnTt3NjsOAKCRcek5VWfbs2ePpk+frqFDh2rYsGGaPn269uzZU9vZAABwyfDhw9WxY0fNmTNHX331ldlxAACNjNul6q233lJkZKTy8vLUu3dvXXPNNdqxY4ciIyP15ptveiMjAADn9eOPP+qxxx7T1q1bdc011+iaa67RCy+8oP3795sdDQDQCFiMmu44cR5XXnml7r33XqWkpDiNP/XUU3r11Vf13Xff1WrA2lZWVqagoCCVlpYqMDDQ7DhA/XN4h7QhyuwUaMhG5kmtrjPt8Pv27dMbb7yhNWvW6J///KcGDRqkDz74wLQ8ruDcBNRfxypOque8jZKkXSkj1MzfpW/PoJFxe6aqqKioxtvT3nvvvSoqKqqVUAAAXKyIiAjNmTNHzz33nK6++mpt3rzZ7EgAgEuc26Xqpptu0tatW6uNf/zxxxo4cGCthAIA4GJ88sknSkxMVLt27TRhwgT16tVL7777rtmxAACXOJfmL9evX+/482233abHH39ceXl56tevnyRp27ZtevPNN7VgwQLvpAQA4DyeeOIJrVmzRj/++KOGDRum9PR0jRs3Ts2aNTM7GgCgEXDpO1U+Pq5NaDWEh/9y3TpwAXynCp4y4TtV/fv31z333KO4uDgFBwfX6bFrA+cmoP7iO1VwhUs/FVVVVd7OAQDARcvNzTU7AgCgEaNqAwAapPXr12vUqFFq0qSJ02XqNbntttvqKBUAoDG6qFJ19OhRbd68WQUFBaqoqHB6b8aMGbUSDACA8xk3bpyKiooUEhKicePGnXO9hnBpOgCgYXO7VOXn52v06NE6duyYjh49qlatWqmkpETNmjVTSEgIpQoAUCfOvDSdy9QBAGZy+5bqs2bN0pgxY3T48GE1bdpU27Zt0w8//KCoqCi9+OKL3sgIAMB5rV69WuXl5dXGKyoqtHr1ahMSAQAaE7dL1c6dO/XII4/I19dXvr6+Ki8vV1hYmF544QU98cQT3sgIAMB5TZ06VaWlpdXGjxw5oqlTp5qQCADQmLhdqpo0aSKLxSJJCg0NVUFBgSQpKCjI8WcAAOqSYRiOc9OZ9u/fr6CgIBMSAQAaE7e/U9WnTx9t375dV111lYYMGaJ58+appKREr776qq6++mpvZAQAoEZ9+vSRxWKRxWLR0KFD5ef3n9NaZWWl9u3bp5EjR5qYEADQGLhdqp599lkdOXJEkvT73/9ekydP1oMPPqguXbpo1apVtR4QAIBzOX3Xv507d2rEiBG6/PLLHe/5+/urU6dOuvPOO01KBwBoLNwuVdHR0Y4/t2nTRjk5ObUaCAAAVz311FOSpE6dOikuLk4BAQEmJwIANEYX/fDf4uJi7dmzRxaLRd26dVObNm1qMxcAAC6bPHmy2REAAI2Y2zeqKCsr08SJE9WhQwcNHjxYgwYNUvv27XXvvffWeOclAAC8rbKyUi+++KKuv/56tW3bVq1atXJaAADwJrdL1bRp0/S3v/1N7777rn7++WeVlpbq3Xff1fbt2/Xb3/7WGxkBADivBQsWKC0tTePHj1dpaamSkpJ0xx13yMfHR/Pnzzc7HgDgEuf25X/vvfeeNm7cqBtvvNExNmLECP3xj3/kDksAAFO8/vrr+uMf/6hbbrlFCxYs0N13363OnTvrmmuu0bZt2zRjxgyzIwIALmFuz1S1bt26xmd+BAUFqWXLlm4HyMjIUEREhAICAhQVFaWtW7eec92PP/5YAwYMUOvWrdW0aVN1795dCxcudPuYAIBLS1FRkeOxHpdffrnjcvRbb71V7733ntv7c+fcdKZPPvlEfn5+uvbaa90+JgCg4XK7VD355JNKSkqS3W53jBUVFenRRx/V7373O7f2lZ2drZkzZ2ru3LnKz8/XwIEDNWrUqHM+RPiyyy7T9OnTtWXLFu3evVtPPvmknnzySS1btszdjwEAuIRcccUVjvNSly5dtGnTJknS3//+d1mtVrf25e656bTS0lJNmjRJQ4cOvbgPAQBosCyGYRgXWun0wxVP++abb1ReXq6OHTtKkgoKCmS1WtW1a1ft2LHD5YPfcMMNuu6665SZmekY69Gjh8aNG6fU1FSX9nHHHXfosssu06uvvurS+mVlZQoKClJpaakCAwNdzgo0God3SBuizE6BhmxkntTqujo95Jw5cxQYGKgnnnhCb731lu6++2516tRJBQUFmjVrlp577jmX93Wx56a77rpLXbt2la+vr9555x3t3LnT5WNybgLqr2MVJ9Vz3kZJ0q6UEWrmf9E3z8YlzKWfitMPV6xNFRUVysvL05w5c5zGY2NjlZub69I+8vPzlZubq6effrrW8wEAGo4zS9NvfvMbXXHFFcrNzVWXLl102223ubyfiz03rVq1Snv37tVrr73m0jmpvLxc5eXljtdlZWUuZwQA1D8ularTD1esTSUlJaqsrFRoaKjTeGhoqIqKis677RVXXKGffvpJJ0+e1Pz58zVt2rRzrlvXJ64T+w+q6tDPXj0GLk0+rVuoyRWhF14RwAX169dP/fr1c3u7izk3ffPNN5ozZ462bt0qPz/XfoOdmpqqBQsWuJ0PAFA/XfT8ZV5ennbv3i2LxaKePXuqT58+F7WfMy8rlCTDMKqNnW3r1q365ZdftG3bNs2ZM0ddunTR3XffXeO6dXniOrH/oAr7TZBRXlEnx8OlxWL1V9i2NyhWgIvWr1/v8rruzFZJrp+bKisrNWHCBC1YsEBXXXWVy/tPTk5WUlKS43VZWZnCwsLcyggAqD/cLlXFxcW666679NFHH6lFixYyDEOlpaUaMmSI/vd//1dt2rRxaT/BwcHy9fWt9pu/4uLiar8hPFtERIQk6eqrr9bBgwc1f/78c5aqujxxVR36mUKFi2aUV5ya5aRUAS5x9dJ0i8WiyspKl9Z199x05MgRbd++Xfn5+Zo+fbokqaqqSoZhyM/PT5s2bdLNN99cbTur1er2DTQAAPWX23f/e/jhh1VWVqZ//OMfOnz4sP71r3/pq6++UllZmVvPAfH391dUVJRsNpvTuM1mU//+/V3ej2EYTpf3nc1qtSowMNBpAQA0fFVVVS4trhYqyf1zU2BgoL788kvt3LnTsSQkJKhbt27auXOnbrjhBo8/JwCg/nN7pmrDhg16//331aNHD8dYz5499corryg2NtatfSUlJWnixImKjo5WTEyMli1bpoKCAiUkJEg6Nct04MABrV69WpL0yiuvqGPHjurevbukU8+tevHFF/Xwww+7+zEAAKiRO+cmHx8fRUZGOm0fEhKigICAauMAgEuX26WqqqpKTZo0qTbepEkTVVVVubWvuLg4HTp0SCkpKbLb7YqMjFROTo7Cw8MlSXa73em5IFVVVUpOTta+ffvk5+enzp0767nnntMDDzzg7scAAFxCUlJSzvv+vHnzXN6Xu+cmAABcek7VmcaOHauff/5Za9asUfv27SVJBw4c0D333KOWLVtq3bp1XglaW7z5LJDyz/do/7Bz34kQuJAr3l8ua+9u5obgOVXwlAnPqTr7ZkknTpxw+gWcO89QNAPPqQLqL55TBVe4/VOxePFijR07Vp06dVJYWJgsFosKCgp09dVX67XXXvNGRgAAzis/P7/aWFlZmaZMmaLbb7/dhEQAgMbE7VIVFhamHTt2yGaz6Z///KcMw1DPnj01bNgwb+QDAOCiBAYGKiUlRbfeeqsmTpxodhwAwCXMrVJ18uRJBQQEaOfOnRo+fLiGDx/urVwAAHjs559/VmlpqdkxAACXOLdKlZ+fn8LDw926PS0AAN728ssvO702DEN2u12vvvqqRo4caVIqAEBj4fblf08++aSSk5P12muvqVWrVt7IBACAWxYuXOj02sfHR23atNHkyZOVnJxsUioAQGPhdql6+eWX9e2336p9+/YKDw/XZZdd5vR+fb/DEgDg0rNv3z6zIwAAGjG3S9XYsWNlsVi8kQUAAAAAGhy3S9X8+fO9EAMAgIv366+/6g9/+IM+/PBDFRcXV3sYPVdRAAC8yeVSdezYMT366KN65513dOLECQ0bNkwvv/yygoODvZkPAIALuu+++2Sz2fSb3/xG119/PVdUAADqlMul6qmnnlJWVpbuueceBQQEaM2aNXrwwQf15ptvejMfAAAX9N577yknJ0cDBgwwOwoAoBFyuVStXbtWK1as0F133SVJuvfeezVgwABVVlbK19fXawEBALiQDh06qHnz5mbHAAA0Uj6urlhYWKiBAwc6Xl9//fXy8/PTjz/+6JVgAAC46qWXXtLjjz+uH374wewoAIBGyOWZqsrKSvn7+ztv7OenkydP1nooAADcER0drV9//VVXXnmlmjVrpiZNmji9f/jwYZOSAQAaA5dLlWEYmjJliqxWq2Ps119/VUJCgtOzqtauXVu7CQEAuIC7775bBw4c0LPPPqvQ0FBuVAEAqFMul6rJkydXG7v33ntrNQwAABcjNzdXn376qXr37m12FABAI+RyqVq1apU3cwAAcNG6d++u48ePmx0DANBIuXyjCgAA6qvnnntOjzzyiD766CMdOnRIZWVlTgsAAN7k8kwVAAD11ciRIyVJQ4cOdRo3DEMWi0WVlZVmxAIANBKUKgBAg/fhhx+aHQEA0IhRqgAADd7gwYPNjgAAaMQoVQCABm/Lli3nfX/QoEF1lAQA0BhRqgAADd5NN91UbezMZ1XxnSoAgDdx9z8AQIP3r3/9y2kpLi7Whg0b1LdvX23atMnseACASxwzVQCABi8oKKja2PDhw2W1WjVr1izl5eWZkAoA0FgwUwUAuGS1adNGe/bsMTsGAOASx0wVAKDB++KLL5xeG4Yhu92u5557Tr179zYpFQCgsaBUAQAavGuvvVYWi0WGYTiN9+vXTytXrjQpFXBhhmHo+AlupFKfHavg7wcXRqkCADR4+/btc3rt4+OjNm3aKCAgwKREwIUZhqHfLPlUeT/8y+woADxEqQIANHjh4eFmRwDcdvxEJYWqAYkOb6mmTXzNjoF6ilIFAGiwPvjgA02fPl3btm1TYGCg03ulpaXq37+/lixZooEDB5qUEHDN9ieHqZk//8NenzVt4uv0/DvgTJQqAECDlZ6ert/+9rfVCpV06jbrDzzwgNLS0ihVqPea+fuqmT//WwY0VNxSHQDQYH3++ecaOXLkOd+PjY3lGVUAAK+jVAEAGqyDBw+qSZMm53zfz89PP/30Ux0mAgA0RpQqAECD1aFDB3355ZfnfP+LL75Qu3bt6jARAKAxolQBABqs0aNHa968efr111+rvXf8+HE99dRTuvXWW01IBgBoTPhGJACgwXryySe1du1aXXXVVZo+fbq6desmi8Wi3bt365VXXlFlZaXmzp1rdkwAwCWOUgUAaLBCQ0OVm5urBx98UMnJyTIMQ5JksVg0YsQIZWRkKDQ01OSUAIBLHaUKANCghYeHKycnR//617/07bffyjAMde3aVS1btjQ7GgCgkaBUAQAuCS1btlTfvn3NjgEAaIS4UQUAAAAAeIBSBQAAAAAeoFQBAAAAgAdML1UZGRmKiIhQQECAoqKitHXr1nOuu3btWg0fPlxt2rRRYGCgYmJitHHjxjpMCwAAAADOTC1V2dnZmjlzpubOnav8/HwNHDhQo0aNUkFBQY3rb9myRcOHD1dOTo7y8vI0ZMgQjRkzRvn5+XWcHAAAAABOMbVUpaWlKT4+XtOmTVOPHj2Unp6usLAwZWZm1rh+enq6HnvsMfXt21ddu3bVs88+q65du+rPf/5zHScHAAAAgFNMK1UVFRXKy8tTbGys03hsbKxyc3Nd2kdVVZWOHDmiVq1anXOd8vJylZWVOS0AAAAAUFtMK1UlJSWqrKys9qT70NBQFRUVubSPl156SUePHtX48ePPuU5qaqqCgoIcS1hYmEe5AQAAAOBMpt+owmKxOL02DKPaWE3WrFmj+fPnKzs7WyEhIedcLzk5WaWlpY6lsLDQ48wAAAAAcJqfWQcODg6Wr69vtVmp4uLiarNXZ8vOzlZ8fLzefPNNDRs27LzrWq1WWa1Wj/MCAAAAQE1Mm6ny9/dXVFSUbDab07jNZlP//v3Pud2aNWs0ZcoUvfHGG7rlllu8HRMAAAAAzsu0mSpJSkpK0sSJExUdHa2YmBgtW7ZMBQUFSkhIkHTq0r0DBw5o9erVkk4VqkmTJmnRokXq16+fY5aradOmCgoKMu1zAAAAAGi8TC1VcXFxOnTokFJSUmS32xUZGamcnByFh4dLkux2u9Mzq5YuXaqTJ0/qoYce0kMPPeQYnzx5srKysuo6PgAAAACYW6okKTExUYmJiTW+d3ZR+uijj7wfCAAAAADcYPrd/wAAAACgIaNUAQAAAIAHKFUAAAAA4AFKFQAAAAB4gFIFAAAAAB6gVAEAAACAByhVAACcJSMjQxEREQoICFBUVJS2bt16znXXrl2r4cOHq02bNgoMDFRMTIw2btxYh2kBAGajVAEAcIbs7GzNnDlTc+fOVX5+vgYOHKhRo0Y5PYz+TFu2bNHw4cOVk5OjvLw8DRkyRGPGjFF+fn4dJwcAmIVSBQDAGdLS0hQfH69p06apR48eSk9PV1hYmDIzM2tcPz09XY899pj69u2rrl276tlnn1XXrl315z//uY6TAwDMQqkCAODfKioqlJeXp9jYWKfx2NhY5ebmurSPqqoqHTlyRK1atTrnOuXl5SorK3NaAAANF6UKAIB/KykpUWVlpUJDQ53GQ0NDVVRU5NI+XnrpJR09elTjx48/5zqpqakKCgpyLGFhYR7lBgCYi1IFAMBZLBaL02vDMKqN1WTNmjWaP3++srOzFRIScs71kpOTVVpa6lgKCws9zgwAMI+f2QEAAKgvgoOD5evrW21Wqri4uNrs1dmys7MVHx+vN998U8OGDTvvularVVar1eO8AID6gZkqAAD+zd/fX1FRUbLZbE7jNptN/fv3P+d2a9as0ZQpU/TGG2/olltu8XZMAEA9w0wVAABnSEpK0sSJExUdHa2YmBgtW7ZMBQUFSkhIkHTq0r0DBw5o9erVkk4VqkmTJmnRokXq16+fY5aradOmCgoKMu1zAADqDqUKAIAzxMXF6dChQ0pJSZHdbldkZKRycnIUHh4uSbLb7U7PrFq6dKlOnjyphx56SA899JBjfPLkycrKyqrr+AAAE1CqAAA4S2JiohITE2t87+yi9NFHH3k/EACgXuM7VQAAAADgAUoVAAAAAHiAUgUAAAAAHqBUAQAAAIAHKFUAAAAA4AFKFQAAAAB4gFIFAAAAAB6gVAEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAcoVQAAAADgAUoVAAAAAHiAUgUAAAAAHqBUAQAAAIAHKFUAAAAA4AFKFQAAAAB4gFIFAAAAAB6gVAEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAdML1UZGRmKiIhQQECAoqKitHXr1nOua7fbNWHCBHXr1k0+Pj6aOXNm3QUFAAAAgBqYWqqys7M1c+ZMzZ07V/n5+Ro4cKBGjRqlgoKCGtcvLy9XmzZtNHfuXPXu3buO0wIAAABAdaaWqrS0NMXHx2vatGnq0aOH0tPTFRYWpszMzBrX79SpkxYtWqRJkyYpKCiojtMCAAAAQHWmlaqKigrl5eUpNjbWaTw2Nla5ubm1dpzy8nKVlZU5LQAAAABQW0wrVSUlJaqsrFRoaKjTeGhoqIqKimrtOKmpqQoKCnIsYWFhtbZvAAAAADD9RhUWi8XptWEY1cY8kZycrNLSUsdSWFhYa/sGAAAAAD+zDhwcHCxfX99qs1LFxcXVZq88YbVaZbVaa21/AAAAAHAm02aq/P39FRUVJZvN5jRus9nUv39/k1IBAAAAgHtMm6mSpKSkJE2cOFHR0dGKiYnRsmXLVFBQoISEBEmnLt07cOCAVq9e7dhm586dkqRffvlFP/30k3bu3Cl/f3/17NnTjI8AAAAAoJEztVTFxcXp0KFDSklJkd1uV2RkpHJychQeHi7p1MN+z35mVZ8+fRx/zsvL0xtvvKHw8HB9//33dRkdAAAAACSZXKokKTExUYmJiTW+l5WVVW3MMAwvJwIAAAAA15l+9z8AAAAAaMgoVQAAAADgAUoVAAAAAHiAUgUAAAAAHqBUAQAAAIAHKFUAAAAA4AFKFQAAAAB4gFIFAAAAAB6gVAEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAcoVQAAAADgAUoVAAAAAHiAUgUAAAAAHqBUAQAAAIAHKFUAAAAA4AFKFQAAAAB4gFIFAAAAAB6gVAEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAHCWjIwMRUREKCAgQFFRUdq6det519+8ebOioqIUEBCgK6+8UkuWLKmjpACA+oBSBQDAGbKzszVz5kzNnTtX+fn5GjhwoEaNGqWCgoIa19+3b59Gjx6tgQMHKj8/X0888YRmzJiht99+u46TAwDM4md2AAAA6pO0tDTFx8dr2rRpkqT09HRt3LhRmZmZSk1Nrbb+kiVL1LFjR6Wnp0uSevTooe3bt+vFF1/UnXfeWZfRqzEMQ8dPVJqaAed2rIK/G+BSQakCAODfKioqlJeXpzlz5jiNx8bGKjc3t8ZtPv30U8XGxjqNjRgxQitWrNCJEyfUpEmTatuUl5ervLzc8bqsrKwW0ld3/ESles7b6JV9AwD+g8v/AAD4t5KSElVWVio0NNRpPDQ0VEVFRTVuU1RUVOP6J0+eVElJSY3bpKamKigoyLGEhYXVzgdAgxQd3lJNm/iaHQOAB5ipAgDgLBaLxem1YRjVxi60fk3jpyUnJyspKclp/YqKCjVv3vxiI9eoaRNf7UoZUav7RO1r2sT3vD9fAOo/ShUAAP8WHBwsX1/farNSxcXF1WajTmvbtm2N6/v5+al169Y1bmO1WmW1Wmsn9HlYLBY18+dUDwDexuV/AAD8m7+/v6KiomSz2ZzGbTab+vfvX+M2MTEx1dbftGmToqOja/w+FQDg0kOpAgDgDElJSVq+fLlWrlyp3bt3a9asWSooKFBCQoKkU5fuTZo0ybF+QkKCfvjhByUlJWn37t1auXKlVqxYodmzZ5v1EQAAdYxrAgAAOENcXJwOHTqklJQU2e12RUZGKicnR+Hh4ZIku93u9MyqiIgI5eTkaNasWXrllVfUvn17vfzyy6bfTh0AUHcsxulv0zYSZWVlCgoKUmlpqQIDA2t13+Wf79H+YdNqdZ9oXK54f7msvbuZG+LwDmlDlLkZ0LCNzJNaXWd2CgAA6gyX/wEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAcoVQAAAADgAdNLVUZGhiIiIhQQEKCoqCht3br1vOtv3rxZUVFRCggI0JVXXqklS5bUUVIAAAAAqM7UUpWdna2ZM2dq7ty5ys/P18CBAzVq1Cinhyqead++fRo9erQGDhyo/Px8PfHEE5oxY4befvvtOk4OAAAAAKeYWqrS0tIUHx+vadOmqUePHkpPT1dYWJgyMzNrXH/JkiXq2LGj0tPT1aNHD02bNk333XefXnzxxTpODgAAAACnmFaqKioqlJeXp9jYWKfx2NhY5ebm1rjNp59+Wm39ESNGaPv27Tpx4oTXsgIAAADAufiZdeCSkhJVVlYqNDTUaTw0NFRFRUU1blNUVFTj+idPnlRJSYnatWtXbZvy8nKVl5c7XpeVldVCegAAAAA4xbRSdZrFYnF6bRhGtbELrV/T+GmpqalasGCBhyldY+3dTZ1/Ov+NNoB6r9V10gTD7BQAAAANhmmX/wUHB8vX17farFRxcXG12ajT2rZtW+P6fn5+at26dY3bJCcnq7S01LH8/PPPKi4uVvPmzWvngwAAAABo1EwrVf7+/oqKipLNZnMat9ls6t+/f43bxMTEVFt/06ZNio6OVpMmTWrcxmq1KjAw0LEEBQWpTZs2550NAwAAAABXmXr3v6SkJC1fvlwrV67U7t27NWvWLBUUFCghIUHSqVmmSZMmOdZPSEjQDz/8oKSkJO3evVsrV67UihUrNHv2bLM+AgAAAIBGztTvVMXFxenQoUNKSUmR3W5XZGSkcnJyFB4eLkmy2+1Oz6yKiIhQTk6OZs2apVdeeUXt27fXyy+/rDvvvNOsjwAAAACgkbMYp+/0AAAAAABwm+l3/0PjYRiGjhw5YnYMwGPNmzfne5loMPi3F0BjVxfnbUoV6kxJSYlCQkLMjgF4rLi4WG3atDE7BuAS/u0F0NjVxXmbUoU64+/vL0kqLCxUYGCgyWkA95WVlSksLMzxsww0BPzb23Cc/jeGv6v6j7+rhqEuz9uUKtSZ09Oup29vDzRUXPqHhoR/exse/q4aDv6uGoa6OG+bekt1AAAAAGjoKFUAAAAA4AFKFeqM1WrVU089JavVanYU4KLwM4yGiJ/bhoO/q4aDv6uGoS7/nnhOFQAAAAB4gJkqAAAAAPAApQoAAAAAPECpAgAAAAAPUKoAAAAAwAOUKtSJjIwMRUREKCAgQFFRUdq6davZkQC3bNmyRWPGjFH79u1lsVj0zjvvmB0JcNszzzyj/v37q1mzZmrRooXZcXAGzpMNA+eChiE1NVV9+/ZV8+bNFRISonHjxmnPnj1ePSalCl6XnZ2tmTNnau7cucrPz9fAgQM1atQoFRQUmB0NcNnRo0fVu3dvLV682OwowEWrqKjQf/3Xf+nBBx80OwrOwHmy4eBc0DBs3rxZDz30kLZt2yabzaaTJ08qNjZWR48e9doxuaU6vO6GG27Qddddp8zMTMdYjx49NG7cOKWmppqYDLg4FotF69at07hx48yOAlyUrKwszZw5Uz///LPZUSDOkw0V54KG46efflJISIg2b96sQYMGeeUYzFTBqyoqKpSXl6fY2Fin8djYWOXm5pqUCgCA+oHzJOB9paWlkqRWrVp57RiUKnhVSUmJKisrFRoa6jQeGhqqoqIik1IBAFA/cJ4EvMswDCUlJenGG29UZGSk145DqUKdsFgsTq8Nw6g2BgBw3/z582WxWM67bN++3eyYuADOk4B3TJ8+XV988YXWrFnj1eP4eXXvaPSCg4Pl6+tb7bdtxcXF1X4rBwBw3/Tp03XXXXedd51OnTrVTRi4jfMk4D0PP/yw1q9fry1btuiKK67w6rEoVfAqf39/RUVFyWaz6fbbb3eM22w2jR071sRkAHBpCA4OVnBwsNkxcJE4TwK1zzAMPfzww1q3bp0++ugjRUREeP2YlCp4XVJSkiZOnKjo6GjFxMRo2bJlKigoUEJCgtnRAJf98ssv+vbbbx2v9+3bp507d6pVq1bq2LGjickA1xUUFOjw4cMqKChQZWWldu7cKUnq0qWLLr/8cnPDNWKcJxsOzgUNw0MPPaQ33nhDf/rTn9S8eXPHTHBQUJCaNm3qlWNyS3XUiYyMDL3wwguy2+2KjIzUwoULvXZLS8AbPvroIw0ZMqTa+OTJk5WVlVX3gYCLMGXKFP3P//xPtfEPP/xQN910U90HggPnyYaBc0HDcK7vI65atUpTpkzxzjEpVQAAAABw8bj7HwAAAAB4gFIFAAAAAB6gVAEAAACAByhVAAAAAOABShUAAAAAeIBSBQAAAAAeoFQBAAAAgAcoVQAAAADgAUoV4EWFhYWKj49X+/bt5e/vr/DwcP33f/+3Dh065PI+vv/+e1ksFu3cudN7QQEAjQLnJcA7KFWAl3z33XeKjo7W119/rTVr1ujbb7/VkiVL9Ne//lUxMTE6fPiw2REBAI0I5yXAeyhVgJc89NBD8vf316ZNmzR48GB17NhRo0aN0vvvv68DBw5o7ty5kiSLxaJ33nnHadsWLVooKytLkhQRESFJ6tOnjywWi2666SbHeitXrlSvXr1ktVrVrl07TZ8+3fFeQUGBxo4dq8svv1yBgYEaP368Dh486Hh//vz5uvbaa7Vy5Up17NhRl19+uR588EFVVlbqhRdeUNu2bRUSEqJnnnnGKVtpaanuv/9+hYSEKDAwUDfffLM+//zzWvwvBwDwBs5LgPdQqgAvOHz4sDZu3KjExEQ1bdrU6b22bdvqnnvuUXZ2tgzDuOC+PvvsM0nS+++/L7vdrrVr10qSMjMz9dBDD+n+++/Xl19+qfXr16tLly6SJMMwNG7cOB0+fFibN2+WzWbT3r17FRcX57TvvXv36i9/+Ys2bNigNWvWaOXKlbrlllu0f/9+bd68Wc8//7yefPJJbdu2zbHfW265RUVFRcrJyVFeXp6uu+46DR06lN9wAkA9xnkJ8DIDQK3btm2bIclYt25dje+npaUZkoyDBw/WuF5QUJCxatUqwzAMY9++fYYkIz8/32md9u3bG3Pnzq1x/5s2bTJ8fX2NgoICx9g//vEPQ5Lx2WefGYZhGE899ZTRrFkzo6yszLHOiBEjjE6dOhmVlZWOsW7duhmpqamGYRjGX//6VyMwMND49ddfnY7XuXNnY+nSpef87wEAMBfnJcC7/Mwqc0BjZvz7N4EWi+Witi8uLtaPP/6ooUOH1vj+7t27FRYWprCwMMdYz5491aJFC+3evVt9+/aVJHXq1EnNmzd3rBMaGipfX1/5+Pg4jRUXF0uS8vLy9Msvv6h169ZOxzt+/Lj27t17UZ8FAGA+zkuAZyhVgBd06dJFFotFu3bt0rhx46q9/89//lMtW7ZUcHCwLBZLtcstTpw4cd79n33pxtkMw6jxxHj2eJMmTZzet1gsNY5VVVVJkqqqqtSuXTt99NFH1fbdokWL82YCAJiH8xLgXXynCvCC1q1ba/jw4crIyNDx48ed3isqKtLrr7+uuLg4WSwWtWnTRna73fH+N998o2PHjjle+/v7S5IqKysdY82bN1enTp3017/+tcbj9+zZUwUFBSosLHSM7dq1S6WlperRo8dFf67rrrtORUVF8vPzU5cuXZyW4ODgi94vAMC7OC8B3kWpArxk8eLFKi8v14gRI7RlyxYVFhZqw4YNGj58uDp06OC4e9HNN9+sxYsXa8eOHdq+fbsSEhKcfisXEhKipk2basOGDTp48KBKS0slnbpL0ksvvaSXX35Z33zzjXbs2KE//OEPkqRhw4bpmmuu0T333KMdO3bos88+06RJkzR48GBFR0df9GcaNmyYYmJiNG7cOG3cuFHff/+9cnNz9eSTT2r79u0e/NcCAHgb5yXAeyhVgJd07dpV27dvV+fOnRUXF6fOnTvr/vvv15AhQ/Tpp5+qVatWkqSXXnpJYWFhGjRokCZMmKDZs2erWbNmjv34+fnp5Zdf1tKlS9W+fXuNHTtWkjR58mSlp6crIyNDvXr10q233qpvvvlG0n9uh9uyZUsNGjRIw4YN05VXXqns7GyPPpPFYlFOTo4GDRqk++67T1dddZXuuusuff/99woNDfVo3wAA7+K8BHiPxTj7olkAAAAAgMuYqQIAAAAAD1CqAAAAAMADlCoAAAAA8AClCgAAAAA8QKkCAAAAAA9QqgAAAADAA5QqAAAAAPAApQoAAAAAPECpAgAAAAAPUKoAAAAAwAOUKgAAAADwAKUKAAAAADzw/wFvCQpj0G3ZUwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for using Bernoulli random variables\n",
    "from scipy.stats import bernoulli\n",
    "\n",
    "theta = 0.7  # probability of success - change this value to see the effect\n",
    "\n",
    "# Create a Bernoulli random variable\n",
    "ber_rv = bernoulli(p = theta)\n",
    "\n",
    "# Make two plots to show the PMF and the CDF:\n",
    "# The first one is a bar chart of the probability mass function, \n",
    "fig, ax = plt.subplots(1,2, figsize=(10, 5))\n",
    "bplot = ax[0].bar([0, 1], ber_rv.pmf([0, 1]))\n",
    "ax[0].set_xticks([0, 1])\n",
    "ax[0].set_xlabel(\"Outcome\")\n",
    "ax[0].set_ylabel(\"Probability Mass\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "for i, bar in enumerate(bplot):\n",
    "  bar.set_color(\"crimson\") if i == 0 else bar.set_color(\"orange\")\n",
    "\n",
    "# The second one is a stair plot of the cumulative distribution function\n",
    "x = np.linspace(-1, 2, 100)\n",
    "ax[1].step(x, ber_rv.cdf(x))\n",
    "ax[1].set_xticks([-1, 0, 1, 2])\n",
    "ax[1].set_xlabel(\"Outcome\")\n",
    "ax[1].set_ylabel(\"Cumulative Probability\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binomial Distribution\n",
    "![alt text](figures/image-5.png)\n",
    "\n",
    "Let $S = X_1 + X_2 + \\ldots + X_n$ where $n$ is a fixed integer and $X_1,\\ldots, X_n$ are __independent__ random variables that are distributed according to the Bernoulli distribution with the __same__ parameter $p$. Then $S$ will be a discrete random variable with a __Binomial Distribution__ with parameters $n$ and $p$, and we write $S\\sim \\mathrm{Binomial}(n;p)$. It has the probability mass function\n",
    "$$\n",
    "\\mathrm{Pr}(S = y) = \\mathrm{Binomial}(n \\vert y, p) := \\left(\\begin{array}{c} n\\\\y \\end{array} \\right) p^y(1-p)^{1-y}.\n",
    "$$\n",
    "\n",
    "Here\n",
    "$$\n",
    "\\left(\\begin{array}{c} n\\\\y \\end{array} \\right)  := \\frac{\n",
    "    n!\n",
    "}{\n",
    "    (n-y)!y!\n",
    "}\n",
    "$$\n",
    "is pronounced \"_n choose y_\" and is the total number of ways to take $y$ objects without replacement from a set of $n$ objects.\n",
    "\n",
    "The binomial distribution models the number of heads you get when flipping a coin $n$ times, where the probability of getting a head in each flip is $p$. It could also model the probability distribution for how many cells will have a given phenotype when you measure $n$ total cells and the phenotype probability is $p$.\n",
    "\n",
    "* What is the mean of a Binomial random variable?\n",
    "* What are the variance and standard deviation?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for using Binomial random variables\n",
    "from scipy.stats import binom\n",
    "\n",
    "n = 10  # number of trials - change this value to see the effect\n",
    "p = 0.7  # probability of success - change this value to see the effect\n",
    "\n",
    "# Create a Binomial random variable\n",
    "bin_rv = binom(n = n, p = p)\n",
    "\n",
    "# Make two plots to show the PMF and the CDF:\n",
    "# The first one is a bar chart of the probability mass function,\n",
    "fig, ax = plt.subplots(1,2, figsize=(10, 5))\n",
    "bplot = ax[0].bar(range(n+1), bin_rv.pmf(range(n+1)))\n",
    "ax[0].set_xticks(range(n+1))\n",
    "ax[0].set_xlabel(\"Outcome\")\n",
    "ax[0].set_ylabel(\"Probability Mass\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "for i, bar in enumerate(bplot):\n",
    "  bar.set_color(\"crimson\")\n",
    "\n",
    "# The second one is a stair plot of the cumulative distribution function\n",
    "x = np.linspace(-1, n+1, 100)\n",
    "ax[1].step(x, bin_rv.cdf(x))\n",
    "ax[1].set_xticks(range(n+1))\n",
    "ax[1].set_xlabel(\"Outcome\")\n",
    "ax[1].set_ylabel(\"Cumulative Probability\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson Distribution\n",
    "![alt text](figures/image-7.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for using Poisson random variables\n",
    "from scipy.stats import poisson\n",
    "\n",
    "lambda_ = 5  # rate of events - change this value to see the effect\n",
    "\n",
    "# Create a Poisson random variable\n",
    "poi_rv = poisson(mu = lambda_)\n",
    "# Make two plots to show the PMF and the CDF:\n",
    "# The first one is a bar chart of the probability mass function,\n",
    "fig, ax = plt.subplots(1,2, figsize=(10, 5))\n",
    "bplot = ax[0].bar(range(20), poi_rv.pmf(range(20)))\n",
    "\n",
    "ax[0].set_xlabel(\"Outcome\")\n",
    "ax[0].set_ylabel(\"Probability Mass\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "for i, bar in enumerate(bplot):\n",
    "  bar.set_color(\"crimson\")\n",
    "xticks = ax[0].get_xticks()\n",
    "\n",
    "# The second one is a stair plot of the cumulative distribution function\n",
    "x = np.arange(-1, 3*lambda_+1)\n",
    "ax[1].step(x+1, poi_rv.cdf(x))\n",
    "ax[1].set_xticks(xticks)\n",
    "ax[1].set_xlabel(\"Outcome\")\n",
    "ax[1].set_ylabel(\"Cumulative Probability\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Geometric Distribution\n",
    "![alt text](figures/image-9.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for using Geometric random variables\n",
    "from scipy.stats import geom\n",
    "\n",
    "p = 0.4  # probability of success - change this value to see the effect\n",
    "\n",
    "# Create a Geometric random variable\n",
    "geo_rv = geom(p = p)\n",
    "\n",
    "# Make two plots to show the PMF and the CDF:\n",
    "# The first one is a bar chart of the probability mass function,\n",
    "fig, ax = plt.subplots(1,2, figsize=(10, 5))\n",
    "bplot = ax[0].bar(range(0, int(5/p)), geo_rv.pmf(range(0, int(5/p))))\n",
    "# ax[0].set_xticks(range(1, 11))\n",
    "ax[0].set_xlabel(\"Outcome\")\n",
    "ax[0].set_ylabel(\"Probability Mass\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "for i, bar in enumerate(bplot):\n",
    "  bar.set_color(\"crimson\")\n",
    "xticks = ax[0].get_xticks()\n",
    "\n",
    "# The second one is a stair plot of the cumulative distribution function\n",
    "x = np.linspace(0, int(5/p), 100)\n",
    "ax[1].step(x, geo_rv.cdf(x))\n",
    "ax[1].set_xticks(xticks)\n",
    "ax[1].set_xlabel(\"Outcome\")\n",
    "ax[1].set_ylabel(\"Cumulative Probability\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common Continuous Distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uniform Distribution\n",
    "![alt text](figures/image-10.png)\n",
    "\n",
    "A continuous random variable $X$ is said to have a uniform distribution with parameters $a$ and $b$ (with $a< b$), denoted by $X\\sim U(a,b)$, if its probability density function is given by\n",
    "$$\n",
    "f_X(x) = \\frac{\n",
    "    1\n",
    "}{\n",
    "    b-a\n",
    "}\\mathbb{1}(a\\leq x \\leq b)\n",
    "$$\n",
    "where $\\mathbb{1}(A)=0$ if statement $A$ is false and $1$ otherwise. This distribution will be essential in implementing the stochastic simulation algorithm and Metropolis-Hastings algorithm later in the course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for using Uniform random variables\n",
    "from scipy.stats import uniform\n",
    "\n",
    "a = 0  # lower bound - change this value to see the effect\n",
    "b = 10  # upper bound - change this value to see the effect\n",
    "\n",
    "# Create a Uniform random variable\n",
    "uni_rv = uniform(loc = a, scale = b - a)\n",
    "\n",
    "# Make two plots to show the PDF and the CDF:\n",
    "# The first one is a line plot of the probability density function,\n",
    "fig, ax = plt.subplots(1,2, figsize=(10, 5))\n",
    "x = np.linspace(a-1, b+1, 100)\n",
    "ax[0].plot(x, uni_rv.pdf(x))\n",
    "ax[0].set_xlabel(\"Outcome\")\n",
    "ax[0].set_ylabel(\"Probability Density\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "xticks = ax[0].get_xticks()\n",
    "\n",
    "# The second one is a line plot of the cumulative distribution function\n",
    "x = np.linspace(a-1, b+1, 100)\n",
    "ax[1].plot(x, uni_rv.cdf(x))\n",
    "ax[1].set_xticks(xticks)\n",
    "ax[1].set_xlabel(\"Outcome\")\n",
    "ax[1].set_ylabel(\"Cumulative Probability\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exponential Distribution\n",
    "![alt text](figures/image-11.png)\n",
    "The exponential distribution will be very important later in the class when we explore the waiting times between stochastic events that describe gene regulatory changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for using Exponential random variables\n",
    "from scipy.stats import expon\n",
    "\n",
    "lambda_ = 0.25  # rate of events - change this value to see the effect\n",
    "\n",
    "# Create an Exponential random variable\n",
    "exp_rv = expon(scale = 1/lambda_)\n",
    "# Make two plots to show the PDF and the CDF:\n",
    "# The first one is a line plot of the probability density function,\n",
    "fig, ax = plt.subplots(1,2, figsize=(10, 5))\n",
    "x = np.linspace(-1, int(5/lambda_+1), 100)\n",
    "ax[0].plot(x, exp_rv.pdf(x))\n",
    "ax[0].set_xlabel(\"Outcome\")\n",
    "ax[0].set_ylabel(\"Probability Density\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "xticks = ax[0].get_xticks()\n",
    "\n",
    "# The second one is a line plot of the cumulative distribution function\n",
    "x = np.linspace(-1, int(5/lambda_+1), 100)\n",
    "ax[1].plot(x, exp_rv.cdf(x))\n",
    "ax[1].set_xticks(xticks)\n",
    "ax[1].set_xlabel(\"Outcome\")\n",
    "ax[1].set_ylabel(\"Cumulative Probability\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Distribution\n",
    "\n",
    "A continuous random variable $X$ has a normal distribution with parameters $\\mu$ and $\\sigma^2$, written $X\\sim N(\\mu, \\sigma^2)$ if it has the probability density function\n",
    "$$\n",
    "f_X(x) = \\frac{\n",
    "    1\n",
    "}{\n",
    "    \\sqrt{2\\pi\\sigma^2}\n",
    "}\\exp\\left(-\\frac{\n",
    "    1\n",
    "}{\n",
    "    2\n",
    "}\\left(\\frac{\n",
    "    x-\\mu\n",
    "}{\n",
    "    \\sigma\n",
    "}\\right)^2\\right).\n",
    "$$\n",
    "\n",
    "\n",
    "An important special case of the normal distribution is the standard normal distribution $N(0,1)$, which has parameters $\\mu=0$ and $\\sigma^2=1$.\n",
    "\n",
    "The normal distribution has a very important role in statistics. One reason is that for large sample sizes, many random quantitites tend to be approximately normally distributed. Specifically, the Central Limit Theorem (CLT) states that for random variables $X_1,\\ldots, X_n$ that are independent and identically distributed with the same mean $\\mu$ and variance $\\sigma^2$, and if\n",
    "$$\n",
    "\\overline{X}:=\\frac{\n",
    "    X_1+\\ldots+X_n\n",
    "}{\n",
    "    n\n",
    "}$$\n",
    "is the sample mean, then the distribution of the random variable $$Z:=\\sqrt{n}\\left(\\frac{\n",
    "    \\overline{X} - \\mu\n",
    "}{\n",
    "    \\sigma\n",
    "}\\right)$$\n",
    "is well-approximated by a standard normal distribution $N(0,1)$ when $n$ is large."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for using Normal random variables\n",
    "from scipy.stats import norm\n",
    "\n",
    "mu = 0  # mean - change this value to see the effect\n",
    "sigma = 1  # standard deviation - change this value to see the effect\n",
    "\n",
    "# Create a Normal random variable\n",
    "norm_rv = norm(loc = mu, scale = sigma)\n",
    "\n",
    "# Make two plots to show the PDF and the CDF:\n",
    "# The first one is a line plot of the probability density function,\n",
    "fig, ax = plt.subplots(1,2, figsize=(10, 5))\n",
    "x = np.linspace(-mu-4*sigma, mu+4*sigma, 100)\n",
    "ax[0].plot(x, norm_rv.pdf(x))\n",
    "ax[0].set_xlabel(\"Outcome\")\n",
    "ax[0].set_ylabel(\"Probability Density\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "xticks = ax[0].get_xticks()\n",
    "\n",
    "# The second one is a line plot of the cumulative distribution function\n",
    "ax[1].plot(x, norm_rv.cdf(x))\n",
    "ax[1].set_xticks(xticks)\n",
    "ax[1].set_xlabel(\"Outcome\")\n",
    "ax[1].set_ylabel(\"Cumulative Probability\")\n",
    "sns.despine(offset=5, trim=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling from distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling From Common Distributions using Numpy\n",
    "\n",
    "Numpy provides a very nice random sampling library that is widely used throughout scientific computing.\n",
    "\n",
    "```np.random.____```\n",
    "\n",
    "| Method    | Description  |\n",
    "| ----------- | ----------- |\n",
    "| rand | uniform random from 0 to 1|\n",
    "| randn | univariate normal from a mean of 0 and a variance of 1 |\n",
    "| randint| random integers from low to high|\n",
    "| choice | pick a uniform random value from an array |\n",
    "| shuffle | shuffles an array along the first axis|\n",
    "\n",
    "Additionally np.random can sample from a list of statistical distributions, here's a short list:\n",
    "\n",
    "| Distribution    |\n",
    "| ----------- |\n",
    "| [beta](https://en.wikipedia.org/wiki/Beta_distribution) |\n",
    "| [gamma](https://en.wikipedia.org/wiki/Gamma_distribution) |\n",
    "| [lognormal](https://en.wikipedia.org/wiki/Log-normal_distribution)|\n",
    "| [multivariate normal](https://en.wikipedia.org/wiki/Multivariate_normal_distribution) |\n",
    "| [poisson](https://en.wikipedia.org/wiki/Poisson_distribution) |\n",
    "| [uniform](https://en.wikipedia.org/wiki/Continuous_uniform_distribution) |  \n",
    "| [power](https://en.wikipedia.org/wiki/Power_law) |\n",
    "\n",
    "\n",
    "We can additionally set the rng state with np.random.seed(integer)\n",
    "\n",
    "| Method    | Description  |\n",
    "| ----------- | ----------- |\n",
    "| seed | set the seed of the RNG |\n",
    "| get_state | get the current state of the Mersenne twister |\n",
    "\n",
    "---\n",
    "\n",
    "```Reading: Kinder, Nelson Section 6.2```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13eb02f90>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generating some simple random data points and plotting them\n",
    "n = 96 #number of data points to sample\n",
    "\n",
    "randomNumberGenerator = 'randn' #e.g., \"rand\", \"randn\", \"randint\"\n",
    "examples_str = {'rand': rng.rand(2,n),\n",
    "            'randn': rng.randn(2,n),\n",
    "            'randint': rng.randint(0,1000,size = (2,n))}\n",
    "\n",
    "# Run the example string to generate the random numbers\n",
    "random_numbers = examples_str[randomNumberGenerator]\n",
    "\n",
    "# Plot the random numbers as 2D points\n",
    "plt.plot(random_numbers[0],random_numbers[1],'o' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/gs/29wgt2xj1jj873ytknj55rsr0000gp/T/ipykernel_61556/2832175815.py:12: RuntimeWarning: covariance is not symmetric positive-semidefinite.\n",
      "  random_numbers = rng.multivariate_normal(np.array([mean1,mean2]), cov, size=n).T\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13ed3ee50>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generating some multivariate Normal (Gaussian) data points and plotting them\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.random as rng\n",
    "\n",
    "n = 674     # Number of data points to sample\n",
    "mean1 = 33  # Mean of the first dimension\n",
    "mean2 = 12  # Mean of the second dimension\n",
    "cov = rng.randn(2,2)*3      # Covariance matrix\n",
    "cov[0,0] = 2; cov[1,1] = 2;\n",
    "\n",
    "# Generate the data\n",
    "random_numbers = rng.multivariate_normal(np.array([mean1,mean2]), cov, size=n).T\n",
    "\n",
    "# Plot the data\n",
    "plt.plot(random_numbers[0],random_numbers[1],'o' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[15.46945553  5.11917194  2.55192263  3.66165228  7.20027539  3.80232118\n",
      "  3.08861361  2.88713874  9.31118179  3.79531303  2.6981572   2.97398713\n",
      "  7.95505461  6.03114563  3.21365428  7.16674331  2.72677315  5.77281731\n",
      "  8.61520666  6.51370992  6.81253826  6.78815157  8.37559196  6.96612804\n",
      " 15.6171441   3.38243215  3.37041859  1.5481363  15.11655993  3.36666401\n",
      " 12.69678981  2.38432325  4.30845684  2.52097568 10.55976222  4.46693083\n",
      "  9.93067719  3.71830587  8.54710744  2.90128772  2.08379406 11.98266163\n",
      "  7.39005531  6.95678188  8.99653487 11.43843969  2.52081003  4.24445984\n",
      "  4.3557828   1.54822055  9.32594139  4.602177    3.25138768  6.13671781\n",
      "  3.85563867  1.76616061  6.78406582  8.93715236 19.31679362  6.42648692\n",
      "  7.28142763 17.16673362 17.2509729   8.39523163  9.80606533 11.38832326\n",
      "  9.08124363  7.34673076  3.32275969 11.19789648  4.46467618 12.99212716\n",
      "  6.25906468 11.22455971  4.33405983 10.93817235 11.15252574  2.88156646\n",
      "  5.03208483  8.5558539  14.53753514 12.02134675 17.31450585  9.87048744\n",
      "  3.65900758 11.92908927  4.38461677 18.61678275  3.55792913  1.42258492\n",
      " 12.10755302 20.70271216  4.38390598  1.67822725  6.65867468  4.1139503\n",
      " 20.75854536  4.54593749  7.18356921  1.10702382  1.81166314 11.76031773\n",
      " 13.93010502  3.49715325  4.23489156  4.07414584  8.05526058 10.8438724\n",
      "  7.68304933  4.37766115  6.89007592  3.82831398  6.84256295  4.57500217\n",
      "  4.12860976  8.09012487  6.01769927  3.54445907  3.55066227  3.10592881\n",
      " 11.63982933 21.45197377  7.4249152   4.46085265  6.84605664  5.32031951\n",
      "  6.06147237 14.5276209   1.98265638  1.38595257 18.9371381   6.66310244\n",
      " 14.92019246  5.04437347  4.42142026  7.02357223  9.74850433 22.29511741\n",
      "  6.96974339  3.59806353 11.60868164  5.97035039 14.0566556   7.02293597\n",
      "  2.78521268 10.65231026 24.6988111   2.92903508 11.71531409  6.77333894\n",
      " 11.42642001  3.83420773  5.53827317 17.76894516  2.71552588  1.54399482\n",
      "  8.49388364  2.7565387  14.01625425  5.59843995 15.61909494 15.20397691\n",
      "  7.7594302  10.73171918  4.49607718 10.55777415  3.93547143 25.82881018\n",
      "  5.02015338  8.65992965  4.20395718  1.65403289  5.07025663 12.00298271\n",
      " 11.52018104 11.821713    6.97177226  7.81587054  7.18042465 11.05818619\n",
      "  4.66782652 14.61718908  3.51107557 14.63721473 17.8478875   6.16584624\n",
      " 12.14767556  7.00837375 10.39023389  5.67777305 15.6699274   5.72533082\n",
      " 17.50785517 14.8759594  11.09796598  1.55920446  5.16918992  5.79824695\n",
      " 18.54389779  1.46281686  9.18181147  3.4439591  12.58241157  8.48137292\n",
      "  2.25075156  4.33488043  6.57540378 10.1973323   7.82289706  8.3730456\n",
      "  7.65442338 18.98053207  6.08877837 12.43941128  5.96376878  3.93799796\n",
      "  8.06299555  3.45716418 10.52800164  6.35556713 13.32349236 17.14797574\n",
      "  2.32130641 14.29132692  4.32480361  4.0112836   8.64180423  8.77814862\n",
      "  3.23526221  7.98392813  8.23887386  6.53871329 16.12580255  6.85203017\n",
      "  7.35776335  4.79854864  5.40174919 25.22585466 10.45640564 12.97051913\n",
      "  6.317597    3.9900681  16.57534438  3.78513463 24.66338576 14.15449195\n",
      "  1.32206136 17.27186853  7.36817759  5.01347025  1.34037781  2.59867901\n",
      "  5.1894925   5.80382023  9.10131375  8.84425376 12.14625396 12.0368248\n",
      "  7.30065014  9.35462948  3.65158839  4.31739068  7.63485967  9.50832771\n",
      "  6.50781284  4.42574952  7.40644256  2.70934652  4.57038626 11.74934722\n",
      " 11.26387982  3.46235025  8.78727901  1.29306935  3.13660469  4.52415388\n",
      "  3.13831816  4.72547989  2.31415845  6.50832112  4.28198396  6.80390638\n",
      "  5.77094002  3.15015449  1.53368661 14.89559876  4.03413575  2.48185916\n",
      "  9.3493968   4.74685102  2.63698136  3.3457169  40.95948688  9.38020866\n",
      "  6.22080444  4.76848621  4.4271782   2.13212636 15.99264987  3.73016024\n",
      "  7.45404301  6.1889496   6.12402024  4.75953602 14.64752125 12.98249501\n",
      "  2.62623541  6.71379776  5.30493614 16.4438718   9.00367891  5.09022031\n",
      " 14.96968781  9.49765714  3.35300787  9.17527393  4.6104752  17.74276343\n",
      "  9.4147276   4.65074373  2.51646333  7.07934501  4.76196711  5.81498502\n",
      "  3.05310879  5.12500558  3.0082961   3.34128411  2.96300063  6.52401928\n",
      "  8.89101581 13.10995608  7.4579416   2.58227866  7.42457761  7.27692555\n",
      " 12.39833225  2.58794806 19.1271023   7.32257286 12.15246671  0.76667145\n",
      "  3.70716249  9.54624762  9.16908691  6.00172949  4.61793606  1.81327562\n",
      "  4.90462031 13.18550639  2.12980463 17.68807902 11.68326263 23.83662117\n",
      "  7.42312435  9.10182658  9.30198267  1.88120327  5.40657998  2.43695781\n",
      "  7.50597147  5.52714615  5.73677308  9.59889866 22.1017045   8.84279016\n",
      "  5.48620134 10.30406219 12.64078527  2.36554977  5.55612431  6.29313027\n",
      "  4.92873915  6.30214262  9.89771788 13.57132609  4.74663551  5.98052498\n",
      "  6.33089749  7.02314666 11.67437945  5.77566901  4.45941768  4.83945162\n",
      " 11.73697374  8.15401563 25.94717807  6.10977486  4.6471171   6.17283346\n",
      "  7.94339674  3.80933195 12.48269414  5.02536941 13.45412276  3.26314443\n",
      " 19.61093369  6.98478795  5.56816887  2.07391685 13.4923855   9.9598199\n",
      "  3.93722064 15.58286248 27.59068869  4.98149702  9.84600475  5.72630695\n",
      "  8.39457205 12.5563752   6.64557248 15.32329584  8.37782446 10.94443877\n",
      " 22.98361856  7.85132107  1.49591676  5.15060109  6.8644395   3.76116042\n",
      "  4.00374738 10.17826849 19.28233196 21.33713808  4.27157632  7.32299875\n",
      "  6.05647172  5.97505169  3.80110204 13.13221284  7.6486263  11.53195377\n",
      " 10.40885199  7.37579532 14.29430117  5.91271068 12.56527304  8.53788676\n",
      "  5.92682073  4.66747282  3.79244835  3.87314208  4.07797347  6.48216988\n",
      "  4.37089566  6.46674014  2.78360703 17.96652407 17.20101678  4.51723223\n",
      " 15.03046785  6.0485765  20.73929037 20.47819251  7.8783964   3.75704942\n",
      "  9.69500487  9.0681375  16.98118389 11.99471659 11.02686829 11.49064961\n",
      "  9.35381808  9.68817245 13.73381372  5.10958849  3.19850954  6.8279582\n",
      "  6.46802089  6.15969987  4.0652813   4.07971957 13.98116794 15.43639497\n",
      " 13.61670176  3.39673721  7.51950723  1.81471904 11.33363432  5.18969365\n",
      "  3.81214735 17.56212604  5.29886525  4.23231591  2.97434498  4.00876039\n",
      "  3.90940031 15.76132461 10.2007712   4.83897719  6.7902723   8.07909607\n",
      "  7.69477588 13.05395649  5.80171961 10.88912319  8.10168306  8.75680976\n",
      "  8.55743419  5.62643003 15.57469393  7.84301527 19.14879907  8.29320258\n",
      "  3.94470592 16.61759404  3.83960437  3.8185937   3.85233693 10.35933797\n",
      " 18.98175326  1.16064044  2.73310484  9.52949061 14.48932725  4.01470145\n",
      "  4.33407937  7.43045716  4.94967472  9.05886857  5.15504442  5.74757284\n",
      "  4.54815354 13.0348149   4.54173606  9.54790099  1.77955589  4.79043121\n",
      "  4.49320677  5.81424232 12.36188593  2.14565531 17.8269734   1.96894546\n",
      " 11.69261275 24.99273408 13.6223215   5.20547095  6.50508206 13.04961391\n",
      "  3.83412473  2.88872975  6.86410573  1.14800466  2.24117637 12.84174191\n",
      " 10.54003251  9.86100633 10.95026654  3.89775304  9.43345223  8.52207467\n",
      "  8.52324045  7.87828877  9.30987538  5.2244045   8.82020315  1.76378767\n",
      "  3.84875657 17.98213532  7.55523906 50.14897139  4.34666028 13.42514854\n",
      "  6.99610474  9.20068673  2.44280939  4.49858694  4.44491207  6.56694063\n",
      " 10.86331159 10.05355218  4.16297512  2.58632796 10.5741931   3.39223905\n",
      " 18.55712634 10.50473368 14.05533472  7.02589341 26.53025191  3.03871521\n",
      "  9.241355    5.38681963 15.99956336 15.32171328  1.36583411  5.01369416\n",
      " 23.76817331  1.75372476 11.84054626  2.55875011  5.34963178 14.7013664\n",
      "  7.21897767 14.7706169  11.44818809 12.67989604  7.59234026  7.44007355\n",
      "  2.71076045  8.65322259  7.9200122   5.60731431  3.92550718 37.92240348\n",
      "  6.2561967   4.22608576  7.06184432  1.91761223 12.99369495  5.86497073\n",
      "  7.86579587  5.80689274  6.90598006 11.68213708  6.05268187  3.66488761\n",
      " 12.1052069   6.27378644  4.79587334  4.01417136 12.07873815  5.33632689\n",
      "  7.56104347  4.67250025  3.77475198  7.89126508 10.32943385  6.66931025\n",
      " 10.421988   17.34108279  9.00537119  4.76977547  5.12021542  3.96082058\n",
      " 13.1051468   9.26629052  8.51610548 10.631898    3.33121221 51.06262478\n",
      "  9.78672583  6.32345717  4.10178786  8.6453425   4.64882714 15.5390734\n",
      "  4.71970206  4.48469984  8.67387744  9.3771251   6.22069405 11.74109369\n",
      "  5.56864375 17.03026559 20.59896925 17.9375231   4.05179609  3.35255593\n",
      "  7.9681511   1.80241557 11.69211767  1.5772762  10.98021186  1.00861762\n",
      "  7.07561795  9.86284497 25.254184   13.78459593  6.0003062   6.76687342\n",
      "  6.30849945  4.6342117   5.08614293  3.57285875  5.77042971  2.93043199\n",
      "  3.61366257  6.31794463 10.08276437  8.62344226  5.34275086  4.26300465\n",
      " 13.23576921  7.61515536 10.15685447  7.23035248  3.44551708 14.49288957\n",
      "  5.25048167  6.04389237  6.69338287 11.45111293  1.44909987  1.98531774\n",
      "  6.09840142  7.46661974  4.36382658  9.46443759  4.38009211  5.26467113\n",
      "  2.32671074  2.89260947 11.17233436 20.41111203  5.94003533  9.35487645\n",
      "  6.48857079  8.95935076  3.23123595  4.27022835  4.54691556  6.54027943\n",
      " 10.85143353  5.22893467 20.07895189  3.80119603 12.66796087  1.62764175\n",
      " 11.91401921  5.72881349  2.88993541  3.41473428 22.00696893  9.38003631\n",
      "  7.98358539  6.78645758 13.61879899  3.39061291  5.48117371  1.54737601\n",
      "  3.73651293  5.15821869 11.23864423  7.0815307   6.53977299  8.22058991\n",
      "  7.48821262  7.6667457   2.70231186 12.5359249   3.79303599  3.043787\n",
      "  4.93776268  6.50161225 24.82273888  4.9803903   2.89098575 16.1567047\n",
      "  7.06352606 24.82192685  4.54122952  5.76252002  8.56602252 11.83492429\n",
      "  3.45052572  7.70533931  6.30042509  3.08302807  1.54302235  8.79050473\n",
      "  7.1337494   4.39270045  9.8217702  18.58926062  5.87972637  2.97554907\n",
      "  2.90626439  3.08735502  5.00089156 18.38205637  4.21937738  1.98708245\n",
      "  4.53497654  1.02788409  6.17624526  8.48182694  5.74036961  7.05348816\n",
      "  6.02385677]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/gs/29wgt2xj1jj873ytknj55rsr0000gp/T/ipykernel_61556/1989406042.py:14: RuntimeWarning: divide by zero encountered in log\n",
      "  pdf = np.exp(-(np.log(x)-mean)**2/(2*sigma**2))/(x*sigma*np.sqrt(2*np.pi))\n",
      "/var/folders/gs/29wgt2xj1jj873ytknj55rsr0000gp/T/ipykernel_61556/1989406042.py:14: RuntimeWarning: invalid value encountered in divide\n",
      "  pdf = np.exp(-(np.log(x)-mean)**2/(2*sigma**2))/(x*sigma*np.sqrt(2*np.pi))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13f4a46d0>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating histograms of log-normal data\n",
    "n = 781     # Number of data points to sample\n",
    "mean = 1.9  # Mean of the lognormal distribution\n",
    "sigma = 0.7 # Log-Standard deviation of the lognormal distribution\n",
    "\n",
    "# Generate the data\n",
    "random_numbers = rng.lognormal(mean,sigma, size=(n))\n",
    "\n",
    "# Plot the histogram of the data\n",
    "plt.hist(random_numbers,density=True,bins=40 )\n",
    "\n",
    "# Add the analytical LogNormal PDF to the plot\n",
    "x = np.linspace(0,max(random_numbers),100)\n",
    "pdf = np.exp(-(np.log(x)-mean)**2/(2*sigma**2))/(x*sigma*np.sqrt(2*np.pi))\n",
    "plt.plot(x,pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sample mean of the poisson data is 60.39\n",
      "The sample variance of the poisson data is 55.95790000000001\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13ebf3d10>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating histogram of some Poisson data\n",
    "n = 200 # Number of data points to sample\n",
    "lam = 60 # Poisson parameter (mean)\n",
    "\n",
    "# Generate the data\n",
    "random_numbers = rng.poisson(lam, size=(n))\n",
    "\n",
    "print(f'The sample mean of the poisson data is {np.mean(random_numbers)}')\n",
    "print(f'The sample variance of the poisson data is {np.var(random_numbers)}')\n",
    "\n",
    "# Plot histogram of the data and compare it to the Poisson distribution\n",
    "plt.hist(random_numbers,density=True,bins=range(max(random_numbers)+1), align='mid')\n",
    "\n",
    "# Add the analytical Poisson distribution to the plot\n",
    "from scipy.stats import poisson\n",
    "x = range(max(random_numbers))\n",
    "plt.plot(x, poisson.pmf(x, lam), 'r-', ms=8, mec='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling arbitrary distributions using the Inverse Transform Sampling method.\n",
    "![alt text](figures/image-14.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example for sampling from an arbitrary discrete distribution using the inverse transform method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13ec495d0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for sampling from an arbitrary discrete distribution using the inverse transform method\n",
    "# Define the discrete distribution\n",
    "x = [1, 2, 3, 4, 5] # The outcomes\n",
    "p = [0.1, 0.2, 0.3, 0.2, 0.2] # The probabilities of the outcomes\n",
    "\n",
    "# Create the cumulative distribution function\n",
    "cdf = np.cumsum(p)\n",
    "\n",
    "# Sample from the distribution\n",
    "n = 1000\n",
    "samples = np.zeros(n)\n",
    "for i in range(n):\n",
    "    u = rng.rand()\n",
    "    samples[i] = x[np.argmax(cdf > u)]\n",
    "    \n",
    "# Plot the histogram of the samples\n",
    "plt.hist(samples,density=True,bins=range(1,7), align='left')\n",
    "\n",
    "# Add the analytical distribution to the plot\n",
    "plt.plot(x, p, 'r-', ms=8, mec='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example for sampling from an arbitrary continuous distribution using the inverse transform method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The inverse of the CDF is [2.0*log(-1/(u - 1.0))]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13f72b110>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example for sampling from an arbitrary continuous distribution using the inverse transform method\n",
    "# Define the continuous distribution\n",
    "# Create a probability density function using sympy\n",
    "x = sym.symbols('x')\n",
    "lam = 0.5\n",
    "pdf_sym = lam*sym.exp(-lam*x) # The probability density function\n",
    "\n",
    "# Create the cumulative distribution function (by integrating the PDF from 0 to x)\n",
    "cdf_sym = sym.integrate(pdf_sym, (x, 0, x))\n",
    "\n",
    "# Create the inverse of the cumulative distribution function (by solving the relation \"u = CDF(x)\" for x)\n",
    "cdf_inv_sym = sym.solve(cdf_sym - sym.symbols('u'), x)\n",
    "\n",
    "print(f'The inverse of the CDF is {cdf_inv_sym}')\n",
    "\n",
    "# Create a function to convert uniform random numbers U(0,1) to samples from the distribution\n",
    "sample = sym.lambdify(sym.symbols('u'), cdf_inv_sym)\n",
    "\n",
    "# Sample from the distribution\n",
    "n = 1000\n",
    "samples = sample(rng.rand(n))\n",
    "\n",
    "# Plot the histogram of the samples\n",
    "plt.hist(samples,density=True,bins=40)\n",
    "\n",
    "# Add the analytical distribution to the plot\n",
    "x = np.linspace(0,20,100)\n",
    "pdf = lam*np.exp(-lam*x)\n",
    "plt.plot(x, pdf, 'r-', ms=8, mec='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing expectations from distributons and summary statistics from samples\n",
    "![alt text](figures/image-12.png)\n",
    "![alt text](figures/image-13.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The computed mean of this distribution is 5.999999999999998\n",
      "The computed variance of this distribution is 4.199999999999996\n",
      "The computed mean of function f(x) is 10.509371983392828\n",
      "The mean of this distribution is 6.0\n",
      "The variance of this distribution is 4.199999999999999\n",
      "The sample mean of this distribution for 1000 samples is 5.881\n",
      "The sample variance of this distribution for 1000 samples is  4.208839000000001\n",
      "The sample mean of function f(x) for 1000 samples is 10.24612548784108\n"
     ]
    }
   ],
   "source": [
    "# Examples for computing expected values (means and variances) from a discrete distribution\n",
    "\n",
    "# Try one of the following discrete distributions\n",
    "dist = binom(n = 20, p = 0.3) # Create a Poisson distribution with lambda = 5\n",
    "# dist = poisson(mu = 5) # Create a Poisson distribution with lambda = 5\n",
    "# dist = geom(p = 0.53) # Create a Poisson distribution with lambda = 5\n",
    "\n",
    "f = lambda x: x**1.3 # Create a function to compute the expected value of. E.g., f(x) = x^(1.3)\n",
    "distRange = np.arange(25) # Create a range of values from 0 to 19\n",
    "\n",
    "pdf = dist.pmf(distRange) # Compute the PMF of the distribution\n",
    "mean = np.sum(pdf*distRange) # Compute the mean of the distribution\n",
    "variance = np.sum(pdf*(distRange-mean)**2) # Compute the variance of the distribution    \n",
    "f_mean = np.sum(pdf*f(distRange)) # Compute the expected value of f(x)\n",
    "\n",
    "print(f'The computed mean of this distribution is {mean}')\n",
    "print(f'The computed variance of this distribution is {variance}')\n",
    "print(f'The computed mean of function f(x) is {f_mean}')\n",
    "\n",
    "# Compare to the built-in methods\n",
    "print(f'The mean of this distribution is {dist.mean()}')\n",
    "print(f'The variance of this distribution is {dist.var()}')\n",
    "\n",
    "# Now let's sample from the distribution and compute the sample mean and variance\n",
    "n = 1000 # Number of samples to draw\n",
    "samples = dist.rvs(size=n) # Draw n samples from the distribution   \n",
    "sampleMean = np.mean(samples) # Compute the sample mean \n",
    "sampleVariance = np.var(samples) # Compute the sample variance  \n",
    "samplefMean = np.mean(f(samples)) # Compute the sample mean of f(x)\n",
    "\n",
    "print(f'The sample mean of this distribution for {n} samples is {sampleMean}')\n",
    "print(f'The sample variance of this distribution for {n} samples is  {sampleVariance}')\n",
    "print(f'The sample mean of function f(x) for {n} samples is {samplefMean}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The computed mean of this distribution is 5.003000750119569\n",
      "The computed variance of this distribution is 8.340835585058656\n",
      "The computed mean of function f(x) is 2003.001500269815\n",
      "The mean of this distribution is 5.0\n",
      "The variance of this distribution is 8.333333333333332\n",
      "The sample mean of this distribution for 1000 samples is 5.075225503500299\n",
      "The sample variance of this distribution for 1000 samples is  8.010215681459917\n",
      "The sample mean of function f(x) for 1000 samples is 1995.2590753092284\n"
     ]
    }
   ],
   "source": [
    "# Examples for computing expected values (means and variances) from a continuous distribution\n",
    "\n",
    "# Try one of the following continuous distributions\n",
    "dist = uniform(loc = 0, scale = 10) # Create a Uniform distribution with a = 0 and b = 10\n",
    "# dist = expon(scale = 1/3) # Create a Exponential distribution with lambda = 3\n",
    "# dist = norm(loc = -3, scale = 2) # Create a Normal distribution with mean = -3 and standard deviation = 2 \n",
    "\n",
    "f = lambda x: x**4 # Create a function to compute the expected value of. E.g., f(x) = x^(4)\n",
    "\n",
    "distRange = np.linspace(-30,30,10000) # Create a range of values from 0 to 19\n",
    "stepSize = distRange[1]-distRange[0] # Compute the step size of the range\n",
    "\n",
    "pdf = dist.pdf(distRange) # Compute the PDF of the distribution\n",
    "mean = np.sum(pdf*distRange)*stepSize # Compute the mean of the distribution\n",
    "variance = np.sum(pdf*(distRange-mean)**2)*stepSize  # Compute the variance of the distribution    \n",
    "f_mean = np.sum(pdf*f(distRange))*stepSize # Compute the expected value of f(x)\n",
    "\n",
    "print(f'The computed mean of this distribution is {mean}')\n",
    "print(f'The computed variance of this distribution is {variance}')\n",
    "print(f'The computed mean of function f(x) is {f_mean}')\n",
    "\n",
    "# Compare to the built-in methods\n",
    "print(f'The mean of this distribution is {dist.mean()}')\n",
    "print(f'The variance of this distribution is {dist.var()}')\n",
    "\n",
    "# Now let's sample from the distribution and compute the sample mean and variance\n",
    "n = 1000 # Number of samples to draw\n",
    "samples = dist.rvs(size=n) # Draw n samples from the distribution   \n",
    "sampleMean = np.mean(samples) # Compute the sample mean \n",
    "sampleVariance = np.var(samples) # Compute the sample variance  \n",
    "samplefMean = np.mean(f(samples)) # Compute the sample mean of f(x)\n",
    "\n",
    "print(f'The sample mean of this distribution for {n} samples is {sampleMean}')\n",
    "print(f'The sample variance of this distribution for {n} samples is  {sampleVariance}')\n",
    "print(f'The sample mean of function f(x) for {n} samples is {samplefMean}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (Spyder)",
   "language": "python3",
   "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": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}