{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 13: Standard Normal, Normal normalizing constant\n", "\n", "\n", "## Stat 110, Prof. Joe Blitzstein, Harvard University\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Proof of the Universality of $\\operatorname{Unif}(0,1)$\n", "\n", "Let $F$ be a _continuous_, _strictly increasing_ CDF.\n", "\n", "Then \n", "\n", "\\begin{align}\n", " &X = F^{-1}(U) \\sim F & &\\text{if } U \\sim \\operatorname{Unif}(0,1) & &\\text{(1)}\\\\\n", " \\\\\n", " &F(X) \\sim \\operatorname{Unif}(0,1) & &\\text{if } X \\sim F & &\\text{(2)}\n", "\\end{align}\n", "\n", "$F$ is just a function, and hence we can treat it like an operator. \n", "\n", "And like $X$, $F(X)$ is just another r.v.\n", "\n", "### Interpreting the Universality of $\\operatorname{Unif}(0,1)$\n", "\n", "_How to interpret this universality?_\n", "\n", "\\begin{align}\n", " &F(x) = P(X \\le x) & &\\text{does not imply that } \\\\\n", " \\\\\n", " \\require{cancel} &\\bcancel{F(X) = P(X \\le X) = 1} \\\\\n", " \\\\\n", " \\\\ \n", " &F(x) = 1 - e^{-x} & &\\text{where } x \\gt 0 \\\\\n", " &F(X) = 1 - e^{-X}\n", "\\end{align}\n", "\n", "_First_ evaluate $F$ at $x$, and _then_ replace $x$ for $X$. \n", "\n", "### Simulating random variable draws using the universality of $\\operatorname{Unif}(0,1)$\n", "\n", "These 2 approaches to universality of the Uniform are quite useful, like when you want to simulate draws from another r.v.\n", "\n", "Let $F(x) = 1 - e^{-x}$, where $x \\gt 0$. This is the exponential random distribution $\\operatorname{Expo}(1)$.\n", "\n", "Say we have $U \\sim \\operatorname{Unif}(0,1)$.\n", "\n", "_How can we leverage universality of $\\operatorname{Unif}(0,1)$ to simulate $X \\sim F$?_\n", "\n", "\\begin{align}\n", " u &= 1 - e^{-x} & &\\text{first we obtain }F^{-1}(x) \\\\\n", " e^{-x} &= 1 - u \\\\\n", " -x &= ln(1 - u) \\\\\n", " x &= - ln(1-u) \\\\\n", " \\\\\n", " \\Rightarrow F^{-1}(u) &= -ln(1-u) \\\\\n", " \\Rightarrow F^{-1}(U) &= -ln(1-U) \\sim F & &\\text{by universality}\n", "\\end{align}\n", "\n", "And so we could simulate 10 i.i.d. draws from $F(x) = 1 - e^{-x}$ by calculating $-ln(1-U)$ 10 times.\n", "\n", "### Symmetry of $\\operatorname{Unif}(0,1)$\n", "\n", "![title](images/L1301.png)\n", "\n", "Note that\n", "\n", "\\begin{align}\n", " 1 - U \\sim \\operatorname{Unif}(0,1) & &\\text{symmetry of Uniform} \\\\\n", " \\\\\n", " a + b U & &\\text{linear transformations are also } \\operatorname{Unif}\n", "\\end{align}\n", "\n", "Non-linear transformations will, in general, __not__ be $\\operatorname{Unif}$.\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Independence of Random Variables\n", "\n", "### General case\n", "\n", "Say we have r.v. $X_1, X_2, \\dots , X_n$.\n", "\n", "#### Definition: independence of random variables\n", "> $X_1, X_2, \\dots , X_n$ are independent if, for all $x_1, x_2, \\dots, x_n$\n", "> \n", "> \\\\begin{align}\n", "> P(X_1 \\le x_1, X_2 \\le x_2, \\dots , X_n \\le x_n) &= P(X_1 \\le x_1) P(X_2 \\le x_2) \\cdots P(X_n \\le x_n)\n", "> \\\\end{align}\n", "\n", "Note that in this general case, $P(X_1 \\le x_1, X_2 \\le x_2, \\dots , X_n \\le x_n)$ is called the __joint CDF__.\n", "\n", "#### Definition: independence of discrete random variables\n", "> Discrete r.v. $X_1, X_2, \\dots , X_n$ are independent if, for all $x_1, x_2, \\dots, x_n$\n", "> \n", "> \\\\begin{align}\n", "> P(X_1 = x_1, X_2 = x_2, \\dots , X_n = x_n) &= P(X_1 = x_1) P(X_2 = x_2) \\cdots P(X_n = x_n)\n", "> \\\\end{align}\n", "\n", "In the discrete case, $P(X_1 = x_1, X_2 = x_2, \\dots , X_n = x_n)$ is called the __joint PMF__.\n", "\n", "### Interpretation\n", "\n", "Simply put, in both the general and discrete cases, knowing any subset of the r.v. gives us __no__ information about the rest.\n", "\n", "This is _stronger_ than pair-wise independence.\n", "\n", "#### Ex. A penny-matching game\n", "\n", "Consider a penny-matching game where 2 players flip a penny. If the faces showing match (HH or TT), then one of the players wins; else the other player wins.\n", "\n", "Let \n", "\n", "\\begin{align}\n", " X_1, X_2 &\\sim \\operatorname{Bern}\\left(\\frac{1}{2}\\right) ~~ \\text{, i.i.d} \\\\\n", " \\\\\n", " X_3 &=\n", " \\begin{cases}\n", " 1 & \\quad \\text{if } X_1 = X_2 \\\\\n", " 0 & \\quad \\text{otherwise}\\\\\n", " \\end{cases}\n", "\\end{align}\n", " \n", "$X_1, X_2, X_3$ are _pair-wise independent_, but not independent.\n", "\n", "- Knowing $X_1, X_2$ gives us complete knowledge of $X_3$.\n", "- However, just knowing $X_1$ tells us nothing about $X_2$, nor can it say anything about $X_3$.\n", "____" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Normal Distribution (Gaussian)\n", "\n", "### Description\n", "\n", "The most important distribution in all statistics, mostly due to the Central Limit Theorem.\n", "\n", "The Central Limit Theorem is surprising; if you sum up a large number of i.i.d. random variables will always look like a bell-shaped curve. This is irrespective of continuous or discrete; beautiful or ugly.\n", "\n", "### Notation\n", "\n", "$X \\sim \\mathcal{N}(\\mu, \\operatorname{Var})$\n", "\n", "### Parameters\n", "\n", "- $\\mu$ mean\n", "- $\\operatorname{Var}$ variance" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAIoCAYAAAA7sh4kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmEL8/7cg+vLSDMSaAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,\n", " AutoMinorLocator)\n", "from scipy.stats import norm\n", "\n", "%matplotlib inline\n", "\n", "plt.xkcd()\n", "\n", "_, ax = plt.subplots(figsize=(12,8))\n", "\n", "# seme Normal parameters\n", "mu_values = [0., 0., 0., -2.]\n", "var_values = [0.4, 1.0, 2.0, 0.5]\n", "params = list(zip(mu_values, var_values))\n", "\n", "# qualitative color scheme\n", "colors = ['#66c2a5', '#fc8d62', '#8da0cb', '#e78ac3']\n", "\n", "x = np.linspace(-6, 6, 500)\n", "for i,(loc,scale) in enumerate(params):\n", " pdf = norm.pdf(x, loc=loc, scale=scale)\n", " ax.plot(x, pdf, color=colors[i], lw=3.2, label=r'$\\mu = {}, \\sigma^2 = {}$'.format(loc, scale))\n", "\n", "# legend styling\n", "legend = ax.legend()\n", "for label in legend.get_texts():\n", " label.set_fontsize('large')\n", "for label in legend.get_lines():\n", " label.set_linewidth(1.5)\n", "\n", "# y-axis\n", "ax.set_ylim([-0.01, 1.0])\n", "ax.set_ylabel(r'$f(X)$')\n", "ax.set_yticks(np.arange(0,1.1,.1))\n", "\n", "# x-axis\n", "ax.set_xlim([-5.0, 5.0])\n", "ax.set_xlabel(r'$X$')\n", "\n", "# x-axis tick formatting\n", "majorLocator = MultipleLocator(1)\n", "majorFormatter = FormatStrFormatter('%d')\n", "minorLocator = MultipleLocator(1)\n", "ax.xaxis.set_major_locator(majorLocator)\n", "ax.xaxis.set_major_formatter(majorFormatter)\n", "ax.xaxis.set_minor_locator(minorLocator)\n", "\n", "ax.grid(color='grey', linestyle='-', linewidth=0.3)\n", "\n", "plt.suptitle(r'Normal PDF: $f(x) = \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{z^{2}}{2}}$')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Probability density function\n", "\n", "For the Standard Normal $\\mathcal{N}(0,1)$\n", "\n", "\\begin{align}\n", " f(z) &= c e^{-\\frac{z^{2}}{2}}\n", "\\end{align}\n", "\n", "where $c$ is the normalizing constant that will let $f(x)$ integrate to 1. \n", "\n", "_But what is $c$?_\n", "\n", "If we can figure out what the integral of the PDF is, then the _inverse_ of that will be the constant $c$ that ensures $f(z) = c e^{-\\frac{z^{2}}{2}} = 1$.\n", "\n", "Consider the indefinite integral of the PDF of $\\mathcal{N}$.\n", "\n", "\\begin{align}\n", " \\int_{-\\infty}^{\\infty} e^{-\\frac{z^2}{2}} ~~ dz\n", "\\end{align}\n", "\n", "There is a theorem that states that this integral, as an indefinite integral, cannot be solved in closed form. But this can be solved...\n", "\n", "First, we start by _multiplying the integral by itself_...\n", "\n", "\\begin{align}\n", " \\int_{-\\infty}^{\\infty} e^{-\\frac{z^2}{2}} ~~ dz \\int_{-\\infty}^{\\infty} e^{-\\frac{z^2}{2}} ~~ dz &= \\int_{-\\infty}^{\\infty} e^{-\\frac{x^2}{2}} ~~ dx \\int_{-\\infty}^{\\infty} e^{-\\frac{y^2}{2}} ~~ dy \\\\\n", " &= \\iint_{-\\infty}^{\\infty} e^{-\\frac{(x+y)^2}{2}} ~~ dxdy \\\\\n", " &= \\int_{0}^{2\\pi} \\int_{0}^{\\infty} e^{-\\frac{r^2}{2}}~ \\underbrace{r}_{\\text{jacobian}} ~ drd\\theta & \\quad \\text{switch to polar} \\\\\n", " &= \\int_{0}^{2\\pi} \\left( \\int_{0}^{\\infty} e^{-u} du \\right) ~ d\\theta & \\quad \\text{let } u = \\frac{r^2}{2} \\text{ , } du = r \\\\\n", " &= \\int_{0}^{2\\pi} \\left( -e^{-\\infty} + e^{-0} \\right) ~ d\\theta \\\\\n", " &= \\int_{0}^{2\\pi} 1 ~ d\\theta \\\\\n", " &= 2 \\pi - 0 \\\\\n", " &= 2\\pi \\\\\n", " \\\\\n", " \\int_{-\\infty}^{\\infty} e^{-\\frac{z^2}{2}} ~~ dz &= \\sqrt{2\\pi} \\\\\n", " \\\\\n", " \\therefore c &= \\boxed{\\frac{1}{\\sqrt{2\\pi}} }\n", "\\end{align}\n", "\n", "\n", "### Expected value\n", "\n", "For the standard normal distribution, $\\mathbb{E}(Z) = 0$. Let's prove that...\n", "\n", "\\begin{align}\n", " \\mathbb{E}(Z) &= \\int_{-\\infty}^{\\infty} z ~ \\frac{e^{-\\frac{z^2}{2}}}{\\sqrt{2\\pi}} ~ dz \\\\\n", " &= \\frac{1}{\\sqrt{2\\pi}} \\int_{-\\infty}^{\\infty} z ~ e^{-\\frac{z^2}{2}} ~ dz \\\\\n", " &= \\frac{1}{\\sqrt{2\\pi}} (0) & \\quad \\text{since this is an odd function} \\\\\n", " &= 0 & \\quad \\blacksquare\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvAAAAHxCAYAAAALEohCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ntzAAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 500)\n", "y = x * (np.e ** ((-x**2)/2))\n", "\n", "_, ax = plt.subplots(figsize=(12,8))\n", "\n", "ax.plot(x, y, color='black')\n", "ax.fill_between(x, y, where=y >= 0, facecolor='blue', interpolate=True)\n", "ax.fill_between(x, y, where=y < 0, facecolor='red', interpolate=True)\n", "ax.axhline(y=0, color='black')\n", "ax.axvline(x=0, color='black')\n", "\n", "# y-axis\n", "ax.set_ylim([-0.7, 0.7])\n", "ax.set_ylabel(r'$g(x)$')\n", "ax.set_yticks(np.arange(-.7,.8,.1))\n", "\n", "# x-axis tick formatting\n", "majorLocator = MultipleLocator(1)\n", "majorFormatter = FormatStrFormatter('%d')\n", "minorLocator = MultipleLocator(1)\n", "ax.xaxis.set_major_locator(majorLocator)\n", "ax.xaxis.set_major_formatter(majorFormatter)\n", "ax.xaxis.set_minor_locator(minorLocator)\n", "\n", "plt.title(\"$g(x)$ is an odd function\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that if $g(x)$ is an _odd function_, then $g(x) + g(-x) = 0$. \n", "\n", "Integrating an odd function $g(x)$ from $-a$ to $a$ is 0, since the portion _above the x-axis_ cancels out the portion _below the x-axis_." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Variance\n", "\n", "For the standard normal distribution, $\\operatorname{Var}(Z) = 1$. Let's prove this as well...\n", "\n", "\\begin{align}\n", " \\operatorname{Var}(Z) &= \\mathbb{E}Z^2 - \\mathbb{E}(Z)^2 \\\\\n", " &= \\int_{-\\infty}^{\\infty} z^2 ~ \\frac{e^{-\\frac{z^2}{2}}}{\\sqrt{2\\pi}} ~ dz - (0)^2 & \\quad \\text{by LOTUS; and by calculations above} \\\\=\n", " &= 2 \\int_{0}^{\\infty} z^2 ~ \\frac{e^{-\\frac{z^2}{2}}}{\\sqrt{2\\pi}} ~ dz & \\quad \\text{this is an even function} \\\\\n", " &= \\frac{2}{\\sqrt{2\\pi}} \\int_{0}^{\\infty} z^2 ~ e^{-\\frac{z^2}{2}} ~ dz & \\quad \\text{set us up for integration by parts} \\\\\n", " &= \\frac{2}{\\sqrt{2\\pi}} \\int_{0}^{\\infty} z ~ z ~ e^{-\\frac{z^2}{2}} ~ dz \\\\\n", " &= \\frac{2}{\\sqrt{2\\pi}} \\int_{0}^{\\infty} u ~ du ~ dv & \\quad \\text{let } u = z \\text{, } \\quad dv = z ~ e^{-\\frac{z^2}{2}} \\\\\n", " & & \\quad du = dz \\text{, } \\quad v = -e^{-\\frac{z^2}{2}} \\\\\n", " &= \\frac{2}{\\sqrt{2\\pi}} \\left( \\left.(uv)\\right\\vert_{0}^{\\infty} - \\int_{0}^{\\infty} v du \\right) \\\\\n", " &= \\frac{2}{\\sqrt{2\\pi}} \\left( 0 + \\int_{0}^{\\infty} e^{-\\frac{z^2}{2}} ~ dz \\right) \\\\\n", " &= \\frac{2}{\\sqrt{2\\pi}} \\left( \\frac{\\sqrt{2\\pi}}{2} \\right) & \\quad \\text{from calculation of normalization constant }c \\\\\n", " &= 1 & \\quad \\blacksquare\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAAHxCAYAAAA7npljAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIiIh6koi4iIiIi4kG/AV75aiITOqjaAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 5, 500)\n", "y = (x**2) * (np.e ** ((-x**2)/2))\n", "\n", "_, ax = plt.subplots(figsize=(12,8))\n", "\n", "ax.plot(x, y, color='black')\n", "ax.fill_between(x, y, where=y >= 0, facecolor='blue', interpolate=True)\n", "ax.axhline(y=0, color='black')\n", "ax.axvline(x=0, color='black')\n", "\n", "# y-axis\n", "ax.set_ylim([-0.01, .8])\n", "ax.set_ylabel(r'$g(x)$')\n", "ax.set_yticks(np.arange(0,.9,.1))\n", "\n", "# x-axis tick formatting\n", "majorLocator = MultipleLocator(1)\n", "majorFormatter = FormatStrFormatter('%d')\n", "minorLocator = MultipleLocator(1)\n", "ax.xaxis.set_major_locator(majorLocator)\n", "ax.xaxis.set_major_formatter(majorFormatter)\n", "ax.xaxis.set_minor_locator(minorLocator)\n", "\n", "plt.title(\"$g(x)$ is an even function\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard Normal Distribution\n", "\n", "This standard normal distribution $\\mathcal{N}(0,1)$ is so important that it has its own name and notation.\n", "\n", "$\\mathcal{Z} \\sim \\mathcal{N}(0,1)$, where mean $\\mu = 0$ and variance $\\sigma^2 = 1$\n", "\n", "### Notation\n", "\n", "The standard normal distribution's CDF is notated by $\\mathbb{\\Phi}(Z)$.\n", "\n", "### Cumulative distribution function\n", "\n", "The cumulative distribution function of $\\Phi(Z)$ is\n", "\n", "\\begin{align}\n", " \\mathbb{\\Phi}(Z) = \\frac{1}{\\sqrt{2\\pi}} \\int_{-\\infty}^{z} e^{-\\frac{t^2}{2}} ~~ dt\n", "\\end{align}\n", "\n", "### Property of $\\Phi(-Z)$\n", "\n", "\\begin{align}\n", " \\mathbb{\\Phi}(-Z) = 1 - \\mathbb{\\Phi}(Z)\n", "\\end{align}\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "View [Lecture 13: Normal distribution | Statistics 110](http://bit.ly/2PmgrWh) on YouTube." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }