Chapter 5 - Joint Distributions.ipynb

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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#-Discrete-Distributions\" data-toc-modified-id=\"-Discrete-Distributions-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Discrete Distributions</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-Joint-PMF\" data-toc-modified-id=\"-Joint-PMF-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Joint PMF</font></a></span></li><li><span><a href=\"#-Marginal-PMF\" data-toc-modified-id=\"-Marginal-PMF-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Marginal PMF</font></a></span></li><li><span><a href=\"#-Joint-and-Marginal-CDF-\" data-toc-modified-id=\"-Joint-and-Marginal-CDF--1.3\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Joint and Marginal CDF </font></a></span></li><li><span><a href=\"#-Conditional-PMF-and-CDF\" data-toc-modified-id=\"-Conditional-PMF-and-CDF-1.4\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Conditional PMF and CDF</font></a></span></li><li><span><a href=\"#-Conditional-Expectation\" data-toc-modified-id=\"-Conditional-Expectation-1.5\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Conditional Expectation</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-Conditional-Expectation-as-A-Function\" data-toc-modified-id=\"-Conditional-Expectation-as-A-Function-1.5.1\"><span class=\"toc-item-num\">1.5.1&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Conditional Expectation as A Function</font></a></span></li><li><span><a href=\"#-Expectation-for-Independent-Variables\" data-toc-modified-id=\"-Expectation-for-Independent-Variables-1.5.2\"><span class=\"toc-item-num\">1.5.2&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Expectation for Independent Variables</font></a></span></li></ul></li></ul></li><li><span><a href=\"#-Continuous-Distributions\" data-toc-modified-id=\"-Continuous-Distributions-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Continuous Distributions</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-Joint-PDF\" data-toc-modified-id=\"-Joint-PDF-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Joint PDF</font></a></span><ul class=\"toc-item\"><li><span><a href=\"#-An-Example-of-Joint-PDF-\" data-toc-modified-id=\"-An-Example-of-Joint-PDF--2.1.1\"><span class=\"toc-item-num\">2.1.1&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> An Example of Joint PDF </font></a></span></li></ul></li><li><span><a href=\"#-Marginal-PDF-\" data-toc-modified-id=\"-Marginal-PDF--2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Marginal PDF </font></a></span></li><li><span><a href=\"#-Joint-CDF-\" data-toc-modified-id=\"-Joint-CDF--2.3\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Joint CDF </font></a></span></li><li><span><a href=\"#-Conditional-PDF-and-CDF-\" data-toc-modified-id=\"-Conditional-PDF-and-CDF--2.4\"><span class=\"toc-item-num\">2.4&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Conditional PDF and CDF </font></a></span></li><li><span><a href=\"#-Independence\" data-toc-modified-id=\"-Independence-2.5\"><span class=\"toc-item-num\">2.5&nbsp;&nbsp;</span><font face=\"gotham\" color=\"purple\"> Independence</font></a></span></li></ul></li></ul></div>"
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "import mpl_toolkits.mplot3d.art3d as art3d\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this chapter, we will only be dealing with joint distributions, which are the most important section of the whole course. Joint distributions are used for formulating all kinds of probability model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Discrete Distributions</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Joint PMF</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The joint probability mass function of two discrete random variable is defined as\n",
    "\n",
    "$$\n",
    "P_{XY}(x, y) = P(X = x, Y=y)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is convenient to define a finite range for $X$ and $Y$, $R_X = \\{x_1, x_2, ...\\}$ and $R_Y = \\{y_1, y_2, ...\\}$ and its <font face=\"gotham\" color=\"red\">cartesian product</font>\n",
    "\n",
    "$$\n",
    "R_{XY}\\subset R_X \\times R_Y = \\{(x_i, y_j)|x_i\\in R_X, y_j \\in R_Y\\}\n",
    "$$\n",
    "\n",
    " is the range for joint distribution."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most common property for probability distribution is\n",
    "\n",
    "$$\n",
    "\\sum_{(x_i,y_j)\\in R_{XY}}P_{XY}(x_i,y_j)=1\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Marginal PMF</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider a probability mass function table."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{array}{|c|c|}\n",
    "\\hline & Y = 0 & Y = 1 & Y= 2 \\\\ \\hline\n",
    "  X = 0 & 1/6  & 1/4 & 1/8  \\\\ \\hline\n",
    "  X = 1 & 1/8  & 1/6 & 1/6  \\\\ \\hline\n",
    "\\end{array}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Find $P(X=0, Y = 1)$. It is easy, just eyeball the table.\n",
    "$$P(X=0, Y = 1) = 1/4$$\n",
    "\n",
    "2. Find $P(X=0| Y = 1)$ and $P(Y = 1| X =0)$\n",
    "$$\n",
    "P(X=0| Y = 1) = \\frac{1/4}{1/4+1/6}=3/5\\\\\n",
    "P(Y = 1| X =0) = \\frac{1/4}{1/6+1/4+1/8}= 6/13\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Find marginal PMFs of $X$ and $Y$"
   ]
  },
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   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Marginal PMF of pY are 7/24, 5/12, 7/24.\n",
      "Marginal PMF of pX are 13/24, 11/24.\n"
     ]
    }
   ],
   "source": [
    "from fractions import Fraction as frac\n",
    "pY_0 = frac(1,6) + frac(1,8)\n",
    "pY_1 = frac(1,4) + frac(1,6)\n",
    "pY_2 = frac(1,8) + frac(1,6)\n",
    "\n",
    "pX_0 = frac(1,6) + frac(1,4) + frac(1,8)\n",
    "pX_1 = frac(1,8) + frac(1,6) + frac(1,6)\n",
    "\n",
    "print('Marginal PMF of pY are {0}, {1}, {2}.'.format(pY_0,pY_1,pY_2))\n",
    "print('Marginal PMF of pX are {0}, {1}.'.format(pX_0,pX_1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reason we call them marginal is because they are written at the margin of the table.\n",
    "\n",
    "\\begin{array}{|c|c|}\n",
    "\\hline  & Y = 0 & Y = 1 & Y= 2 & P_X(x)\\\\ \\hline\n",
    "  X = 0 & 1/6  & 1/4 & 1/8 & 13/24 \\\\ \\hline\n",
    "  X = 1 & 1/8  & 1/6 & 1/6 & 11/24\\\\ \\hline\n",
    " P_Y(y) & 7/24  & 5/12 & 7/24  &  \\\\ \\hline\n",
    "\\end{array}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. Are $X$ and $Y$ independent?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If independent, a conditional probability should equal to marginal probability, for instance\n",
    "\n",
    "$$\n",
    "P(X=0| Y = 1)= \\frac{1/4}{1/4+1/6} =3/5\\\\\n",
    "P_X(X=0)=13/24\n",
    "$$\n",
    "\n",
    "They are not equal, which means they are not independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relationship of marginal PMF and conditional PMF is \n",
    "\n",
    "$$\n",
    "P(X|Y) = \\frac{P(X,Y)}{P_Y(Y)}\n",
    "$$\n",
    "\n",
    "i.e. \n",
    "\n",
    "$$\n",
    "\\text{Conditional PMF} = \\frac{\\text{Joint PMF}}{\\text{Marginal PMF}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Joint and Marginal CDF </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The joint CDF of two random variables $X$ and $Y$ is defined as \n",
    "\n",
    "$$\n",
    "F_{XY}(x,y)=P(X\\leq x, Y\\leq y)\n",
    "$$\n",
    "\n",
    "where $0\\leq F_{XY}(x,y) \\leq 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For instance, the joint CDF of $P(X\\leq 2, Y\\leq 1)$ in range $(-6,\\ 6)$ is the probability of the shaded area."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-6, 1)\n",
    "y = 2*np.ones(len(x))\n",
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "\n",
    "ax.plot([1, -5], [2, 2], color = 'b')\n",
    "ax.scatter(1, 2, s = 80, zorder = 3, color = 'red')\n",
    "ax.plot([1, 1], [2, -5], color = 'b')\n",
    "ax.axis([-5, 6, -5, 6])\n",
    "ax.scatter(np.random.uniform(low = -5, high = 6, size = 50),\n",
    "           np.random.uniform(low = -5, high = 6, size = 50))\n",
    "ax.fill_between(x, y, -5, color = 'red', alpha =.2)\n",
    "ax.text(1, 2.1, '$(1, 2)$', size = 15)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Marginal CDF $F_X(x)$ and $F_Y(y)$ are denoted\n",
    "\n",
    "$$\n",
    "F_X(x) = P(X\\leq x, Y\\leq \\infty)\\\\\n",
    "F_Y(y) = P(X\\leq \\infty, Y\\leq y)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Conditional PMF and CDF</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $A$ is a random event, the conditional PMF of $X$ given $A$ is denoted as\n",
    "\n",
    "$$\n",
    "P_{X|A}(X = x_i) = \\frac{P(X=x_i,A)}{P(A)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a PMF as below\n",
    "\n",
    "\\begin{array}{|c|c|}\n",
    "\\hline & X = -2 & X = -1 & X = 0 & X = 1 & X = 2 \\\\ \\hline\n",
    "  Y = 2 & 0  & 0 & 1/13 & 0 & 0  \\\\ \\hline\n",
    "  Y = 1 & 0  & 1/13 & 1/13 & 1/13 & 0  \\\\ \\hline\n",
    "  Y = 0 & 1/13  & 1/13 & 1/13 & 1/13 & 1/13  \\\\ \\hline\n",
    "  Y = -1 & 0  & 1/13 & 1/13 & 1/13 & 0  \\\\ \\hline\n",
    "  Y = -2 & 0  & 0 & 1/13 & 0 & 0  \\\\ \\hline\n",
    "\\end{array}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mathematically, it is defined as $G=\\{(x, y)|x, y \\in \\mathbb{Z},| x|+| y | \\leq 2\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Find the marginal PMFs of $X$ and $Y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Marginal PMF of pY are 1/13, 3/13, 5/13, 3/13, 1/13.\n",
      "Marginal PMF of pX are 1/13, 3/13, 5/13, 3/13, 1/13.\n"
     ]
    }
   ],
   "source": [
    "pY_2 = frac(1,13)\n",
    "pY_1 = frac(1,13)*3\n",
    "pY_0 = frac(1,13)*5\n",
    "pY_m1 = frac(1,13)*3\n",
    "pY_m2 = frac(1,13)\n",
    "\n",
    "pX_2 = frac(1,13)\n",
    "pX_1 = frac(1,13)*3\n",
    "pX_0 = frac(1,13)*5\n",
    "pX_m1 = frac(1,13)*3\n",
    "pX_m2 = frac(1,13)\n",
    "\n",
    "print('Marginal PMF of pY are {0}, {1}, {2}, {3}, {4}.'.format(pY_2,pY_1,pY_0,pY_m1,pY_m2))\n",
    "print('Marginal PMF of pX are {0}, {1}, {2}, {3}, {4}.'.format(pX_2,pX_1,pX_0,pX_m1,pX_m2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We add marginals to the table \n",
    "\n",
    "\\begin{array}{|c|c|}\n",
    "\\hline & X = -2 & X = -1 & X = 0 & X = 1 & X = 2 & P_Y(y) \\\\ \\hline\n",
    "  Y = 2 & 0  & 0 & 1/13 & 0 & 0  & 1/13\\\\ \\hline\n",
    "  Y = 1 & 0  & 1/13 & 1/13 & 1/13 & 0 & 3/13 \\\\ \\hline\n",
    "  Y = 0 & 1/13  & 1/13 & 1/13 & 1/13 & 1/13 & 5/13 \\\\ \\hline\n",
    "  Y = -1 & 0  & 1/13 & 1/13 & 1/13 & 0 & 3/13 \\\\ \\hline\n",
    "  Y = -2 & 0  & 0 & 1/13 & 0 & 0 &  1/13\\\\ \\hline\n",
    "  P_X(x) &1/13 &3/13 & 5/13 & 3/13 & 1/13 \\\\ \\hline\n",
    "\\end{array}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Find the conditional PMF of $X$ given $Y = 1$, i.e. $P(X|Y=1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{array}{|c|c|}\n",
    "\\hline & X = -2 & X = -1 & X = 0 & X = 1 & X = 2\\\\ \\hline\n",
    "  Y = 1 & 0  & 1/3 & 1/3 & 1/3 & 0  \\\\ \\hline\n",
    "\\end{array}\n",
    "\n",
    "It shows that given $Y=1$, $X$ is uniformly distributed over $\\{-1,0,1\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Are X and Y independent?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No, for instance $P(X=0|Y=1) \\neq P_X(X = 0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If random event $A$ is replaced by a discrete random variable $Y$, the conditional density PMFs are defined as\n",
    "\n",
    "$$\n",
    "\\begin{array}{l}\n",
    "P_{X | Y}\\left(x_{i} | y_{j}\\right)=\\frac{P_{X Y}\\left(x_{i}, y_{j}\\right)}{P_{Y}\\left(y_{j}\\right)} \\\\\n",
    "P_{Y | X}\\left(y_{j} | x_{i}\\right)=\\frac{P_{X Y}\\left(x_{i}, y_{j}\\right)}{P_{X}\\left(x_{i}\\right)}\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "where $x_i$ and $y_j$ are realizations of $X$ and $Y$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Conditional Expectation</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The expectation can be conditional on a random event or a realization of random variable. \n",
    "\n",
    "$$\\begin{align}\n",
    "E[X | A]&=\\sum_{x_{i}\\in R_{X}}x_{i} P_{X | A}\\left(x_{i}|A\\right) \\\\\n",
    "E[X | Y=y_{j}]&=\\sum_{x_{i} \\in R_{X}} x_{i} P_{X | Y}\\left(x_{i} | Y=y_{j}\\right)\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the PMF example in last section, let's try to answer questions below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Find $E[X|Y = 1]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate the conditional expectation, we must use conditional probability as weight:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "E[X|Y = 1]= -1 \\left(\\frac{1}{3}\\right)+ 0  \\left(\\frac{1}{3}\\right)+1 \\left(\\frac{1}{3}\\right)=0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Find $E[X|−1 < Y < 2]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, calculate the conditional PMF\n",
    "\n",
    "$$\n",
    "P_{X|-1<Y<2}(x_i |-1<Y<2) = -2\\frac{1/13}{8/13}-\\frac{2/13}{8/13}+0\\frac{3/13}{8/13}+ \\frac{2/13}{8/13} + 2\\frac{1/13}{8/13}=0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font face=\"gotham\" color=\"purple\"> Conditional Expectation as A Function</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you paid attention to the conditional expection expression\n",
    "\n",
    "$$\n",
    "E[X | Y=y_{j}]=\\sum_{x_{i} \\in R_{X}} x_{i} P_{X | Y}\\left(x_{i} | Y=y_{j}\\right)\n",
    "$$\n",
    "\n",
    "you would find that it is actually a function of $Y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a joint PMF below\n",
    "\n",
    "$$\n",
    "\\begin{array}{|c|c|}\n",
    "\\hline       &  X = 0 & X = 1 & P_Y(y) \\\\ \\hline\n",
    "       Y = 0 & 1/5  & 2/5   & 3/5\\\\ \\hline\n",
    "       Y = 1 & 2/5  & 0 & 2/5 \\\\ \\hline\n",
    "       P_X(x) &3/5  & 2/5 \\\\ \\hline\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. What are the conditional PMF $P_{X|Y}(x|0)$ and $P_{X|Y}(x|1)$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "P_{X|Y}(X= 0|Y = 0) = \\frac{1/5}{3/5}=1/3\\\\\n",
    "P_{X|Y}(X= 1|Y = 0) = \\frac{2/5}{3/5}=2/3\\\\\n",
    "P_{X|Y}(X= 0|Y = 1) = \\frac{2/5}{2/5}=1\\\\\n",
    "P_{X|Y}(X= 1|Y = 1) = 0\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Let $Z = E[X|Y]$, find PMF of $Z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember that $Z$ is a function of $Y$. To calculate conditional expectation, we need to use conditional probability as well.\n",
    "\n",
    "$$\n",
    "E[X|Y = 0] = 0 \\left(\\frac{\\frac{1}{5}}{\\frac{1}{5}+\\frac{2}{5}}\\right)+1\\left(\\frac{\\frac{2}{5}}{\\frac{1}{5}+\\frac{2}{5}}\\right) =\\frac{2}{3}\\\\\n",
    "E[X|Y = 1]  = 0\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Find $E[Z]$, and check that if $E[Z] = E[X]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because $E[X|Y]$ itself is a variable, it must have an expectation as well\n",
    "\n",
    "$$\n",
    "E[Z] = E[E[X|Y]] = P_Y(Y = 0)E[X|Y = 0]+ P_Y(Y = 1)E[X|Y = 1] = \\frac{3}{5}\\cdot\\frac{2}{3}+\\frac{2}{5}\\cdot0=\\frac{2}{5}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Actually, $E[Z] = E[E[X|Y]] = E[X]$ must hold, it is the <font face=\"gotham\" color=\"red\">law of iterated expectation</font>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font face=\"gotham\" color=\"purple\"> Expectation for Independent Variables</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the rules of expectation for independent variables are here, they are fairly straightforward, because conditioning on $Y$ does not provide any extra information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "1. $E[X | Y]=E[ X]$\n",
    "2. $E[g(X) | Y]=E[g(X)]$\n",
    "3. $E[X Y]=E[ X] E [Y]$\n",
    "4. $E[g(X) h(Y)]=E[g(X)] E[h(Y)]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Continuous Distributions</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Joint PDF</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Joint PDF of $X$ and $Y$ is defined as\n",
    "\n",
    "$$\n",
    "P((X, Y) \\in A)=\\iint_{A} f_{X Y}(x, y) d x d y =1\n",
    "$$\n",
    "\n",
    "where $f_{XY}(x, y)$ is a non-negative function, mapping $\\mathbb{R}^2$ to $\\mathbb{R}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we are particularly interested in the case that $A$ is a rectangular,\n",
    "\n",
    "$$\n",
    "P(a\\geq X \\geq b, c\\geq Y \\geq d) =\\int_c^d\\int_a^b f_{X Y}(x, y) d x d y\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And within $A$, there are infinite amount of small rectangles\n",
    "\n",
    "$$\n",
    "P(a\\geq X \\geq a+\\delta, c\\geq Y \\geq c+\\delta )\\approx f_{XY}(a,c)\\delta^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font face=\"gotham\" color=\"purple\"> An Example of Joint PDF </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider an example other than normal distribution.\n",
    "\n",
    "$$\n",
    "f_{X Y}(x, y)=\\left\\{\\begin{array}{ll}\n",
    "x+c y^{2} & 0 \\leq x \\leq 1,\\quad 0 \\leq y \\leq 1 \\\\\n",
    "0 & \\text { otherwise }\n",
    "\\end{array}\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Find out constant $c$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the property $\\iint_{A} f_{X Y}(x, y) d x d y =1$\n",
    "\n",
    "\\begin{align}\n",
    "\\int^1_0\\int^1_0(x+cy^2)dxdy &= 1\\\\\n",
    "\\int^1_0\\left[\\frac{x^2}{2}+cxy^2\\right]^1_0dy &= 1\\\\\n",
    "\\int^1_0\\left[\\frac{1}{2}+cy^2\\right]dy &= 1\\\\\n",
    "\\left[\\frac{y}{2}+c\\frac{y^3}{3}\\right]^1_0&=1\\\\\n",
    "\\frac{1}{2}+\\frac{c}{3}&=1\\\\\n",
    "c&=\\frac{3}{2}\\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Find out $P(0 ≤ X ≤ 1/2,0 ≤ Y ≤ 1/2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plug in $c$, perform double integration\n",
    "\n",
    "\\begin{align}\n",
    "\\int^{1/2}_{0}\\int^{1/2}_0\\left(x+\\frac{3}{2}y^2\\right)dxdy &=\n",
    "\\int_0^{1/2}\\left[\\frac{x^2}{2}+\\frac{3}{2}y^2x\\right]_0^{1/2}dy \\\\\n",
    "&=\\int_0^{1/2}\\left[\\frac{1}{8}+\\frac{3}{4}y^2\\right]dy\\\\\n",
    "&=\\left[\\frac{1}{8}+\\frac{y^3}{4}\\right]_0^{1/2}\\\\\n",
    "&=\\frac{3}{32}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The joint distribution is depicted as below, the volume between the curved plane and $xy$ plane is $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = np.linspace(0, 1), np.linspace(0, 1)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = X + 3/2*Y**2\n",
    "\n",
    "fig = plt.figure(figsize = (8, 8))\n",
    "ax = fig.gca(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, cmap = 'coolwarm')\n",
    "ax.contourf(X, Y, Z, zdir='z', offset=0, cmap='coolwarm')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Marginal PDF </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maringal PDF of $X$ and $Y$ are\n",
    "\n",
    "\\begin{equation}\n",
    "f_{X}(x)=\\int_{-\\infty}^{\\infty} f_{X Y}(x, y) d y,\\quad \\text { for all } x \\\\\n",
    "f_{Y}(y)=\\int_{-\\infty}^{\\infty} f_{X Y}(x, y) d x,\\quad \\text { for all } y\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use the same example as in last section to find out $f_X(x)$ and $f_Y(y)$.\n",
    "\n",
    "$$\n",
    "f_{X}(x)=\\int_{0}^{1}\\left(x+\\frac{3}{2}y^2\\right)  d y =x+\\frac{1}{2}\\\\\n",
    "f_{Y}(y)=\\int_{0}^{1}\\left(x+\\frac{3}{2}y^2\\right)  d x =\\frac{3}{2} y^{2}+\\frac{1}{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Joint CDF </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Joint CDF and joint PDF has relationship as follows:\n",
    "\n",
    "$$\n",
    "F_{X Y}(x, y)=\\int_{-\\infty}^{y} \\int_{-\\infty}^{x} f_{X Y}(u, v) d u d v \\\\\n",
    "f_{X Y}(x, y)=\\frac{\\partial^{2}}{\\partial x \\partial y} F_{X Y}(x, y)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same PDF as above, find the CDF.\n",
    "\n",
    "$$\n",
    "f_{X Y}(x, y)=\\left\\{\\begin{array}{ll}\n",
    "x+\\frac{3}{2} y^{2} & 0 \\leq x \\leq 1,\\quad 0 \\leq y \\leq 1 \\\\\n",
    "0 & \\text { otherwise }\n",
    "\\end{array}\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "F_{XY}(x,y)=\\int_{0}^{y} \\int_{0}^{x} f_{X Y}(u, v) d u d v&=\\int_{0}^{y} \\int_{0}^{x} \\left(u+\\frac{3}{2}v^2\\right) d u d v\\\\\n",
    "& = \\int_0^y\\left[\\frac{u^2}{2}+\\frac{3}{2}v^2u\\right]^x_0dv\\\\\n",
    "& =  \\int_0^y\\left(\\frac{x^2}{2}+\\frac{3}{2}v^2x\\right)dv\\\\\n",
    "& = \\left[\\frac{x^2}{2}v+\\frac{3}{2}\\frac{v^3}{3}x\\right]^y_0\\\\\n",
    "& =\\frac{x^2y}{2}+\\frac{y^3x}{2}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Conditional PDF and CDF </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the conditional PDF of $X$ given that $X\\in A$\n",
    "\n",
    "\\begin{align}\n",
    "P(x\\leq X \\leq x+\\delta|X \\in A)\\approx f_{X|X\\in A}(x)\\cdot \\delta &= \\frac{P(x\\leq X \\leq x+\\delta,X \\in A)}{P(A)}\\\\\n",
    "&=\\frac{P(x\\leq X \\leq x+\\delta)}{P(A)}\\\\\n",
    "&\\approx\\frac{f_X(x)\\delta}{P(A)}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have shown that \n",
    "\n",
    "$$\n",
    "f_{X|X\\in A}(x) = \\frac{f_X(x)}{P(A)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can imagin $P(A)$ as a scaling factor that normalize the conditional PDF into an area of $1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For two jointly continuous random variables $X$ and $Y$, we can\n",
    "define the following conditional concepts:\n",
    "1. The conditional PDF of $X$ given $Y=y$ :\n",
    "$$\n",
    "f_{X | Y}(x | y)=\\frac{f_{X Y}(x, y)}{f_{Y}(y)}\n",
    "$$\n",
    "2. The conditional probability that $X \\in A$ given $Y=y:$\n",
    "$$\n",
    "P(X \\in A | Y=y)=\\int_{A} f_{X | Y}(x | y) d x\n",
    "$$\n",
    "3. The conditional CDF of $X$ given $Y=y$\n",
    "$$\n",
    "F_{X | Y}(x | y)=P(X \\leq x | Y=y)=\\int_{-\\infty}^{x} f_{X | Y}(x | y) d x\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intuition of the first expression, i.e. conditional PDF is\n",
    "\n",
    "$$\n",
    "P(x\\leq X \\leq x+\\delta| y\\leq Y\\leq y+\\epsilon)\\approx \\frac{f_{XY}(xy)\\delta\\epsilon}{f_Y(y)\\epsilon}=f_{X|Y}(x|y)\\delta\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conditional probability must satisfy the basic rule of probability as well, \n",
    "\n",
    "$$\n",
    "\\int_{-\\infty}^\\infty f_{X|Y}(x|y)dx = 1\n",
    "$$\n",
    "\n",
    "because\n",
    "\n",
    "$$\n",
    "\\frac{\\int_{-\\infty}^\\infty f_{XY}(xy)dx}{f_Y(y)} = 1\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rearrange the conditional PDF, we obtain the multiplication rule\n",
    "\n",
    "$$\n",
    "f_{XY}(xy)=f_{X|Y}(x|y)f_Y(y)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Independence</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If continuous variables $X$ and $Y$ are independent, then knowing either of them does not provide information for the other. That is \n",
    "\n",
    "$$\n",
    "f_{X|Y}(x|y) = f_X(x),\\qquad \\text{or} \\qquad f_{Y|X}(y|x) = f_Y(y)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus the multiplication rule for independent distribution\n",
    "\n",
    "$$\n",
    "f_{XY}(xy)=f_X(x)f_Y(y)\n",
    "$$\n",
    "\n",
    "Other rules derived from this are \n",
    "\n",
    "\\begin{align}\n",
    "E[XY]&= E[X]E[Y]\\\\\n",
    "\\text{Var}(X+Y)&=\\text{Var}(X)+\\text{Var}(Y)\\\\\n",
    "E[g(X)h(Y)]&=E[g(X)]E[h(Y)]\n",
    "\\end{align}"
   ]
  }
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