確率1 (基礎概念).ipynb

{
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  "name": "",
  "signature": "sha256:7ff7cc0effecc9a36f137c07a289e833b975d97dcbf9b184628f9d148ee774e2"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4eca\u56de\u304b\u3089\u78ba\u7387\u8ad6\u306b\u5165\u3063\u3066\u3044\u304d\u307e\u3059\u3002\u3053\u306e\u30ce\u30fc\u30c8\u3067\u306f\u78ba\u7387\u3001\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3001\u78ba\u7387\u5206\u5e03\u3001\u671f\u5f85\u5024\u30fb\u5206\u6563\u306a\u3069\u78ba\u7387\u8ad6\u306e\u57fa\u672c\u7684\u306a\u8a9e\u5f59\u306e\u78ba\u8a8d\u3092\u3057\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# \u78ba\u7387\u306e\u89e3\u91c8\n",
      "**\u4e8b\u8c61(event)** $A$ \u306e\u751f\u3058\u308b**\u78ba\u7387(probability)**\u3092 $P(\\mathbf{A})$ \u3068\u8868\u8a18\u3059\u308b\u4e8b\u306b\u3057\u307e\u3059\u3002\u305d\u3082\u305d\u3082\u4e8b\u8c61\u3068\u306f\u4e00\u4f53\u4f55\u3067\u3042\u308b\u304b\uff1f\u3068\u3044\u3046\u554f\u984c\u3082\u3042\u308a\u307e\u3059\u304c\u3001\u3068\u308a\u3042\u3048\u305a\u306f\u7d20\u6734\u306b\u300c\u751f\u3058\u305f\u304b\u751f\u3058\u306a\u304b\u3063\u305f\u304b\u3092\u660e\u78ba\u306b\u5224\u65ad\u3067\u304d\u308b\u73fe\u8c61\u300d\u3068\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002\u4f8b\u3048\u3070\u300c\u3042\u308b\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u30661\u306e\u76ee\u304c\u51fa\u308b\u300d\u3068\u3044\u3046\u73fe\u8c61\u306f\u4e8b\u8c61\u3068\u8003\u3048\u3066\u826f\u3044\u3067\u3057\u3087\u3046\u3002\n",
      "\n",
      "\u3055\u3066\u3001\u3067\u306f\u300c\u3042\u308b\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u30661\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u300d\u3068\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\uff1f\u3053\u308c\u306f\u54f2\u5b66\u7684\u306a\u554f\u984c\u3067\u3042\u308a\u3001\u660e\u78ba\u306a\u7b54\u3048\u306f\u3042\u308a\u307e\u305b\u3093\u3002\n",
      "\u3053\u3053\u3067\u306f\u3001**\u983b\u5ea6\u8ad6(frequentism)**\u3068**\u4e3b\u89b3\u8ad6(subjectivism)**\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u983b\u5ea6\u8ad6\n",
      "\u78ba\u7387\u306e\u983b\u5ea6\u8ad6\u7684\u89e3\u91c8\u3068\u306f\u300c\u6570\u3092\u6570\u3048\u308b\u300d\u4e8b\u306b\u57fa\u3065\u304f\u78ba\u7387\u306e\u89e3\u91c8\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u9ad8\u6821\u6570\u5b66\u3067\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u8003\u3048\u65b9\u3092\u3057\u307e\u3057\u305f\n",
      "\n",
      "> \u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u3066\u51fa\u308b\u76ee\u306f6\u901a\u308a\u3042\u308a\u3001\u305d\u308c\u3089\u306f\u540c\u69d8\u306b\u78ba\u304b\u3089\u3057\u3044\u70ba\u30011\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u306f 1/6 \u3067\u3042\u308b\n",
      "\n",
      "\u3053\u3046\u3057\u3066\u6c42\u307e\u308b\u78ba\u7387\u306f **\u7d44\u5408\u305b\u8ad6\u7684\u78ba\u7387(conbinatorial probability)** \u3068\u547c\u3070\u308c\u307e\u3059\u3002\u5b9f\u969b\u306e\u7d71\u8a08\u306e\u554f\u984c\u3067\u306f\u300c\u540c\u69d8\u306b\u78ba\u304b\u3089\u3057\u3044\u300d\u3068\u3044\u3046\u4e8b\u3092\u4eee\u5b9a\u3067\u304d\u308b\u3053\u3068\u304c\u3081\u3063\u305f\u306b\u306a\u3044\u70ba\u3001\u3053\u306e\u8003\u3048\u65b9\u306f\u3042\u307e\u308a\u4f7f\u308f\u308c\u307e\u305b\u3093\u3002\n",
      "\n",
      "\u305d\u306e\u4ee3\u308f\u308a\u306b\u7528\u3044\u3089\u308c\u308b\u306e\u306f **\u7d71\u8a08\u7684\u78ba\u7387(statistical probability)** \u3068\u3044\u3046\u8003\u3048\u65b9\u3067\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u7d71\u8a08\u7684\u78ba\u7387\u3011\n",
      "\n",
      "\u4e92\u3044\u306b\u5f71\u97ff\u3092\u53ca\u307c\u3055\u306a\u3044\u72ec\u7acb\u306a\u8a66\u884c\u3092 $n$ \u56de\u884c\u3063\u305f\u6642\u306b\u3001\u4e8b\u8c61 $A$ \u304c $k$ \u56de\u751f\u3058\u305f\u3068\u3059\u308b\u3002\u3053\u3053\u3067 $n\\rightarrow \\infty$ \u3068\u3057\u305f\u6642\u306b $k/n$ \u304c\u3042\u308b\u5b9a\u6570 $p$ \u306b\u8fd1\u3065\u3044\u3066\u3044\u304f\u306a\u3089\u3070\uff0c $p$ \u3092 \u4e8b\u8c61 $A$ \u306e\u751f\u3058\u308b\u7d71\u8a08\u7684\u78ba\u7387\u3068\u8a00\u3046\u3002\n",
      "\n",
      "----"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u30661\u306e\u76ee\u304c\u51fa\u308b\u7d71\u8a08\u7684\u78ba\u7387\u3092\u8abf\u3079\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4eca\u306f\u672c\u7269\u306e\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u308b\u4e8b\u306f\u51fa\u6765\u306a\u3044\u306e\u3067\u3001\u64ec\u4f3c\u4e71\u6570\u3067\u4ee3\u7528\u3057\u3066\u307f\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "NMAX = 10000\n",
      "rate = []\n",
      "k = 0\n",
      "for n in range(1, NMAX+1):\n",
      "    v = random.randint(1, 6+1) # \u30b5\u30a4\u30b3\u30ed\u3092\u632f\u308b\n",
      "    if v == 1:\n",
      "        k += 1 # 1\u304c\u51fa\u305f\u56de\u6570\u3092\u6570\u3048\u308b\n",
      "    rate.append(float(k)/n)\n",
      "ylim(0.1, 0.3)\n",
      "plot(rate)\n",
      "plot(ones(NMAX)/6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "[<matplotlib.lines.Line2D at 0x641e510>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Oz7PjZVm1Kp6Rscsu27f+MScDQ+PwKV+PZ0n97ndw4YX56cuW5ZfvjjLXS9PHe3f5JRVL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\nSZIkSZIkSVLX/j9JmaQ7SuvNgwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x62c6c90>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u7dd1\u306e\u7dda\u306f $1/6$ \u3067\u3059\u3002\u6700\u521d\u306f $1/6$ \u304b\u3089\u5927\u304d\u304f\u305a\u308c\u3066\u3044\u307e\u3059\u304c\u56de\u6570\u3092\u5897\u3084\u3057\u3066\u3044\u304f\u3068, \u3053\u306e\u5024\u306b\u8fd1\u3065\u3044\u3066\u3044\u304f\u4e8b\u304c\u89b3\u5bdf\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u4e3b\u89b3\u8ad6\n",
      "\u983b\u5ea6\u8ad6\u306e\u826f\u3044\u6240\u306f\u305d\u306e\u5ba2\u89b3\u6027\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u8ab0\u304c\u8a08\u7b97\u3057\u3066\u3082 $P(A)$ \u306f\u540c\u3058\u5024\u306b\u306a\u308a\u307e\u3059(\u5b9f\u969b\u306b\u306f\u7121\u9650\u56de\u306e\u8a66\u884c\u306f\u51fa\u6765\u307e\u305b\u3093\u304c)\u3002\n",
      "\u4e00\u65b9\u3067\u3001\u983b\u5ea6\u8ad6\u7684\u306a\u89e3\u91c8\u304c\u56f0\u96e3\u30fb\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u554f\u984c\u3082\u6ca2\u5c71\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001A\u3055\u3093\u304c\u3042\u308b\u6bba\u4eba\u4e8b\u4ef6\u306e\u72af\u4eba\u3067\u3042\u308b\u78ba\u7387\u3092\u8003\u3048\u305f\u3044\u3068\u3057\u307e\u3057\u3087\u3046\u3002A\u3055\u3093\u304c\u72af\u4eba\u3067\u3042\u308b\u304b\u5426\u304b\u306f\u65e2\u306b\u78ba\u5b9a\u3057\u305f\u4e8b\u67c4\u3067\u3059\u304b\u3089\u3001\u8a66\u884c\u306a\u3069\u3059\u308b\u3053\u3068\u306f\u51fa\u6765\u307e\u305b\u3093\u3002\u4ed6\u306b\u3082\u4f8b\u3048\u3070\u3001B\u3055\u3093\u306b\u3042\u308b\u5546\u54c1\u306e\u5e83\u544a\u3092\u898b\u305b\u305f\u3068\u3057\u3066\u3001\u305d\u308c\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u304f\u308c\u308b\u78ba\u7387\u3092\u8003\u3048\u305f\u3044\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u983b\u5ea6\u8ad6\u7684\u306b\u3053\u306e\u78ba\u7387\u3092\u8003\u3048\u308b\u306a\u3089\u3070\u3001B\u3055\u3093\u306b\u4f55\u56de\u3082(\u4f55\u5343\u56de\u3082)\u540c\u3058\u5e83\u544a\u3092\u898b\u305b\u308b\u3068\u3044\u3046\u8a66\u884c\u304c\u5fc5\u8981\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u305d\u3093\u306a\u3053\u3068\u306f\u307e\u305a\u7121\u7406\u3067\u3059\u3002\n",
      "\n",
      "**\u4e3b\u89b3\u8ad6(subjectivism)**\u3068\u547c\u3070\u308c\u308b\u78ba\u7387\u89e3\u91c8\u3067\u306f\u3001$P(A)$\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u89e3\u91c8\u3057\u307e\u3059\u3002\n",
      "\u3053\u306e\u89e3\u91c8\u306f\u6570\u5b66\u8005**\u30c8\u30fc\u30de\u30b9\u30fb\u30d9\u30a4\u30ba(Thomas Bayes)**\u306e\u540d\u3092\u53d6\u3063\u3066**\u30d9\u30a4\u30ba\u8ad6(Bayesian)**\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u4e3b\u89b3\u7684\u78ba\u7387(\u30d9\u30a4\u30ba\u78ba\u7387)\u3011\n",
      "\n",
      "\u4e8b\u8c61 $A$ \u306e\u751f\u3058\u308b\u78ba\u7387 $P(A)$ \u3068\u306f\u3001$A$ \u304c\u751f\u3058\u308b\u3068\u3044\u3046\u4e8b\u306b\u5bfe\u3059\u308b**\u78ba\u4fe1\u306e\u5ea6\u5408\u3044**\u3092\u6570\u91cf\u5316\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "\u4f8b\u3048\u3070\u3001\u3042\u308b\u6bba\u4eba\u4e8b\u4ef6\u306b\u3064\u3044\u3066 $P(\\text{A\u304c\u72af\u4eba}) = 0.9$ \u306a\u3089\u3070A\u304c\u72af\u4eba\u3060\u3068\u3044\u3046\u4e8b\u3092\u304b\u306a\u308a\u5f37\u304f\u78ba\u4fe1\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u4e8b\u306b\u306a\u308a\u307e\u3059\u3002 $P(\\text{A\u304c\u72af\u4eba})=0.6$ \u306a\u3089\u3070\u3001\u72af\u4eba\u304b\u305d\u3046\u3067\u306a\u3044\u304b\u3068\u8a00\u308f\u308c\u308c\u3070\u72af\u4eba\u3067\u3042\u308b\u3068\u601d\u3046\u3068\u3044\u3046\u611f\u3058\u3067\u3057\u3087\u3046\u304b\u3002 $P(\\text{A\u304c\u72af\u4eba}) = 0.5$ \u306a\u3089\u3070\u3001\u72af\u4eba\u304b\u305d\u3046\u3067\u306a\u3044\u304b\u5168\u304f\u5206\u304b\u3089\u306a\u3044\u3068\u3044\u3046\u4e8b\u3067\u3059\u3002\n",
      "\n",
      "\u4e3b\u89b3\u7684\u306a\u78ba\u7387(\u30d9\u30a4\u30ba\u78ba\u7387)\u306f\u305d\u308c\u3092\u8003\u3048\u308b\u4e3b\u4f53\u306b\u3088\u3063\u3066\u5024\u304c\u5909\u308f\u308a\u3046\u308b\u3068\u3044\u3046\u4e8b\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5ba2\u89b3\u6027\u306e\u4f4e\u3055\u304b\u3089\u79d1\u5b66\u7684\u3067\u306a\u3044\u3068\u6279\u5224\u3055\u308c\u308b\u4e8b\u3082\u591a\u3044\u3067\u3059\u3002\n",
      "\n",
      "\u4e00\u65b9\u3067\u3001\u300c\u30d9\u30a4\u30ba\u8ad6\u306f\u4eba\u9593\u306e\u8003\u3048\u65b9\u306b\u8fd1\u3044\u300d\u3068\u3044\u3046\u610f\u898b\u3082\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u8868\u304c\u51fa\u308b\u78ba\u7387\u304c1/2\u3060\u3068\u4e3b\u5f35\u3059\u308b\u6642\u3001\u79c1\u9054\u306f\u5b9f\u969b\u306b\u306f\u8a66\u884c\u3092\u884c\u3063\u3066\u983b\u5ea6\u3092\u6570\u3048\u305f\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u300c\u8868\u304c\u51fa\u308b\u304b\u88cf\u304c\u51fa\u308b\u304b\u5168\u304f\u4e88\u60f3\u51fa\u6765\u306a\u3044\u304b\u3089$1/2$\u300d\u3068\u3044\u3046\u65b9\u304c\u5b9f\u969b\u306e\u79c1\u9054\u306e\u8003\u3048\u65b9\u306b\u8fd1\u3044\u3067\u3057\u3087\u3046\u3002\n",
      "\u307e\u305f\u3001**\u30d9\u30a4\u30ba\u78ba\u7387\u306f\u65b0\u3057\u3044\u60c5\u5831\u3092\u5f97\u308b\u5ea6\u306b\u5909\u5316\u3059\u308b**\u3068\u3044\u3046\u70b9\u3082\u91cd\u8981\u3067\u3059\u3002\u5148\u307b\u3069\u306e\u4f8b\u3067\u8a00\u3048\u3070\u65b0\u305f\u306a\u8a3c\u62e0\u3092\u5f97\u308b\u5ea6\u306bA\u304c\u72af\u4eba\u3067\u3042\u308b\u78ba\u7387\u306f\u5897\u3048\u305f\u308a\u6e1b\u3063\u305f\u308a\u3059\u308b\u3067\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u983b\u5ea6\u8ad6\u7684\u306a\u8003\u3048\u65b9\u3068\u4e3b\u89b3\u8ad6\u7684\u306a\u8003\u3048\u65b9\u306e\u9055\u3044\u3092\u6b21\u306e\u7c21\u5358\u306a\u554f\u984c\u3067\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\n",
      "\n",
      "> \u78ba\u73871/2\u3067\u8868\u304c\u51fa\u308b\u30b3\u30a4\u30f3\u309210\u56de\u6295\u3052\u305f\u3089\u5168\u3066\u8868\u304c\u51fa\u305f\u3002\u6b21\u306b\u6295\u3052\u3066\u8868\u304c\u51fa\u308b\u78ba\u7387\u306f\uff1f\n",
      "\n",
      "\u983b\u5ea6\u8ad6\u7684\u3067\u306f\u300c10\u56de\u5168\u3066\u8868\u300d\u3068\u3044\u3046\u4e8b\u5b9f\u306f\u610f\u5473\u3092\u6301\u3061\u307e\u305b\u3093\u3002\u8868\u304c\u51fa\u308b\u78ba\u7387\u306f\u3084\u306f\u308a1/2\u3067\u4e0d\u5909\u3067\u3059\u3002\n",
      "\u4e3b\u89b3\u8ad6\u7684\u3067\u306f\u300c10\u56de\u5168\u3066\u8868\u300d\u3068\u3044\u3046\u7d50\u679c\u3092\u53d7\u3051\u3066\u300c\u78ba\u73871/2\u300d\u3068\u3044\u3046\u5f53\u521d\u306e\u4fe1\u5ff5\u3092\u6539\u3081\u308b\u4e8b\u3092\u8a31\u3057\u307e\u3059\u3002\u300c\u5b9f\u306f\u8868\u304c\u51fa\u308b\u78ba\u7387\u306e\u65b9\u304c\u5927\u304d\u3044\u306e\u3067\u306f\u306a\u3044\u304b\uff1f\u300d\u3068\u8003\u3048\u308b\u4e8b\u304c\u53ef\u80fd\u3067\u3059\u3002\u3053\u3053\u3067\u3001\u30d9\u30a4\u30ba\u78ba\u7387\u8ad6\u3067\u306f\u5408\u7406\u7684\u306a\u4fe1\u5ff5\u306e\u6539\u8a02\u65b9\u6cd5\u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3044\u3046\u4e8b\u304c\u91cd\u8981\u3067\u3059\u3002\u4f8b\u3048\u3070\u300c10\u56de\u3082\u8868\u304c\u51fa\u7d9a\u3051\u305f\u306e\u3060\u304b\u3089\u3001\u6b21\u306f\u3055\u3059\u304c\u306b\u88cf\u304c\u51fa\u3084\u3059\u3044\u3060\u308d\u3046\u300d\u3068\u3044\u3046\u8003\u3048\u65b9\u306f\u975e\u5408\u7406\u7684\u3067\u3042\u308b\u4e8b\u304c\u793a\u3055\u308c\u307e\u3059\u3002\u8a73\u3057\u304f\u306f\u5f8c\u3067\u8aac\u660e\u3057\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# \u516c\u7406\u7684\u78ba\u7387\u8ad6\n",
      "\n",
      "\u78ba\u7387\u306e\u89e3\u91c8\u306e\u554f\u984c\u306f\u54f2\u5b66\u7684\u306a\u554f\u984c\u3067\u3059\u3002\u6570\u5b66\u7684\u306b\u78ba\u7387\u3092\u53b3\u5bc6\u306b\u53d6\u308a\u6271\u3046\u5834\u5408\u306b\u306f\u300c\u78ba\u7387\u3068\u306f\u4f55\u3067\u3042\u308b\u304b\uff1f\u300d\u3068\u3044\u3046\u4e8b\u306f\u4e00\u65e6\u5fd8\u308c\u3066\u3001\u300c\u78ba\u7387\u3068\u547c\u3070\u308c\u308b\u4f55\u304b\u304c\u3042\u3063\u305f\u3068\u3057\u3066\u3001\u305d\u308c\u306f\u3069\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6e80\u305f\u3059\u3079\u304d\u304b\uff1f\u300d\u3068\u3044\u3046\u4e8b\u3092\u62bd\u8c61\u7684\u306b\u8a18\u8ff0\u3059\u308b\u4e8b\u304b\u3089\u51fa\u767a\u3057\u307e\u3059\u3002\u3053\u308c\u306f**\u516c\u7406\u7684\u78ba\u7387\u8ad6(axiomatic probability theory)**\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u53b3\u5bc6\u306b\u66f8\u304f\u3068\u975e\u5e38\u306b\u9577\u304f\u306a\u308b\u306e\u3067\u5fc5\u8981\u6700\u5c0f\u9650\u306e\u4e8b\u67c4\u3060\u3051\u66f8\u3044\u3066\u3044\u304d\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u78ba\u7387\u7a7a\u9593\n",
      "\u307e\u305a**\u6a19\u672c\u7a7a\u9593(sample space)**\u3068\u547c\u3070\u308c\u308b\u96c6\u5408 $\\Omega$ \u3092\u8003\u3048\u307e\u3059\u3002$\\Omega$ \u306e\u8981\u7d20\u3092**\u6a19\u672c(sample)**\u3068\u547c\u3073\u307e\u3059\u3002\n",
      "\u7d9a\u3044\u3066**\u4e8b\u8c61\u7a7a\u9593(event space)**\u3068\u547c\u3070\u308c\u308b\u96c6\u5408 $\\mathcal{F}$ \u3092\u8003\u3048\u307e\u3059\u3002$\\mathcal{F}$ \u306e\u500b\u3005\u306e\u5143\u306f $\\Omega$ \u306e\u90e8\u5206\u96c6\u5408\u3067\u3059\u3002\u3053\u308c\u3092**\u4e8b\u8c61(event)**\u3068\u547c\u3073\u307e\u3059\u3002\u4e8b\u8c61 $A,B\\in\\mathcal{F}$ \u304c\u4ea4\u308f\u3089\u306a\u3044($A\\cap B=\\emptyset$)\u6642\u3001\u3053\u308c\u3089\u306f**\u6392\u53cd(exclusive)**\u3067\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002\n",
      "\u4e8b\u8c61$A$\u306e\u88dc\u96c6\u5408$A^c = \\Omega-A$ \u3092**\u4f59\u4e8b\u8c61(complement event)**\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u308c\u306f\u300c$A$\u304c\u8d77\u3053\u3089\u306a\u3044\u300d\u3068\u3044\u3046\u4e8b\u8c61\u3067\u3059\u3002\n",
      "$A,B$ \u306e\u548c\u96c6\u5408 $A\\cup B$ \u3092**\u548c\u4e8b\u8c61(sum event)**\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u308c\u306f\u300c$A$\u307e\u305f\u306f$B$\u304c\u8d77\u3053\u308b\u300d\u3068\u3044\u3046\u4e8b\u8c61\u3067\u3059\u3002\n",
      "$A,B$ \u306e\u7a4d\u96c6\u5408 $A\\cap B$ \u3092**\u7a4d\u4e8b\u8c61(product event)**\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u308c\u306f\u300c$A$\u3082$B$\u3082\u8d77\u3053\u308b\u300d\u3068\u3044\u3046\u4e8b\u8c61\u3067\u3059\u3002\n",
      "$\\mathcal{F}$ \u306f\u5fc5\u305a $\\emptyset$ \u3068 $\\Omega$ \u3092\u542b\u3080\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u3092**\u7a7a\u4e8b\u8c61(empty event)**\u53ca\u3073**\u5168\u4e8b\u8c61(whole event)**\u3068\u547c\u3073\u307e\n",
      "\u3059\u3002\u305d\u308c\u4ee5\u4e0a\u5c0f\u3055\u306a\u4e8b\u8c61\u304c\u7a7a\u4e8b\u8c61\u3057\u304b\u306a\u3044\u3088\u3046\u306a\u4e8b\u8c61\u3092**\u6839\u5143\u4e8b\u8c61(elementary event)**\u3068\u547c\u3073\u307e\u3059\u3002($\\mathcal{F}$ \u306f$\\sigma$-\u5b8c\u5168\u52a0\u6cd5\u65cf\u3068\u3044\u3046\u3082\u306e\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u304c\u3001\u3053\u3053\u3067\u306f\u7701\u7565\u3057\u307e\u3059\u3002)\n",
      "\n",
      "**\u78ba\u7387\u6e2c\u5ea6(probability measure)**(\u3082\u3057\u304f\u306f\u5358\u306b\u78ba\u7387 $P$) \u306f\u5404\u4e8b\u8c61 $A\\in\\mathcal{F}$ \u306b $0$ \u4ee5\u4e0a $1$ \u4ee5\u4e0b\u306e\u5b9f\u6570\u5024 $P(A)$ \u3092\u5272\u308a\u5f53\u3066\u308b\u95a2\u6570 $P:\\mathcal{F}\\rightarrow[0,1]$ \u3067\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3082\u306e\u3067\u3059\u3002\n",
      "\n",
      "1. $P(\\Omega)= 1$\n",
      "2. \u3010\u5b8c\u5168\u52a0\u6cd5\u6027\u3011$A_1,A_2,\\ldots\\in\\mathcal{F}$ \u304c\u6392\u53cd\u306e\u6642 $P\\left(A_1\\cup A_2\\cup\\cdots\\right) = P(A_1)+P(A_2)+\\cdots $\n",
      "\n",
      "\u4ee5\u4e0a $(\\Omega,\\mathcal{F},P)$ \u306e3\u3064\u3067\uff11\u3064\u306e\u78ba\u7387\u7684\u306a\u73fe\u8c61\u304c\u8a18\u8ff0\u3055\u308c\u307e\u3059\u3002\u3053\u308c**\u78ba\u7387\u7a7a\u9593(probability space)**\u3068\u547c\u3073\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u306e\u30e2\u30c7\u30eb\u3092\u4f5c\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u5834\u5408\u306e\u6a19\u672c\u7a7a\u9593\u306f\u4f8b\u3048\u3070$ \\Omega = \\{1,2,3,4,5,6\\}$ \u3068\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "\u4e8b\u8c61\u7a7a\u9593\u306f$\\mathcal{F}=\\{\\emptyset,\\{1\\},\\{2\\},\\{3\\},\\{4\\},\\{5\\},\\{6\\},\\{1,2\\},\\{1,3\\},\\ldots,\\{1,2,3,4,5,6\\}\\}$ \u3068\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "\u78ba\u7387 $P$ \u306f\n",
      "$$P(\\{1\\}) = P(\\{2\\}) = \\cdots = P(\\{6\\}) = \\frac{1}{6}$$\n",
      "\u3068\u3059\u308c\u3070\u5f8c\u306f\u81ea\u52d5\u7684\u306b\u5b9a\u307e\u308a\u307e\u3059\u3002\u4f8b\u3048\u30702\u4ee5\u4e0b\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u306f\u5b8c\u5168\u52a0\u6cd5\u6027\u3092\u4f7f\u3063\u3066\n",
      "\n",
      "$$P(\\{1,2\\})=P(\\{1\\}\\cup\\{2\\})=P(\\{1\\})+P(\\{2\\})=\\frac{1}{6}+\\frac{1}{6}=\\frac{1}{3}$$\n",
      "\n",
      "\u3068\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u78ba\u7387\u6e2c\u5ea6\u306e\u6027\u8cea\n",
      "$P(\\Omega)=1$ \u3068\u5b8c\u5168\u52a0\u6cd5\u6027\u304b\u3089\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6027\u8cea\u304c\u5c0e\u304b\u308c\u307e\u3059\u3002\u8a3c\u660e\u306f\u7701\u7565\u3057\u307e\u3059\u306e\u3067\u3084\u3063\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002\n",
      "\n",
      "1. $P(A^c) = 1-P(A)$\n",
      "2. $P(A\\cup B) = P(A) + P(B) - P(A\\cap B)$\n",
      "3. $A,B$ \u304c\u6392\u53cd\u306e\u6642 $P(A\\cup B) = P(A) + P(B)$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u78ba\u7387\u5206\u5e03\n",
      "\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u3068\u305d\u306e\u78ba\u7387\u3092\u8868\u306b\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "$$\\begin{array}{|c|c|c|c|c|c|c|} \\hline\n",
      "\\text{\u51fa\u76ee} & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline\n",
      "\\text{\u78ba\u7387} & 1/6 & 1/6 & 1/6 & 1/6 & 1/6 & 1/6 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\n",
      "\u3053\u308c\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = array([1,2,3,4,5,6])\n",
      "p = ones(6)/6\n",
      "bar(x, p, width=0.1, align='center')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<Container object of 6 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEACAYAAAC57G0KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x62bcf90>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u6b21\u306f\u30b5\u30a4\u30b3\u30ed\u3092\u4e8c\u3064\u632f\u3063\u305f\u51fa\u76ee\u3068\u78ba\u7387\u306e\u95a2\u4fc2\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\n",
      "\n",
      "$$\\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}\\hline\n",
      "\\text{\u51fa\u76ee\u306e\u548c} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\\\ \\hline\n",
      "\\text{\u78ba\u7387} & 1/36 & 2/36 & 3/36 & 4/36 & 5/36 & 6/36 & 5/36 & 4/36 & 3/36 & 2/36 & 1/36 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\n",
      "\u5bfe\u5fdc\u3059\u308b\u30b0\u30e9\u30d5\u306f\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = array([2,3,4,5,6,7,8,9,10,11,12])\n",
      "p = array([1,2,3,4,5,6,5,4,3,2,1], dtype=float)/36\n",
      "bar(x, p, width=0.1, align='center')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<Container object of 11 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x62bc450>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u3053\u306e\u3088\u3046\u306b**\u6a19\u672c\u304c\u5b9f\u6570\u5024\u3067\u3042\u308b\u5834\u5408**\u306b\u306f\u3001\u78ba\u7387 $P$ \u3092 $x$ \u8ef8\u4e0a\u306e\u5206\u5e03\u3068\u3057\u3066\u6349\u3048\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\u540c\u69d8\u306b\u6a19\u672c\u304c $xy$ \u5e73\u9762\u5185\u306e\u70b9 $(x,y)$ \u3067\u3042\u308b\u3088\u3046\u306a\u5206\u5e03\uff0c $xyz$ \u7a7a\u9593\u5185\u306e\u70b9 $(x,y,z)$ \u3067\u3042\u308b\u69d8\u306a\u5206\u5e03\u306a\u3069\u3092\u8003\u3048\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\u4e00\u822c\u306b\u6a19\u672c\u7a7a\u9593\u304c $\\mathbb{R}^n$ \u3067\u3042\u308b\u69d8\u306a\u78ba\u7387\u901f\u5ea6 $P$ \u3092 $n$ \u6b21\u5143**\u78ba\u7387\u5206\u5e03(probability distribution)**\u3068\u547c\u3073\u3001\u6a19\u672c\u3092\u8868\u3059\u5909\u6570 $\\mathbf{X}$ \u3092**\u78ba\u7387\u5909\u6570(probability variable)**\u3068\u547c\u3073\u307e\u3059\u3002\n",
      "\n",
      "\u4eca\u306e\u30b5\u30a4\u30b3\u30ed\u306e\u4f8b\u306e\u3088\u3046\u306b\u98db\u3073\u98db\u3073\u306e\u4e00\u70b9\u3067\u306e\u307f $0$ \u4ee5\u5916\u306e\u5024\u3092\u53d6\u308b\u3088\u3046\u306a\u78ba\u7387\u5206\u5e03\u3092**\u96e2\u6563\u78ba\u7387\u5206\u5e03(discrete probability distribution)**\u3068\u547c\u3073\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u9023\u7d9a\u78ba\u7387\u5206\u5e03\n",
      "\u96e2\u6563\u7684\u3067\u306f\u306a\u3044\u78ba\u7387\u5206\u5e03\u3092**\u9023\u7d9a\u7684\u78ba\u7387\u5206\u5e03(continuous probability distribution)**\u3068\u547c\u3073\u307e\u3059\u3002\n",
      "\u9023\u7d9a\u7684\u78ba\u7387\u5206\u5e03\u306b\u304a\u3051\u308b\u78ba\u7387\u306f\u4e00\u70b9\u6bce\u3067\u306f\u306a\u304f\u3001 $P(a \\leq X \\leq b)$ \u306a\u3069\u306e\u3088\u3046\u306b\u533a\u9593\u306b\u5bfe\u3057\u3066\u4e0e\u3048\u307e\u3059\u3002\u6a19\u672c\u304c\u7121\u9650\u500b\u5b58\u5728\u3059\u308b\u70ba\u3001\u7279\u5b9a\u306e\u4e00\u70b9\u304c\u9078\u3070\u308c\u308b\u78ba\u7387\u306f $0$ \u3067\u3042\u308b\u304b\u3089\u3067\u3059\u3002\u78ba\u7387\u5909\u6570 $X$ \u306b\u5bfe\u3057\u3066\u95a2\u6570\n",
      "\n",
      "$$ F(x) = P(X \\leq x) $$\n",
      "\n",
      "\u3092**\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570(cumulative distribution function)**\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u308c\u304c\u4e0e\u3048\u3089\u308c\u308c\u3070\n",
      "\n",
      "$$ P(a\\leq X \\leq b) = P(X\\leq b) - P(X\\leq a) = F(b) - F(a) $$\n",
      "\n",
      "\u306b\u3088\u3063\u3066\u4efb\u610f\u306e\u533a\u9593\u306e\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\u307e\u305f\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306e\u5c0e\u95a2\u6570\n",
      "\n",
      "$$ \\pi(x) = \\frac{\\mathrm{d}}{\\mathrm{d}x}F(x) $$\n",
      "\n",
      "\u3092**\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570(probability density function)** \u3068\u547c\u3073\u307e\u3059\u3002\u3064\u307e\u308a\n",
      "\n",
      "$$ F(x) = \\int_{-\\infty}^x \\pi(x)\\mathrm{d} x $$\n",
      "\n",
      "\u3067\u3059\u306e\u3067\n",
      "\n",
      "$$\\color{red}{ P(a\\leq X\\leq b) = \\int_a^b \\pi(x)\\mathrm{d} x } $$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u533a\u9593 $[a,b]$ \u306b\u304a\u3044\u3066 $y=\\pi(x)$ \u3068 $x$ \u8ef8\u3067\u56f2\u307e\u308c\u308b\u533a\u9593\u306e\u9762\u7a4d\u304c $P(a\\leq X\\leq b)$ \u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u4f8b\u3048\u3070\u533a\u9593 $[0,1]$ \u304b\u3089\u7121\u4f5c\u70ba\u306b\u4e00\u70b9\u3092\u9078\u3076\u3068\u3044\u3046\u8a66\u884c\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u6642\u3001\u4efb\u610f\u306e\u70b9 $x=a$ \u306b\u5bfe\u3057\u3066 $P(x=a)=0$ \u3067\u3059\u3002\u4f8b\u3048\u3070\u7121\u9650\u500b\u3042\u308b\u70b9\u306e\u4e2d\u304b\u3089 $x=\\pi=3.141592\\cdots$ \u304c\u30d4\u30c3\u30bf\u30ea\u9078\u3070\u308c\u308b\u78ba\u7387\u306f $0$ \u3067\u3059\u3002\u5f93\u3063\u3066\u9023\u7d9a\u5206\u5e03\u3067\u306f\u4e00\u70b9\u6bce\u306b\u8003\u3048\u3066\u3082\u610f\u5473\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u4e00\u65b9\u3001$[0,1]$ \u5185\u306b\u3042\u308b\u533a\u9593 $[a,b]$ \u5185\u306e\u70b9\u304c\u9078\u3070\u308c\u308b\u78ba\u7387\u306f\u305d\u306e\u9577\u3055 $b-a$ \u306b\u6bd4\u4f8b\u3057\u307e\u3059\u3002 $P(0\\leq x\\leq 1)=1$ \u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308c\u3070\n",
      "\n",
      "$$ P(a\\leq x\\leq b) = b-a \\qquad (0\\leq a\\leq b\\leq 1)$$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\n",
      "\n",
      "$$ \\pi(x) = \\left\\{\\begin{array}{ll}\n",
      "0 & (x < 0\\text{\u307e\u305f\u306f}1 < x) \\\\\n",
      "1 & (0\\leq x \\leq 1) \\\\\n",
      "\\end{array}\\right. $$\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(-1, 2)\n",
      "p = 0*x\n",
      "p[logical_and(0 <= x, x <= 1)] = 1\n",
      "ylim(0, 2)\n",
      "plot(x, p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "[<matplotlib.lines.Line2D at 0x641a450>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n5k+SJEmSJEmSJEmSJEmSJEmSJElSav4P2yijPeMakuYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x641a310>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u5909\u6570\u5909\u63db\n",
      "\n",
      "\u78ba\u7387\u5909\u6570\u3092\u4ed6\u306e\u78ba\u7387\u5909\u6570\u306b\u5909\u63db\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\n",
      "\n",
      "\u78ba\u7387\u5909\u6570 $X$ \u306e\u5bc6\u5ea6\u95a2\u6570\u304c $\\pi_X(x)$, \u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u304c $F_X(x)$ \u3001\u78ba\u7387\u5909\u6570 $Y$ \u306e\u5bc6\u5ea6\u95a2\u6570\u304c $\\pi_Y(y)$, \u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u304c $F_Y(y)$ \u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u3053\u3067 $X,Y$ \u306e\u9593\u306b $X=g(Y)$ \u306e\u95a2\u4fc2\u304c\u3042\u308b\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u975e\u5e38\u306b\u72ed\u3044\u533a\u9593\u3067\u306f $g$ \u306f\u5358\u8abf\u5897\u52a0\u304b\u5358\u8abf\u6e1b\u5c11\u3067\u3042\u308b\u3068\u8003\u3048\u3066\u826f\u3044\u306e\u3067\n",
      "\n",
      "$$ P(y \\leq Y \\leq y+\\mathrm{d}y) = P(y \\leq g^{-1}(X)\\leq y+\\mathrm{d}y) = P(g(y)\\leq X \\leq g(y+\\mathrm{d}y))\\text{\u307e\u305f\u306f}P(g(y+\\mathrm{d}y)\\leq X\\leq g(y))$$\n",
      "\n",
      "\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u7528\u3044\u3066\u66f8\u304d\u76f4\u305b\u3070\n",
      "\n",
      "$$ F_Y(y+\\mathrm{d}x)-F_Y(y) = |F_X(g(y+\\mathrm{d}y))-F_X(g(y))|$$\n",
      "\n",
      "\u3064\u307e\u308a\n",
      "\n",
      "$$ \\frac{F_Y(y+\\mathrm{d}y)-F_Y(y)}{\\mathrm{d} y} = \\left|\\frac{F_X(g(y+\\mathrm{d}y))-F_X(g(y))}{\\mathrm{d}y}\\right|$$\n",
      "\n",
      "\u3067\u3059\u306e\u3067\n",
      "\n",
      "$$ F_Y'(y) = |g'(y)F_X'(g(y))| $$\n",
      "\n",
      "\u3064\u307e\u308a\n",
      "\n",
      "$$ \\pi_Y(y) = |g'(y)|\\pi_x(g(y))\\qquad(\\because \\pi_x(g(y)) \\geq 0)$$\n",
      "\n",
      "\u306b\u3088\u3063\u3066\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u5909\u63db\u304c\u51fa\u6765\u307e\u3059\u3002\u591a\u5909\u6570\u306e\u5834\u5408\u3082\u540c\u69d8\u3067\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u5909\u6570\u5909\u63db\u3011\n",
      "\n",
      "\u78ba\u7387\u5909\u6570 $X,Y$ \u306e\u9593\u306b $X=g(Y)$ \u306e\u95a2\u4fc2\u304c\u3042\u308b\u6642\u3001\u5bc6\u5ea6\u95a2\u6570\u306b\u3064\u3044\u3066\n",
      "$$\\pi_Y(y) = |g'(y)|\\pi_X(g(y))$$\n",
      "\u304c\u6210\u308a\u7acb\u3064\u3002\n",
      "\n",
      "$n$ \u6b21\u5143\u78ba\u7387\u5909\u6570 $\\mathbf{X},\\mathbf{Y}$ \u306e\u9593\u306b $\\mathbf{X}=\\mathbf{g}(\\mathbf{Y})$ \u306e\u95a2\u4fc2\u304c\u3042\u308b\u6642\u3001\u5bc6\u5ea6\u95a2\u6570\u306b\u3064\u3044\u3066\n",
      "$$\\pi_{\\mathbf{Y}}(\\mathbf{y}) = |\\mathrm{def}\\mathrm{J}_{\\mathbf{g}}(\\mathbf{y})|\\pi_{\\mathbf{X}}(\\mathbf{g}(\\mathbf{Y}))$$\n",
      "\u304c\u6210\u308a\u7acb\u3064\u3002\u4f46\u3057 $\\mathrm{J}_{\\mathbf{g}}$ \u306f $g$ \u306e**\u30e4\u30b3\u30d3\u884c\u5217(Jacobian matrix)**\u3067\u3042\u308a\n",
      "\n",
      "$$ \\mathrm{J}_{\\mathbf{g}}(\\mathbf{y}) \\stackrel{\\mathrm{def}}{=} \\begin{pmatrix}\n",
      "\\frac{\\partial g_1}{\\partial y_1} & \\frac{\\partial g_1}{\\partial y_2} & \\cdots & \\frac{\\partial g_1}{\\partial y_n} \\\\\n",
      "\\frac{\\partial g_2}{\\partial y_1} & \\frac{\\partial g_2}{\\partial y_2} & \\cdots & \\frac{\\partial g_2}{\\partial y_n} \\\\\n",
      "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
      "\\frac{\\partial g_n}{\\partial y_1} & \\frac{\\partial g_n}{\\partial y_2} & \\cdots & \\frac{\\partial g_n}{\\partial y_n} \\\\\n",
      "\\end{pmatrix} $$\n",
      "\n",
      "----"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u78ba\u7387\u5909\u6570 $X$ \u3092 \u533a\u9593 $[0,1]$ \u304b\u3089\u306e\u30e9\u30f3\u30c0\u30e0\u306a\u5b9f\u6570\u3068\u3059\u308b\u3002\u3053\u306e\u6642$Y=X^2$ \u306f\u3069\u306e\u3088\u3046\u306a\u5206\u5e03\u306b\u5f93\u3046\u3067\u3057\u3087\u3046\u304b\uff1f\n",
      "\n",
      "\u5148\u307b\u3069\u3084\u3063\u305f\u3088\u3046\u306b $X$ \u306e\u5bc6\u5ea6\u95a2\u6570\u306f\n",
      "$$\\pi_X(x) =  \\left\\{\\begin{array}{ll}\n",
      "0 & (x < 0\\text{\u307e\u305f\u306f}1 < x) \\\\\n",
      "1 & (0\\leq x \\leq 1) \\\\\n",
      "\\end{array}\\right. $$\n",
      "\u3067\u3059\u3002\u3053\u3053\u3067 $X=\\sqrt{Y}$ \u306e\u95a2\u4fc2\u304c\u3042\u308b\u306e\u3067\n",
      "\n",
      "$$\\pi_Y(y) = \\left|\\frac{1}{2\\sqrt{y}}\\right|\\pi_X(\\sqrt{y}) = \n",
      " \\left\\{\\begin{array}{ll}\n",
      "0 & (\\sqrt{y} < 0\\text{\u307e\u305f\u306f}1 < \\sqrt{y}) \\\\\n",
      "\\frac{1}{2\\sqrt{y}} & (0\\leq \\sqrt{y} \\leq 1) \\\\\n",
      "\\end{array}\\right. =\n",
      " \\left\\{\\begin{array}{ll}\n",
      "0 & (y > 1) \\\\\n",
      "\\frac{1}{2\\sqrt{y}} & (0\\leq y \\leq 1) \\\\\n",
      "\\end{array}\\right. $$\n",
      "\u304c\u6c42\u3081\u308b\u5bc6\u5ea6\u95a2\u6570\u3067\u3059\u3002\u4ee5\u4e0b\u3067\u5b9f\u9a13\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10000\n",
      "X = random.uniform(0, 1, N)  # \u533a\u9593[0,1]\u304b\u3089N\u30b5\u30f3\u30d7\u30eb\u53d6\u308b\n",
      "Y = X**2 # \u5024\u3092\u5909\u63db\u3059\u308b\n",
      "hist(Y, bins=20, normed=True) #Y\u306e\u5206\u5e03(\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0)\u3092\u4f5c\u6210\n",
      "\n",
      "x = linspace(0, 1)\n",
      "plot(x, 1/(2*sqrt(x)), color='red', label=u'\u03c0(y)=1/2\u221ay')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.legend.Legend at 0x693a610>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yqKgwO5/k5Ia/gvynzp0DL6ekhP1fbyfc7WyhbZi7uiuAScBqYNCFqy3wWy7w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\nEREREREREREREREREREREZF48P8BP5+7U/yd2/8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6947110>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "## \u540c\u6642\u5206\u5e03\u3001\u5468\u8fba\u5316\n",
      "\u4e8b\u8c61 $A,B$ \u306b\u5bfe\u3057\u3066 $P(A\\cap B)$ \u3092 $A,B$ \u306e**\u540c\u6642\u78ba\u7387(joint probability)**\u3068\u547c\u3073 $P(A,B)$ \u3068\u66f8\u304d\u307e\u3059\u3002$A_1,A_2,\\ldots,A_n$ \u306b\u5bfe\u3059\u308b\u540c\u6642\u78ba\u7387 $P(A_1,A_2,\\ldots,A_n)$ \u3082\u540c\u69d8\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\n",
      "\n",
      "$n$ \u6b21\u5143\u306e\u78ba\u7387\u5909\u6570 $\\mathbf{X}=(X_1,X_2,\\ldots,X_n)^T$ \u306e\u5f93\u3046\u78ba\u7387\u5206\u5e03\u3092 $X_1,X_2,\\ldots,X_n$ \u306e**\u540c\u6642\u5206\u5e03(joint distribution)**\u3068\u547c\u3073\u307e\u3059\u3002\u540c\u6642\u5206\u5e03\u306e\u78ba\u7387\u6e2c\u5ea6\u3092\u3042\u308b\u5909\u6570\u306b\u3064\u3044\u3066\u8db3\u3057\u5408\u308f\u305b\u308b\u4e8b\u3092**\u5468\u8fba\u5316(marginalization)**\u3068\u547c\u3073\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u78ba\u7387\u5206\u5e03\u3092\u8003\u3048\u307e\u3059\u3002\n",
      "$$ \\begin{array}{|c|c|c|c|}\\hline\n",
      "    & X=0  & X=1 & X=2 \\\\ \\hline\n",
      "Y=0 & 2/12 & 3/12 & 2/12 \\\\ \\hline\n",
      "Y=1 & 3/12 & 1/12 & 1/12 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\u3053\u308c\u3092 $Y$ \u306b\u3064\u3044\u3066\u8db3\u3057\u5408\u308f\u305b\u308b($Y$ \u306b\u3064\u3044\u3066\u5468\u8fba\u5316\u3059\u308b)\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b $X$ \u306e\u78ba\u7387\u5206\u5e03\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\n",
      "$$ \\begin{array}{|c|c|c|}\\hline\n",
      "X=0  & X=1 & X=2 \\\\ \\hline\n",
      "5/12 & 4/12 & 3/12 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\u540c\u69d8\u306b $X$ \u306b\u3064\u3044\u3066\u5468\u8fba\u5316\u3059\u308b\u3068 $Y$ \u306e\u78ba\u7387\u5206\u5e03\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\n",
      "$$ \\begin{array}{|c||c|c|c|}\\hline\n",
      "Y=0 & 7/12 \\\\ \\hline\n",
      "Y=1 & 5/12 \\\\ \\hline\n",
      "\\end{array}$$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u4ee5\u4e0b\u306e\u5bc6\u5ea6\u95a2\u6570\u3067\u8868\u3055\u308c\u308b\u9023\u7d9a\u5206\u5e03\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002\u5f8c\u306e\u56de\u306b\u8aac\u660e\u3057\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\u3068\u547c\u3070\u308c\u308b\u3082\u306e\u306e\uff11\u3064\u3067\u3059\u3002\n",
      "\n",
      "$$\\pi(x, y) = 360xy^2(1-x-y) $$\n",
      "\n",
      "\u4f46\u3057\u3001$x,y\\geq 0, x+y\\leq 1$ \u4ee5\u5916\u3067\u306e\u5bc6\u5ea6\u306f $0$ \u3067\u3059\u3002\u3053\u308c\u3092 $y$ \u306b\u3064\u3044\u3066\u5468\u8fba\u5316\u3059\u308b\u3068\u3044\u3046\u3053\u3068\u306f $y$ \u306b\u3064\u3044\u3066\u7a4d\u5206\u3059\u308b\u3068\u3044\u3046\u4e8b\u3067\u3059\u3002\n",
      "\n",
      "$$\\pi(x) = \\int_0^{1-x}360xy^2(1-x-y)\\mathrm{d} y = 30x(1-x)^4$$\n",
      "\n",
      "\u540c\u69d8\u306b $x$ \u3064\u3044\u3066\u5468\u8fba\u5316\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "$$\\pi(y) = \\int_0^{1-x}360xy^2(1-x-y)\\mathrm{d}x = 60y^2(1-y)^3$$\n",
      "\n",
      "\u3053\u306e\u69d8\u5b50\u3092\u56f3\u793a\u3057\u3066\u307f\u308b\u3068\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "fig = figure()\n",
      "ax = Axes3D(fig)\n",
      "X, Y = meshgrid(linspace(0, 1, 20), linspace(0, 1, 20))\n",
      "xlim(0, 1)\n",
      "ylim(0, 1)\n",
      "Z = 360*X*Y**2*(1-X-Y)\n",
      "Z[X+Y>1]=0\n",
      "ax.plot_wireframe(X, Y, Z)\n",
      "\n",
      "x = linspace(0, 1)\n",
      "y = 30*x*(1-x)**4\n",
      "ax.plot(x, y, zs=0, zdir='x', c='red')\n",
      "\n",
      "x = linspace(0, 1)\n",
      "y = 60*x**2*(1-x)**3\n",
      "ax.plot(x, y, zs=1, zdir='y', c='green')\n",
      "ax.view_init(elev=45)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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evXsZMWIEEAjmGj16NIMGDUr6uvFgCl85GIaB3+8PuvpUVa2wDFg8RZ0rInQB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\nY/TaAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6d93510>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u3061\u306a\u307f\u306b\u3001\u4eca\u306e\u69d8\u306a\u7a4d\u5206\u8a08\u7b97\u306f[Maxima](http://maxima.sourceforge.net/)\u306a\u3069\u306e\u6570\u5f0f\u51e6\u7406\u30b7\u30b9\u30c6\u30e0\u306b\u884c\u308f\u305b\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u306e\u3067\u3001\u8a66\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002Python\u306b\u3082[SymPy](http://sympy.org/en/index.html)\u3068\u3044\u3046\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306f\n",
      "\n",
      "$$\\pi(x) = \\int_0^{1-x}360xy^2(1-x-y)\\mathrm{d} y = 30x(1-x)^4$$\n",
      "\n",
      "\u306e\u8a08\u7b97\u3092SymPy\u3067\u3084\u3063\u305f\u4f8b\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import  sympy\n",
      "x = sympy.Symbol('x')\n",
      "y = sympy.Symbol('y')\n",
      "pxy = 360 * x *y**2 * (1-x-y) # \u03c0(x,y)\n",
      "px = sympy.integrate(pxy, (y, 0, 1-x)) # y\u306b\u3064\u3044\u3066\u7a4d\u5206\n",
      "sympy.factor(px) # \u7d50\u679c\u3092\u56e0\u6570\u5206\u89e3\u3057\u3066\u8868\u793a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "30*x*(x - 1)**4"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u30fb\u6761\u4ef6\u4ed8\u304d\u5206\u5e03\n",
      "\n",
      "\u4e8b\u8c61 $A,B$ \u306b\u5bfe\u3057\u3066 $P(A)>0$ \u306e\u6642\n",
      "\n",
      "$$P(B|A) \\stackrel{\\mathrm{def}}{=} \\frac{P(A,B)}{P(A)}$$\n",
      "\n",
      "\u3092 $A$ \u304c\u4e0e\u3048\u3089\u308c\u305f\u6642\u306e $B$ \u306e**\u6761\u4ef6\u4ed8\u304d\u78ba\u7387(conditional probability)**\u3068\u547c\u3073\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u30b5\u30a4\u30b3\u30ed\u306e\u76ee\u304c\u5947\u6570\u3060\u3068\u5206\u304b\u3063\u3066\u3044\u308b\u6642\u306b\u3001\u305d\u308c\u304c $4$ \u4ee5\u4e0a\u3067\u3042\u308b\u78ba\u7387\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\u307e\u305a\n",
      "$$P(\\text{\u5947\u6570}) = \\frac{1}{2}$$\n",
      "\u3067\u3059\u3002\u307e\u305f\u3001\n",
      "$$P(\\text{\u5947\u6570},\\text{4\u4ee5\u4e0a}) = \\frac{1}{6}$$\n",
      "\u3067\u3059\u3002\u5f93\u3063\u3066\n",
      "$$P(\\text{4\u4ee5\u4e0a}|\\text{\u5947\u6570}) = \\frac{1/6}{1/2} = \\frac{1}{3}$$\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u78ba\u7387\u5206\u5e03\u306b\u5bfe\u3059\u308b**\u6761\u4ef6\u4ed8\u304d\u5206\u5e03(conditional distribution)**\u3082\u540c\u69d8\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u5148\u307b\u3069\u306e\u9023\u7d9a\u5206\u5e03$\\pi(x, y) = 360xy^2(1-x-y) $\u306b\u5bfe\u3057\u3066\u6761\u4ef6\u4ed8\u304d\u5206\u5e03 $\\pi(x|y=1/2)$ \u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u307e\u305a\n",
      "$$\\pi(x, y=1/2) = 360x\\left(\\frac{1}{2}\\right)^2\\left(1-x-\\frac{1}{2}\\right) = 45x(1-2x)$$\n",
      "\u3067\u3059\u3002\u307e\u305f\u3001$\\pi(y) = 60y^2(1-y)^3$ \u3060\u3063\u305f\u306e\u3067\n",
      "$$\\pi(y=1/2) = 60\\left(\\frac{1}{2}\\right)^2\\left(1-\\frac{1}{2}\\right)^3 = \\frac{15}{8}$$\n",
      "\u3067\u3059\u3002\u5f93\u3063\u3066\n",
      "\n",
      "$$\\pi(x|y=1/2) = \\frac{\\pi(x, y=1/2)}{\\pi(y=1/2)} = 24x(1-2x)$$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002 $x+y\\leq 1$ \u306a\u306e\u3067 $x$ \u306e\u52d5\u304f\u7bc4\u56f2\u306f $[0,1/2]$ \u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u72ec\u7acb\u6027\u30fb\u4e57\u6cd5\u5b9a\u7406\n",
      "\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u30fb\u6761\u4ef6\u4ed8\u304d\u5206\u5e03\u306e\u516c\u5f0f\u3088\u308a\n",
      "\n",
      "$$ P(A,B) = P(A)P(B|A) $$\n",
      "\n",
      "\u3084\n",
      "\n",
      "$$ \\pi(x,y)=\\pi(y)\\pi(x|y)$$\n",
      "\n",
      "\u306a\u3069\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3053\u308c\u3092\u78ba\u7387\u30fb\u78ba\u7387\u5206\u5e03\u306e**\u4e57\u6cd5\u5b9a\u7406(multiplication theorem)**\u3068\u547c\u3073\u307e\u3059\u3002\n",
      "\u3053\u3053\u3067\n",
      "\n",
      "$$ P(A,B) = P(A)P(B) $$\n",
      "\n",
      "\u304c\u6210\u308a\u7acb\u3064\u6642\u3001\u4e8b\u8c61 $A,B$ \u306f**\u72ec\u7acb(independent)**\u3067\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002\u72ec\u7acb\u3067\u306a\u3044\u4e8b\u3092**\u5f93\u5c5e(dependent)**\u3067\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002\u5225\u306e\u5f0f\u3067\u8868\u305b\u3070$A,B$ \u304c\u72ec\u7acb\u3067\u3042\u308b\u3068\u306f $P(B)=P(B|A)$ \u304c\u6210\u308a\u7acb\u3064\u4e8b\u3067\u3059\u3002\u3064\u307e\u308a\u3001$A$\u304c\u751f\u3058\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3082\u3001$B$\u304c\u751f\u3058\u308b\u78ba\u7387\u306b\u4f55\u306e\u5f71\u97ff\u3082\u53ca\u307c\u3055\u306a\u3044\u3068\u3044\u3046\u4e8b\u3067\u3059\u3002\u540c\u69d8\u306b\u78ba\u7387\u5909\u6570\u306b\u5bfe\u3059\u308b\u72ec\u7acb\u6027\u3082\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\n",
      "\n",
      "$X_1,\\ldots,X_n$ \u304c\u540c\u4e00\u306a\u5206\u5e03\u306b\u5f93\u3046\u72ec\u7acb\u306a\u78ba\u7387\u5909\u6570\u3067\u3042\u308b\u3053\u3068\u3092**\u72ec\u7acb\u540c\u5206\u5e03(independent and identically distributed)**\u3067\u3042\u308b\u3068\u547c\u3073\u3001\u300c$X_1,\\ldots,X_n$ \u304ci.i.d.\u306e\u6642\u300d\u3068\u304b\u300c$X_1,\\ldots,X_n\\stackrel{\\text{i.i.d.}}{\\sim}P$\u306e\u6642\u300d\u306a\u3069\u3068\u66f8\u304d\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u30d9\u30a4\u30ba\u306e\u5b9a\u7406\n",
      "\n",
      "\u78ba\u7387\u306e\u4e57\u6cd5\u5b9a\u7406\u3088\u308a\uff0c\u4e8b\u8c61 $A,B$ \u306b\u5bfe\u3057\u3066 $P(A)>0,P(B)>0$ \u306e\u6642\n",
      "\n",
      "$$ P(A)P(B|A) = P(B)P(A|B) \\quad(=P(A,B))$$\n",
      "\n",
      "\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u5f93\u3063\u3066\n",
      "\n",
      "$$\\color{red}{ P(B|A) = \\frac{P(A|B)}{P(A)} P(B) } $$\n",
      "\n",
      "\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3053\u308c\u3092**\u30d9\u30a4\u30ba\u306e\u5b9a\u7406(Bayes's theorem)**\u3068\u8a00\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u516c\u7406\u7684\u78ba\u7387\u8ad6\u306e\u5b9a\u7406\u3067\u3042\u308a\u78ba\u7387\u306e\u89e3\u91c8\u306b\u5bc4\u3089\u305a\u6210\u7acb\u3059\u308b\u306e\u3067\u3059\u304c\u3001\u4e3b\u89b3\u8ad6\u306e\u7acb\u5834\u3067\u306e\u89e3\u91c8\u304c\u91cd\u8981\u3067\u3059\u3002\n",
      "\n",
      "$P(B)$ \u306f $A$ \u306b\u3064\u3044\u3066\u4f55\u3082\u77e5\u3089\u306a\u3044\u72b6\u6cc1\u3067\u306e $B$ \u306e\u8d77\u3053\u308b\u78ba\u7387\u3067\u3042\u308a\u3001**\u4e8b\u524d\u78ba\u7387(prior probability)**\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u4e00\u65b9 $P(B|A)$ \u306f $A$ \u304c\u751f\u3058\u305f\u3068\u3044\u3046\u4e8b\u3092\u77e5\u3063\u305f\u4e0a\u3067\u306e $B$ \u306e\u8d77\u3053\u308b\u78ba\u7387\u3067\u3042\u308a\u3001**\u4e8b\u5f8c\u78ba\u7387(posterior probability)**\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u306f**\u65b0\u305f\u306a\u77e5\u8b58\u3092\u5f97\u308b\u4e8b\u306b\u3088\u308b\u4fe1\u5ff5\u306e\u6539\u8a02**\u306e\u6cd5\u5247\u3092\u8868\u3057\u3066\u3044\u308b\u3068\u8003\u3048\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "1000\u4eba\u306b1\u4eba\u306e\u5272\u5408\u3067\u767a\u75c7\u3059\u308b\u764c\u306b\u306a\u3063\u3066\u3044\u308b\u78ba\u7387 $P(\\text{\u30ac\u30f3})$ \u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002\u4f55\u3082\u77e5\u3089\u306a\u3044\u72b6\u614b\u3067\u306e\u4e8b\u524d\u78ba\u7387\u306f $P(\\text{\u30ac\u30f3})=0.001$ \u3068\u306a\u308a\u307e\u3059\u3002\n",
      "\u3053\u3053\u3067\u300199%\u306e\u6b63\u78ba\u3055\u306e\u691c\u8a3a\u3092\u53d7\u3051\u3066\u967d\u6027\u3068\u5224\u5b9a\u3055\u308c\u305f\u6642\u306e\u4e8b\u5f8c\u78ba\u7387 $P(\\text{\u30ac\u30f3}|\\text{\u967d\u6027})$ \u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\u307e\u305a\n",
      "\n",
      "$$ P(\\text{\u967d\u6027}|\\text{\u30ac\u30f3}) = 0.99\\qquad(\\text{99%\u6b63\u78ba}) $$\n",
      "\n",
      "\u3067\u3059\u3002\u307e\u305f, \u967d\u6027\u5224\u5b9a\u304c\u51fa\u308b\u306e\u306f\u300c\u30ac\u30f3\u3092\u767a\u75c7\u3057\u3066\u304a\u308a\u8a3a\u65ad\u304c\u6b63\u3057\u3044\u5834\u5408\u300d\u3068\u300c\u30ac\u30f3\u3092\u767a\u75c7\u3057\u3066\u3044\u306a\u3044\u306e\u306b\u8a3a\u65ad\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u5834\u5408\u300d\u306e\uff12\u901a\u308a\u3067\u3059\u304b\u3089\n",
      "\n",
      "$$ P(\\text{\u967d\u6027}) = P(\\text{\u967d\u6027},\\text{\u30ac\u30f3}) + P(\\text{\u967d\u6027},\\text{\u30ac\u30f3\u3067\u306a\u3044}) = P(\\text{\u967d\u6027}|\\text{\u30ac\u30f3})P(\\text{\u30ac\u30f3}) + P(\\text{\u967d\u6027}|\\text{\u30ac\u30f3\u3067\u306a\u3044})P(\\text{\u30ac\u30f3\u3067\u306a\u3044}) = 0.99\\times 0.001 + 0.01\\times 0.999 = 0.01098$$\n",
      "\n",
      "\u3067\u3059\u3002\u5f93\u3063\u3066\u3001\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u3088\u308a\u6c42\u3081\u308b\u4e8b\u5f8c\u78ba\u7387\u306f\n",
      "\n",
      "$$P(\\text{\u30ac\u30f3}|\\text{\u967d\u6027}) = \\frac{P(\\text{\u967d\u6027}|\\text{\u30ac\u30f3})}{P(\\text{\u967d\u6027})}P(\\text{\u30ac\u30f3}) = \\frac{0.99}{0.01098}\\times 0.001 = 0.09$$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u8a3a\u65ad\u3067\u967d\u6027\u304c\u51fa\u305f\u4e8b\u3067\u764c\u3067\u3042\u308b\u78ba\u7387\u304c0.1%\u304b\u30899%\u306b\u4e0a\u6607\u3057\u305f\u3068\u3044\u3046\u4e8b\u306b\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u78ba\u7387\u5206\u5e03\u306b\u5bc6\u5ea6\u95a2\u6570\u306b\u5bfe\u3057\u3066\u3082\u540c\u69d8\u306b\n",
      "\n",
      "$$\\color{red}{ \\pi(\\mathbf{x}|\\mathbf{y}) = \\frac{\\pi(\\mathbf{y}|\\mathbf{x})}{\\pi(\\mathbf{y})}\\pi(\\mathbf{x}) }$$\n",
      "\n",
      "\u3068\u3044\u3046\u7b49\u5f0f\u304c\u6210\u7acb\u3057\uff0c$\\pi(\\mathbf{x})$ \u3092**\u4e8b\u524d\u5206\u5e03(prior distribution)**\u3001$\\pi(\\mathbf{x}|\\mathbf{y})$ \u3092**\u4e8b\u5f8c\u5206\u5e03(posterior distribution)**\u3068\u547c\u3073\u307e\u3059\u3002\u5206\u6bcd\u306e $\\pi(\\mathbf{y})$ \u306f $\\mathbf{x}$ \u306b\u3088\u3089\u306a\u3044\u5b9a\u6570\u306a\u306e\u3067\u3082\u3063\u3068\u5358\u7d14\u306b\n",
      "\n",
      "$$\\color{red}{ \\pi(\\mathbf{x}|\\mathbf{y})\\propto \\pi(\\mathbf{y}|\\mathbf{x})\\pi(\\mathbf{x}) }$$\n",
      "\n",
      "\u3068\u66f8\u304f\u3053\u3068\u304c\u51fa\u6765\u307e\u3059\u3002\u6bd4\u4f8b\u5b9a\u6570\u306f\u78ba\u7387\u306e\u548c\u304c1\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u304b\u3089\u8a08\u7b97\u3059\u308b\u4e8b\u304c\u51fa\u6765\u3001\u5177\u4f53\u7684\u306b\u66f8\u3044\u3066\u307f\u308c\u3070\n",
      "\n",
      "$$\\color{red}{ \\pi(\\mathbf{x}|\\mathbf{y}) = \\frac{\\pi(\\mathbf{y}|\\mathbf{x})\\pi(\\mathbf{x})}{\\int\\pi(\\mathbf{y}|\\mathbf{x})\\pi(\\mathbf{x})\\mathrm{d}\\mathbf{x}} }$$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u671f\u5f85\u5024\u30fb\u5206\u6563\u30fb\u6a19\u6e96\u504f\u5dee\n",
      "\u78ba\u7387\u5206\u5e03\u306e\u7279\u5fb4\u3092\u8868\u3059\u5404\u7a2e\u6570\u5024\u3092**\u7d71\u8a08\u91cf(statistics)**\u3068\u547c\u3073\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u671f\u5f85\u5024\u3011\n",
      "\n",
      "$\\mathbf{X}=\\mathbf{x}_1,\\mathbf{x}_2,\\ldots,\\mathbf{x}_n$ \u306e\u3044\u305a\u308c\u304b\u306e\u5024\u3092\u53d6\u308b\u96e2\u6563\u7684\u78ba\u7387\u5206\u5e03\u3068\u95a2\u6570 $f(\\mathbf{X})$\u306b\u5bfe\u3057\u3066\n",
      "$$\\mathrm{E}[f(\\mathbf{X})] \\stackrel{\\mathrm{def}}{=} \\sum_{i=1}^n f(\\mathbf{x}_i)P(\\mathbf{X}=\\mathbf{x}_i)$$\n",
      "\u3092 $f(\\mathbf{X})$ \u306e**\u671f\u5f85\u5024(expected value)**\u3068\u547c\u3076\u3002\n",
      "\n",
      "\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570 $\\pi(\\mathbf{x})$ \u3067\u8868\u3055\u308c\u308b\u9023\u7d9a\u7684\u78ba\u7387\u5206\u5e03\u3068\u95a2\u6570 $f(\\mathbf{X})$ \u306b\u5bfe\u3057\u3066\u306f\n",
      "$$\\mathrm{E}[f(\\mathbf{X})] \\stackrel{\\mathrm{def}}{=} \\int f(\\mathbf{x})\\pi(\\mathbf{x})\\mathrm{d}\\mathbf{x}$$\n",
      "\u3092 $f(\\mathbf{X})$ \u306e\u671f\u5f85\u5024\u3068\u547c\u3076\u3002\u7a4d\u5206\u306f$\\mathbf{x}$ \u306e\u5909\u57df\u5168\u4f53\u306b\u3064\u3044\u3066\u53d6\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "$\\mathrm{E}[\\mathbf{X}]$ \u306e\u4e8b\u3092\u7279\u306b $\\mathbf{X}$ \u306e**\u5e73\u5747(mean)**\u3068\u547c\u3073\u307e\u3059\u3002\u307e\u305f $\\mathrm{E}[X^n]$ \u306f\u5206\u5e03\u306e$n$\u6b21\u306e**\u30e2\u30fc\u30e1\u30f3\u30c8(moment)**\u3068\u547c\u3070\u308c\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\n",
      "\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u306e\u5206\u5e03\n",
      "$$\\begin{array}{|c|c|c|c|c|c|c|} \\hline\n",
      "X & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline\n",
      "P(X) & 1/6 & 1/6 & 1/6 & 1/6 & 1/6 & 1/6 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\u306b\u5bfe\u3057\u3066 $\\mathrm{E}[X], \\mathrm{E}[X^2], \\mathrm{E}[X^3]$ \u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = array([1,2,3,4,5,6])\n",
      "p = ones(6)/6\n",
      "EX  = sum(x * p)\n",
      "EX2 = sum(x**2 * p)\n",
      "EX3 = sum(x**3 * p)\n",
      "print EX\n",
      "print EX2\n",
      "print EX3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3.5\n",
        "15.1666666667\n",
        "73.5\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u4ee5\u4e0b\u306e\u9023\u7d9a\u5206\u5e03\u306b\u5bfe\u3057\u3066 $\\mathrm{E}[X],\\mathrm{E}[X^2], \\mathrm{E}[X^3]$ \u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002\n",
      "$$ \\pi(x) = \\left\\{\\begin{array}{ll}\n",
      "0 & (x < 0\\text{\u307e\u305f\u306f}1 < x) \\\\\n",
      "1 & (0\\leq x \\leq 1) \\\\\n",
      "\\end{array}\\right. $$\n",
      "\n",
      "$$ \\mathrm{E}[X] = \\int_{-\\infty}^{\\infty}x\\pi(x)\\mathrm{d}x = \\int_0^1x\\mathrm{d} x = \\frac{1}{2},\\quad\n",
      "\\mathrm{E}[X^2] = \\int_0^1x^2\\mathrm{d} x = \\frac{1}{3},\\quad\n",
      "\\mathrm{E}[X^3] = \\int_0^1x^3\\mathrm{d} x = \\frac{1}{4} $$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "----\n",
      "\u3010\u671f\u5f85\u5024\u306e\u6027\u8cea\u3011\n",
      "\n",
      "\n",
      "1. $\\mathrm{E}[c] = c\\qquad\\text{($c$\u306f\u5b9a\u6570)}$\n",
      "2. $\\mathrm{E}[aX+bY] = a\\mathrm{E}[X] + b\\mathrm{E}[Y]\\qquad\\text{($a,b$\u306f\u5b9a\u6570)}$\n",
      "3. $X,Y$ \u304c\u72ec\u7acb\u306a\u3089\u3070 $\\mathrm{E}[XY] = \\mathrm{E}[X]\\mathrm{E}[Y]$\n",
      "4. \u591a\u6b21\u5143\u306e\u78ba\u7387\u5909\u6570 $\\mathbf{X}$ \u306b\u5bfe\u3057\u3066 $\\mathrm{E}[\\mathbf{A}\\mathbf{X}\\mathbf{B}] = \\mathbf{A}\\mathrm{E}[\\mathbf{X}]\\mathbf{B}\\qquad (\\text{$\\mathbf{A},\\mathbf{B}$ \u306f\u5b9a\u6570\u884c\u5217)}$\n",
      "\n",
      "----"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "----\n",
      "\u3010\u5206\u6563\u3011\n",
      "\n",
      "\u4e00\u6b21\u5143\u306e\u5e73\u5747\u304c $\\mu = \\mathrm{E}[X]$ \u3067\u3042\u308b\u78ba\u7387\u5909\u6570 $X$ \u306b\u5bfe\u3057\u3066\n",
      "\n",
      "$$\\mathrm{V}[X] \\stackrel{\\mathrm{def}}{=}\\mathrm{E}[(X-\\mu)^2]$$\n",
      "\n",
      "\u3092 $X$ \u306e**\u5206\u6563(variance)**\u3068\u547c\u3073\uff0c$\\sigma[X]\\stackrel{\\mathrm{def}}{=}\\sqrt{\\mathrm{V}[X]}$ \u3092**\u6a19\u6e96\u504f\u5dee(standard deviation)**\u3068\u547c\u3076\u3002\n",
      "\n",
      "\u3053\u3053\u3067\u671f\u5f85\u5024\u306e\u6027\u8cea\u3088\u308a\n",
      "\n",
      "$$\\mathrm{E}[(X-\\mu)^2] = \\mathrm{E}[X^2-2\\mu X+\\mu^2]=\\mathrm{E}[X^2]-2\\mu \\mathrm{E}[X]+\\mu^2=\\mathrm{E}[X^2]-(\\mathrm{E}[X])^2\\qquad (\\because \\mu=\\mathrm{E}[X])$$\n",
      "\n",
      "\u3059\u306a\u308f\u3061\n",
      "$$ \\color{red}{ \\mathrm{V}[X] = \\mathrm{E}[X^2] - (\\mathrm{E}[X])^2} $$\n",
      "\u304c\u6210\u308a\u7acb\u3064\u3002\n",
      "\n",
      "----\n",
      "\n",
      "$X$ \u304c\u5e73\u5747 $\\mu$ \u304b\u3089\u96e2\u308c\u3066\u3044\u308b\u307b\u3069 $(X-\\mu)^2$ \u306e\u5024\u306f\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002\u5f93\u3063\u3066\u5206\u6563\u30fb\u6a19\u6e96\u504f\u5dee\u306f**\u5206\u5e03\u306e\u5e83\u304c\u308a\u306e\u5ea6\u5408\u3044**\u3092\u8868\u3059\u7d71\u8a08\u91cf\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u306e\u5206\u5e03\n",
      "$$\\begin{array}{|c|c|c|c|c|c|c|} \\hline\n",
      "X & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline\n",
      "P(X) & 1/6 & 1/6 & 1/6 & 1/6 & 1/6 & 1/6 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\u306b\u304a\u3044\u3066\n",
      "$$ \\mathrm{E}[X] = \\frac{7}{2},\\quad \\mathrm{E}[X^2] = \\frac{91}{6}$$\n",
      "\u306a\u306e\u3067\n",
      "$$\\mathrm{V}[X] = \\frac{91}{6}-\\left(\\frac{7}{2}\\right)^2 = \\frac{35}{12}$$\n",
      "$$\\sigma[X] = \\sqrt{\\frac{35}{12}}= 1.70\\cdots $$\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "-----\n",
      "\u3010\u5171\u5206\u6563\u30fb\u76f8\u95a2\u4fc2\u6570\u3011\n",
      "\n",
      "$\\mu_X = \\mathrm{E}[X], \\mu_Y = \\mathrm{E}[Y]$ \u3067\u3042\u308b\u78ba\u7387\u5909\u6570 $X,Y$ \u306b\u5bfe\u3057\u3066\n",
      "\n",
      "$$\\mathrm{Cov}[X,Y] \\stackrel{\\mathrm{def}}{=} \\mathrm{E}[(X-\\mu_X)(Y-\\mu_Y)] = \\mathrm{E}[XY]-\\mathrm{E}[X]\\mathrm{E}[Y]$$\n",
      "\n",
      "\u3092 $X,Y$ \u306e**\u5171\u5206\u6563(covariance)**\u3068\u547c\u3076\u3002\u307e\u305f\u3053\u308c\u3092\u5404\u5909\u6570\u306e\u6a19\u6e96\u504f\u5dee\u3067\u5272\u3063\u305f\u91cf\u3092**\u76f8\u95a2\u4fc2\u6570(correlation coefficient)**\u3068\u547c\u3076\u3002\n",
      "\n",
      "$$\\mathrm{Corr}[X,Y] = \\frac{\\mathrm{Cov}[X,Y]}{\\sigma[X]\\sigma[Y]}$$\n",
      "\n",
      "----\n",
      "\n",
      "$\\mathrm{Corr}[X,Y] > 0$ \u306e\u5834\u5408\u306f $(X-\\mu_X)$ \u3068 $(Y-\\mu_Y)$ \u306f\u540c\u3058\u7b26\u53f7\u3092\u53d6\u308b\u50be\u5411\u304c\u3042\u308b\u3068\u3044\u3046\u4e8b\u306b\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001$X$ \u306e\u5927\u5c0f\u3068 $Y$ \u306e\u5927\u5c0f\u304c\u3042\u308b\u7a0b\u5ea6\u9023\u52d5\u3059\u308b\u50be\u5411\u306b\u3042\u308b\u3068\u3044\u3046\u4e8b\u3067\u3059\u3002\u3053\u308c\u3092**\u6b63\u306e\u76f8\u95a2(positive correlation)**\u304c\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002\u540c\u69d8\u306b $\\mathrm{Corr}[X,Y] < 0$ \u306e\u6642\u306f**\u8ca0\u306e\u76f8\u95a2(negative correlation)**\u304c\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002\n",
      "\u76f8\u95a2\u4fc2\u6570\u306f\u5fc5\u305a $-1\\leq \\mathrm{Corr}[X,Y] \\leq 1$ \u3068\u306a\u308b(\u8a3c\u660e\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044)\u306e\u3067\u3001\u76f8\u95a2\u306e\u7a0b\u5ea6\u306e\u5f37\u3055\u3092\u30b9\u30b1\u30fc\u30eb\u3092\u63c3\u3048\u3066\u6bd4\u8f03\u3059\u308b\u4e8b\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u72ec\u7acb\u6027\u3068\u5171\u5206\u6563\u3011\n",
      "\n",
      "\n",
      "\u671f\u5f85\u5024\u306e\u6027\u8cea\u3088\u308a$X, Y$ \u304c\u72ec\u7acb\u306a\u3089\u3070 $E[XY] = E[X]E[Y]$ \u304c\u6210\u308a\u7acb\u3064\u306e\u3067 $\\mathrm{Cov}[X, Y] = 0$ \u3068\u306a\u308b\u3002\u3059\u306a\u308f\u3061\u3001**\u72ec\u7acb\u306a\u3089\u3070\u7121\u76f8\u95a2**\u3067\u3042\u308b\u3002\u3053\u306e\u9006\u306f\u6210\u7acb\u305b\u305a\u3001\u7121\u76f8\u95a2\u3067\u3082\u72ec\u7acb\u3067\u3042\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u3002\n",
      "\n",
      "----\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\n",
      "$$ \\begin{array}{|c|c|c|c|}\\hline\n",
      "    & Y=1  & Y=2 & Y=3 \\\\ \\hline\n",
      "X=1 & 1/12 & 3/12 & 3/12 \\\\ \\hline\n",
      "X=2 & 2/12 & 2/12 & 1/12 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\n",
      "\u306b\u5f93\u3046\u4e8c\u6b21\u5143\u78ba\u7387\u5909\u6570 $X,Y$ \u306e\u5171\u5206\u6563\u30fb\u76f8\u95a2\u4fc2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u5f31\u3044\u8ca0\u306e\u76f8\u95a2\u304c\u3042\u308b\u3068\u3044\u3046\u4e8b\u304c\u5224\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = array([1,2])\n",
      "Y = array([1,2,3])\n",
      "P = array([[1,3,3],[2,2,1]], dtype=float)/12\n",
      "EX = sum(X * sum(P, axis=1))     # E[X]\n",
      "EY = sum(Y * sum(P, axis=0))     # E[Y]\n",
      "VX = sum((X - EX)**2 * sum(P, axis=1)) # V[X]\n",
      "VY = sum((Y - EY)**2 * sum(P, axis=0)) # V[Y]\n",
      "\n",
      "COV = sum(outer(X - EX, Y-EY) * P)\n",
      "CORR = COV / (sqrt(VX) * sqrt(VY) )\n",
      "print \"V[X]=\",VX,\", V[Y]=\",VY\n",
      "print \"COV[X,Y]=\",COV\n",
      "print \"CORR[X,Y]=\",CORR"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "V[X]= 0.243055555556 , V[Y]= 0.576388888889\n",
        "COV[X,Y]= -0.118055555556\n",
        "CORR[X,Y]= -0.315410286581\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "----\n",
      "\u3010\u5206\u6563\u5171\u5206\u6563\u884c\u5217\u3011\n",
      "\n",
      "\u5e73\u5747\u304c$\\boldsymbol{\\mu}=\\mathrm{E}[\\mathbf{X}]$\u3067\u3042\u308b$n$\u6b21\u5143\u78ba\u7387\u5909\u6570 $\\mathbf{X}$ \u306b\u5bfe\u3057\u3066, \u5404\u6210\u5206\u304c\u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3055\u308c\u308b $n$ \u6b21\u6b63\u65b9\u884c\u5217\u3092**\u5206\u6563\u5171\u5206\u6563\u884c\u5217(variance-covariance matrix)**\u3068\u547c\u3076\u3002\n",
      "\n",
      "$$\\boldsymbol{\\Sigma}_{ij} = \\mathrm{E}[(X_i - \\mathrm{E}[X_i])(Y_i - \\mathrm{E}[Y_i])]$$\n",
      "\n",
      "\u3064\u307e\u308a\u3001$\\boldsymbol{\\Sigma}_{ii}=\\mathrm{V}[X_i], \\boldsymbol{\\Sigma}_{ij} = \\mathrm{Cov}[X_i, X_j]\\quad(i\\neq j)$ \u3067\u3042\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "\u3053\u308c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u304d\u8868\u3059\u4e8b\u304c\u3067\u304d\u308b\u70ba\u3001\u5206\u6563\u306e\u591a\u6b21\u5143\u5206\u5e03\u3078\u306e\u4e00\u822c\u5316\u3068\u307f\u306a\u3059\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\n",
      "$$\\boldsymbol{\\Sigma} = \\mathrm{E}[(\\mathbf{X}-\\boldsymbol{\\mu})(\\mathbf{X}-\\boldsymbol{\\mu})^T] = \\boldsymbol{\\Sigma} = \\mathrm{E}[\\mathbf{X}\\mathbf{X}^T]-\\mathrm{E}[\\mathbf{X}]E[\\mathbf{X}]^T $$\n",
      "\n",
      "\u307e\u305f\u3001\u5206\u6563\u5171\u5206\u6563\u884c\u5217 $\\boldsymbol{\\Sigma}$ \u306f\u5fc5\u305a\u534a\u6b63\u5b9a\u5024\u5bfe\u79f0\u884c\u5217\u306b\u306a\u308a\u307e\u3059\u3002\u5bfe\u79f0\u884c\u5217\u3067\u3042\u308b\u306e\u306f\u5b9a\u7fa9\u3088\u308a\u660e\u3089\u304b\u3067\u3001\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb $\\mathbf{a}$ \u306b\u5bfe\u3057\u3066\n",
      "\n",
      "$$\\mathbf{a}^T\\boldsymbol{\\Sigma}\\mathbf{a} = \\mathbf{a}^T\\mathrm{E}[\\mathbf{X}\\mathbf{X}^T]\\mathbf{a}-\\mathbf{a}^T\\mathrm{E}[\\mathbf{X}]E[\\mathbf{X}]^T\\mathbf{a}= \\mathrm{E}[(\\mathbf{a}^T\\mathbf{X})(\\mathbf{a}^T\\mathbf{X})^T]-\\mathrm{E}[\\mathbf{a}^T\\mathbf{X}]^2=\\mathrm{V}[\\mathbf{a}^T\\mathbf{X}]\\geq 0$$\n",
      "\n",
      "\u3068\u306a\u308b\u304b\u3089\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\n",
      "\u5148\u307b\u3069\u306e\u5206\u5e03\n",
      "$$ \\begin{array}{|c|c|c|c|}\\hline\n",
      "    & Y=1  & Y=2 & Y=3 \\\\ \\hline\n",
      "X=1 & 1/12 & 3/12 & 3/12 \\\\ \\hline\n",
      "X=2 & 2/12 & 2/12 & 1/12 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\n",
      "\u3067\u306f$\\mathrm{V}[X] = 0.243, \\mathrm{V}[Y]= 0.576, \\mathrm{Cov}[X,Y] = -0.118$\u306a\u306e\u3067, $\\mathbf{X}=(X,Y)$ \u306e\u5206\u6563\u5171\u5206\u6563\u884c\u5217\u306f\n",
      "$$\\boldsymbol{\\Sigma} = \\begin{pmatrix}\n",
      "0.243 & -0.118 \\\\\n",
      "-0.118 & 0.576\n",
      "\\end{pmatrix} $$\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u9023\u7d9a\u5206\u5e03\u306e\u5834\u5408\u3082\u540c\u69d8\u3067\u3059\u3002\u5148\u307b\u3069\u4f7f\u3063\u305f\u5206\u5e03$\\pi(x, y) = 360xy^2(1-x-y) $\u306e\u5206\u6563\u5171\u5206\u6563\u884c\u5217\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002\n",
      "\u307e\u305a\u3001\u3053\u308c\u3092 $y$ \u306b\u3064\u3044\u3066\u5468\u8fba\u5316\u3059\u308b\u3068$\\pi(x) = 30x(1-x)^4$\n",
      "\n",
      "\u3068\u306a\u308b\u306e\u3067\u3057\u305f\u304b\u3089\n",
      "\n",
      "$$ \\mathrm{E}[X] = \\int_0^1 x\\pi(x)\\mathrm{d}x = \\frac{2}{7} $$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u5f93\u3063\u3066\n",
      "\n",
      "$$\\mathrm{V}[X] = \\int_0^1 (x-2/7)^2\\pi(x)\\mathrm{d} x = \\frac{5}{196},\\quad\\sigma[X] = \\sqrt{\\frac{5}{196}}=\\frac{\\sqrt{5}}{14}$$\n",
      "\n",
      "\u3067\u3059\u3002\u540c\u69d8\u306b\u8a08\u7b97\u3059\u308b\u3068$\\mathrm{E}[Y]=3/7,\\mathrm{V}[Y] = 6/196, \\sigma[Y] = \\frac{\\sqrt{6}}{14}$\u3068\u306a\u308a\u307e\u3059\u3002\u307e\u305f\n",
      "\n",
      "$$ \\mathrm{Cov}[X,Y] = \\int_0^1\\int_0^{1-x} (x-2/7)(y-3/7)\\pi(x,y)\\mathrm{d}y\\mathrm{d}x = -\\frac{3}{196} $$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u3059\u306a\u308f\u3061\n",
      "$$\\boldsymbol{\\Sigma} = \\frac{1}{196}\\begin{pmatrix} 5 & -3 \\\\ -3 & 6 \\end{pmatrix}$$\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5206\u5e03\u306f$Y$\u306e\u65b9\u304c $X$ \u3088\u308a\u5206\u5e03\u306e\u5e83\u304c\u308a\u306e\u5ea6\u5408\u3044\u304c\u82e5\u5e72\u5927\u304d\u304f\u3001\u8ca0\u306e\u76f8\u95a2\u304c\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u5224\u308a\u307e\u3059\u3002\u5b9f\u969b\u306b\u5206\u5e03\u3092\u56f3\u793a\u3057\u3066\u307f\u308b\u3068\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = figure()\n",
      "ax = Axes3D(fig)\n",
      "X, Y = meshgrid(linspace(0, 1, 20), linspace(0, 1, 20))\n",
      "xlim(0, 1)\n",
      "ylim(0, 1)\n",
      "Z = 360*X*Y**2*(1-X-Y)\n",
      "Z[X+Y>1]=0\n",
      "axes().set_aspect('equal')\n",
      "xlabel('X')\n",
      "ylabel('Y')\n",
      "contour(X, Y, Z)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.contour.QuadContourSet instance at 0x826acf8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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T4iIpOGYnLPqWQrmFRY0KZyx1HLgGLRZTlkLOzo99KZQbK3t73tmyhXvnz7Pz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6920210>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 1)\n",
      "plot(x, 30*x*(1-x)**4, label=u'\u03c0(x)')\n",
      "plot(x, 60*x**2*(1-x)**3, label=u'\u03c0(y)')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.legend.Legend at 0x6e312d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yeChLb7Rx5oy6aeruRR3U1XqD/A2kqCdQ4sRql6WePa29IQdAp1Kd8LZ5M33v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\nEEIIIYQQQgghhBBCCCGEEEIIIYRO/wdaMAa5CTtvTgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x81e3e10>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# \u60c5\u5831\u91cf\n",
      "\n",
      "----\n",
      "\n",
      "\u6839\u5143\u4e8b\u8c61 $A_1,A_2,\\ldots,A_n$ \u306e\u305d\u308c\u305e\u308c\u304c\u78ba\u7387 $p_1,p_2,\\ldots,p_n$ \u3067\u751f\u3058\u308b\u96e2\u6563\u7684\u78ba\u7387\u5206\u5e03 $P$ \u306b\u5bfe\u3057\u3066\n",
      "\n",
      "$$\\mathrm{H}(P)\\stackrel{\\mathrm{def}}{=} -\\sum_{i=1}^np_i\\log p_i $$\n",
      "\n",
      "\u3092\u5206\u5e03 $P$ \u306e**\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc(entropy)**\u3068\u547c\u3076\u3002\u4efb\u610f\u306e\u5206\u5e03\u306b\u5bfe\u3057\u3066\u5e38\u306b $\\mathrm{H}(P)\\geq 0$ \u3067\u3042\u308b\u3002\n",
      "\n",
      "\u9023\u7d9a\u7684\u5206\u5e03\u306b\u5bfe\u3059\u308b\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f\n",
      "\n",
      "$$\\mathrm{H}(\\pi) = -\\int \\pi(\\mathbf{x})\\log\\pi(\\mathbf{x})\\mathrm{d}\\mathbf{x}$$\n",
      "\n",
      "\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u3053\u308c\u306f\u8ca0\u306e\u5024\u3082\u53d6\u308a\u3046\u308b\u3002\n",
      "\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306e\u8a08\u7b97\u306b\u304a\u3044\u3066\u306f $0\\log 0 = 0$ \u3067\u3042\u308b\u3068\u3059\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3068\u306f\u5206\u5e03 $P$ \u306b\u5bfe\u3059\u308b\u8a66\u884c\u30fb\u89b3\u5bdf\u3092\u884c\u3046\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u308b\u3053\u3068\u304c\u51fa\u6765\u308b\u5e73\u5747\u7684\u306a\u60c5\u5831\u91cf\u306e\u5927\u304d\u3055\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\n",
      "\u8868\u306e\u51fa\u308b\u78ba\u7387\u304c $p$ \u3067\u3042\u308b\u30b3\u30a4\u30f3\u6295\u3052\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f\n",
      "\n",
      "$$ \\mathrm{H} = -p\\log p -(1-p)\\log(1-p) $$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u6a2a\u8ef8\u306b $p$ \u3092\u53d6\u3063\u3066\u3053\u308c\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p = linspace(0.0001, 0.9999)\n",
      "plot(p, -p*log(p)-(1-p)*log(1-p))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[<matplotlib.lines.Line2D at 0x83feed0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oBoaXc+ztwHfAA+W8F4mUWY71zTdWZ+Hrr6FGjXhDFhFJH1OmwH33wfTp5b+f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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6947650>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u3053\u306e\u30b0\u30e9\u30d5\u3092\u898b\u308b\u3068\u3001$p=1$ \u306e\u6642\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f $0$\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3069\u3046\u3044\u3046\u3053\u3068\u304b\u3068\u8a00\u3046\u3068 $p=1$ \u306a\u3089\u3070\u7d76\u5bfe\u306b\u8868\u304c\u51fa\u308b\u3068\u3042\u3089\u304b\u3058\u3081\u5206\u304b\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u8a66\u884c\u3092\u884c\u3063\u305f\u6240\u3067\u65b0\u3057\u3044\u60c5\u5831\u306f\u5f97\u3089\u308c\u306a\u3044\u3068\u3044\u3046\u4e8b\u3067\u3059\u3002$p=0$\u306e\u6642\u3082\u540c\u69d8\u3067\u3059\u3002$p=0.99$ \u306e\u6240\u3067\u306f $\\mathrm{H}=0.056$ \u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u6642\u3001\u8868\u304c\u51fa\u308b\u304b\u88cf\u304c\u51fa\u308b\u304b\u3092\u5b8c\u5168\u306b\u4e88\u6e2c\u3059\u308b\u4e8b\u306f\u51fa\u6765\u306a\u3044\u306e\u3067\u3001\u5b9f\u969b\u306b\u8a66\u884c\u3092\u884c\u3046\u3068\u3044\u304f\u3089\u304b\u306e\u60c5\u5831\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3069\u3046\u305b99%\u306e\u78ba\u7387\u3067\u8868\u3060\u3068\u3044\u3046\u4e8b\u306f\u5206\u304b\u3063\u3066\u3044\u308b\u306e\u3067\u5f97\u3089\u308c\u308b\u60c5\u5831\u91cf\u306f\u5fae\u5c0f\u3067\u3059\u3002$p=0.5$ \u306e\u6240\u3067\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u304c\u6700\u5927\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u304c\u3001\u3053\u306e\u6642\u306f\u8868\u3068\u88cf\u306e\u51fa\u65b9\u306f\u4e8b\u524d\u306b\u5168\u304f\u4e88\u6e2c\u51fa\u6765\u307e\u305b\u3093\u306e\u3067\u3001\u5b9f\u969b\u306b\u8a66\u884c\u3092\u884c\u3046\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u60c5\u5831\u91cf\u306f\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u6b21\u306f\u78ba\u7387 $p$ \u3067\u8868\u304c\u51fa\u308b\u30b3\u30a4\u30f3\u3092\uff12\u56de\u9023\u7d9a\u3067\u632f\u3063\u305f\u5834\u5408\u306b\u5f97\u3089\u308c\u308b\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u6c42\u3081\u3066\u307f\u308b\u3068\n",
      "\n",
      "$$\\mathrm{H}' = -p^2\\log p^2 - p(1-p)\\log p(1-p) - (1-p)p\\log (1-p)p - (1-p)^2\\log (1-p)^2 = -2p\\log p-2(1-p)\\log (1-p)$$\n",
      "\n",
      "\u3064\u307e\u308a $\\mathrm{H}'=2\\mathrm{H}$ \u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u30b3\u30a4\u30f3\u3092\u4e00\u56de\u632f\u308b\u3068\u5e73\u5747 $\\mathrm{H}$ \u306e\u60c5\u5831\u91cf\u304c\u5f97\u3089\u308c\u308b\u306e\u3067\u3001\u4e8c\u56de\u632f\u308c\u3070\u5e73\u5747 $2\\mathrm{H}$ \u306e\u60c5\u5831\u91cf\u304c\u5f97\u3089\u308c\u308b\u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002$n$\u56de\u632f\u308c\u3070 $n\\mathrm{H}$ \u306e\u60c5\u5831\u91cf\u304c\u5f97\u3089\u308c\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4eca\u306e\u4f8b\u304b\u3089\u4e88\u60f3\u51fa\u6765\u308b\u3068\u601d\u3044\u307e\u3059\u304c\u3001\u7d50\u679c\u304c\u5168\u304f\u4e88\u60f3\u51fa\u6765\u306a\u3044\u6642\u3064\u307e\u308a $p_1,p_2,\\ldots,p_n$ \u304c\u5168\u3066\u7b49\u3057\u3044\u6642\u306b\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f\u6700\u5927\u3068\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u6700\u5927\u306e\u5206\u5e03\u3011\n",
      "\n",
      "\u96e2\u6563\u7684\u5206\u5e03 $P$ \u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f $p_1=p_2=\\cdots=p_n=1/n$ \u306e\u6642\u306b\u6700\u5927\u3068\u306a\u308a $\\mathrm{H}(P) = \\log n$ \u3067\u3042\u308b\u3002\n",
      "\n",
      "\u3010\u8a3c\u660e\u3011\n",
      "\n",
      "$p_1+p_2+\\cdots+p_n=1$ \u3068\u3044\u3046\u6761\u4ef6\u4e0b\u3067\n",
      "$$\\mathrm{H}(P)= -\\sum_{i=1}^np_i\\log p_i$$\n",
      "\u304c\u6700\u5927\u3068\u306a\u308b\u6761\u4ef6\u3092\u8003\u3048\u308b\u3002\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570 $\\lambda$ \u3092\u5c0e\u5165\u3057\u3066\n",
      "\n",
      "$$ F(p_1,\\ldots,p_n,\\lambda) = -\\sum_{i=1}^np_i\\log p_i - \\lambda\\left(\\sum_{i=1}^n p_i - 1\\right) $$\n",
      "\n",
      "\u3068\u7f6e\u304f\u3068\n",
      "\n",
      "$$ \\frac{\\partial F}{\\partial p_i} = -\\log p_i - 1 - \\lambda,\\quad \\frac{\\partial F}{\\partial \\lambda} = -\\sum_{i=1}^np_i + 1$$\n",
      "\n",
      "\u3067\u3042\u308b\u306e\u3067\u3001\u3053\u308c\u3089\u304c\u5168\u3066 $0$ \u3068\u306a\u308b\u3053\u3068\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u5f93\u3063\u3066\u7b2c\u4e00\u5f0f\u3088\u308a\n",
      "\n",
      "$$ p_i = \\exp(-1 - \\lambda) $$\n",
      "\n",
      "\u3059\u306a\u308f\u3061\uff0c$p_i$ \u306f\u5168\u3066\u7b49\u3057\u3044\u4e8b\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002 $p_1=p_2=\\cdots=p_n=1/n$ \u306e\u6642\u306b\u6700\u5927\u3068\u306a\u308b\u3053\u3068\u306f\u660e\u3089\u304b\u3002(\u8a3c\u660e\u7d42)\n",
      "\n",
      "----\n",
      "\n",
      "\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f\u751f\u3058\u308b\u73fe\u8c61\u306e\u4e88\u6e2c\u304c\u5168\u304f\u51fa\u6765\u306a\u3044\u72b6\u614b\u3067\u6700\u5927\u306b\u306a\u308b\u305f\u3081\u3001\u73fe\u8c61\u306e**\u7121\u79e9\u5e8f\u3055\u306e\u5ea6\u5408\u3044**\u3092\u8868\u3057\u3066\u3044\u308b\u3068\u8003\u3048\u308b\u4e8b\u3082\u51fa\u6765\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "----\n",
      "\uff12\u3064\u306e\u96e2\u6563\u7684\u306a\u5206\u5e03 $P,Q$ \u306b\u5bfe\u3057\u3066\n",
      "\n",
      "$$\\mathrm{D}_{\\mathrm{KL}}(P||Q)\\stackrel{\\mathrm{def}}{=} \\sum_{i=1}^n p_i \\log \\frac{p_i}{q_i} $$\n",
      "\n",
      "\u3092\u5206\u5e03 $P,Q$ \u306e**\u30ab\u30eb\u30d0\u30c3\u30af\u30fb\u30e9\u30a4\u30d6\u30e9\u30fc\u60c5\u5831\u91cf(Kullback-Leibler divergence)**\u3068\u547c\u3076\u3002\n",
      "\n",
      "\uff12\u3064\u306e\u9023\u7d9a\u7684\u306a\u5206\u5e03 $p(\\mathbf{x}),q(\\mathbf{x})$ \u306b\u5bfe\u3057\u3066\u306f\n",
      "\n",
      "$$\\mathrm{D}_{\\mathrm{KL}}(p||q) \\stackrel{\\mathrm{def}}{=}\\int p(\\mathbf{x})\\log\\frac{p(\\mathbf{x})}{q(\\mathbf{x})}\\mathrm{d}\\mathbf{x}$$\n",
      "\n",
      "\u3068\u5b9a\u7fa9\u3059\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "\u30ab\u30eb\u30d0\u30c3\u30af\u30fb\u30e9\u30a4\u30d6\u30e9\u30fc\u60c5\u5831\u91cf\u306f\u30d9\u30a4\u30ba\u7d71\u8a08\u5b66\u306b\u304a\u3044\u3066\u7279\u306b\u91cd\u8981\u306a\u610f\u5473\u3092\u6301\u3061\u307e\u3059\u3002\u4e8b\u524d\u5206\u5e03 $q(\\mathbf{x})$ \u304c\u65b0\u3057\u3044\u30c7\u30fc\u30bf $I$ \u3092\u5f97\u308b\u4e8b\u306b\u3088\u3063\u3066\u4e8b\u5f8c\u5206\u5e03 $p(\\mathbf{x})$ \u306b\u5909\u5316\u3057\u305f\u5834\u5408\u306b $I$ \u304b\u3089\u5f97\u3089\u308c\u308b\u60c5\u5831\u91cf\u306e\u5e73\u5747\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u3082\u3063\u3068\u5206\u304b\u308a\u3084\u3059\u304f\u3044\u3048\u3070\u30c7\u30fc\u30bf $I$ \u306e\u4fa1\u5024\u3060\u3068\u8a00\u3048\u308b\u3067\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u3042\u308b\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u8868\u304c\u51fa\u308b\u78ba\u7387 $\\theta$ \u3092\u63a8\u5b9a\u3057\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u4e8b\u524d\u5206\u5e03\u3092 $\\pi(\\theta) = 6\\theta(1-\\theta)\\qquad(0\\leq \\theta \\leq 1)$ \u3068\u3057\u307e\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xlabel(u'theta')\n",
      "x = linspace(0, 1)\n",
      "plot(x, 6*x*(1-x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[<matplotlib.lines.Line2D at 0x867f650>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1gaFY3/ze/E6Ulpb2y/1QKEQoFDrqmJkzbXZMPk+JiCS1zp2hSRN4+umCp0WG\nw2HCHnTOxzJ3sgywBmgBbAe+wAZVv851TDVgJnAHML+A88Q0z/3666FVK+jYMYbIRESSzJ//DDfd\nBO3bx3Z8vMsPtAJexWbOvAm8ABxJv0OAYcANwObI9zKwgdjcoib3TZvg4outT+q3v40xMhGRJDJ9\nOvToAYsWxVbrPRC1ZR59FA4ftn1SRUSCKCvLFjYNHw6XXRb9+KRP7j/9BNWqwRdfwNln+xiViIjP\n+veH2bPh/fejH5v05QdGj7aBBiV2EQm6u+6ySrdb85ua4pGESO7Z2fZOpumPIpIKjj8ebr8dBg+O\n32skRHKfNQsyMuDKK11HIiLijy5dYOhQOHAgPudPiOTev7/9oiXdJVxEJFmcey6cf35s/e7F4XxA\ndcsW+wU3bYLjjvMxGhERx6ZMgWeesYkkBTVuk3ZAddAgK+urxC4iqaZVK9izBxYs8P7cTlvuBw/a\n9MfZs+Gcc3yMREQkQbz8MixdapVw81PclnsstWXiZsIEqFdPiV1EUtfdd0PNmrB7N5x8snfnddot\nM3iwaraLSGo7+WS47joYOdLb8zrrllm5Ev70J6sjU7asj1GIiCSYefOsHPCaNUfvGZ10A6pDhtg2\nekrsIpLqGje2YokzZ3p3Tict9/37bSB18WL7KiKS6gYPhhkzYPz4X38/qVruY8fCpZcqsYuIHHH7\n7ZCeDtu3e3M+J8l90CANpIqI5HbccdCmDQwb5s35fO+WWbgQbr4Z1q2D0qV9fHURkQS3dClccw1s\n3AhlIhPVk6ZbZtAg20JPiV1E5NcaNIAzz4SpU0t+Ll9b7nv3ZnPWWTbd59RTfXxlEZEkMWoUvPsu\nfPyxPU6Klvvbb0PLlkrsIiIFuflmWLgQNmwo2XliSe4tgdXAWuCxAo55LfL8UuCCgk40eDB06lTU\nEEVEUkeFCrZT05AhJTtPtOReGhiAJfg6QFvgvDzHXA3UBGoBHYBBhZ3wiiuKFWeghMNh1yEkDF2L\nHLoWOVL9WnTsCCNGWHHF4oqW3BsB64BNQAYwFmid55jrgLci9xcAJwKn5XeyTp20IQfoDzc3XYsc\nuhY5Uv1a1Kplg6t5FzQVRbTkXhXYkuvx1sj3oh1zRn4na9euqOGJiKSmTp1KtsdqtOR+9NZJ+cvb\nHs/35048McaziYikuOuug/Xri//z0TpJGgNpWJ87QA8gC+id65jBQBjrsgEbfG0K7MxzrnVAjeKH\nKiKSktZKbLIFAAAD8UlEQVRj45qeKhM5cXWgHLCE/AdUp0XuNwbmex2EiIh4rxWwBmt594h8r2Pk\ndsSAyPNLgQt9jU5ERERERIrHs0VPARDtWtyOXYNlwBygvn+h+S6WvwuAhkAmcKMfQTkQy3UIAYuB\nFdh4VlBFuxaVgelYd/AK4G7fIvPfcGyccnkhxzjNm6Wx7pnqQFmi99FfQnD76GO5Fn8ETojcb0lq\nX4sjx80EpgA3+RWcj2K5DicCK8mZTlzZr+B8Fsu1SANeiNyvDOzGxgGD6HIsYReU3IucN72uLePp\noqckF8u1mAd8H7m/gALWBwRALNcC4EFgHPA/3yLzVyzX4TZgPLZeBGCXX8H5LJZrsQM4PnL/eCy5\nZ/oUn99mA3sLeb7IedPr5O7poqckF8u1yO0ect6ZgybWv4vW5JSviHWNRTKJ5TrUAioB6cBC4E5/\nQvNdLNdiKFAX2I51RTzkT2gJqch50+uPOJ4uekpyRfmdmgHtgUvjFItrsVyLV4HukWNL4W85ar/E\nch3KYjPOWgAVsU9387G+1iCJ5Vo8jnXXhLA1MjOABsCP8QsroRUpb3qd3LcBZ+Z6fCY5Hy8LOuaM\nyPeCJpZrATaIOhTrcy/sY1kyi+VaXETOQrjK2BTcDGBS3KPzTyzXYQvWFfNz5DYLS2hBS+6xXIsm\nQK/I/fXARuBc7BNNqnGeN7XoKUcs16Ia1u/Y2NfI/BfLtchtBMGcLRPLdagNfIYNOFbEBtjq+Bei\nb2K5Fq8AT0fun4Yl/0o+xedCdWIbUHWWN7XoKUe0azEMGyRaHLl94XeAPorl7+KIoCZ3iO06/B2b\nMbMc+H++RuevaNeiMjAZyxPLscHmoBqDjS0cwj69tSd186aIiIiIiIiIiIiIiIiIiIiIiIiIiEgQ\nnQDcH7kfwuZKF8VdQBUvAxLxm9eFw0QSwUnAAyX4+buB33kTioiIeGUs8BM5q37TgQ+Ar4F3ch13\nEbYZxkJsU4jTgb9ghalWA4uACsA/IudZDgzx4xcQEZGj/Z6cGh1Nge+wlngpYC5WfbNs5P7JkePa\nAG9G7qfz6+XdJ+W6/zZwTVyiFvFQUHc1kdRWKs/9L7C6HWAFqqpjm6TUxYp0gRXq2p7n545oDjyC\nFfKqhNV9meJ10CJeUnKXVHAw1/3D5Pzdr8TKyubnSK3sCsBArAtnG1alsEIcYhTxlAZUJYh+BI4r\n5PlsrBrhKeSUWy5LTmndH8nZ3u1IIt8NHAvcTDA3l5GAUctdgmg3MAfrd/8Z+E8+x2Rgg6evYVMn\nywB9gVXASGAwNijbBNtMZUXkPAviG7qIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiEgS+P96boRT\n5fvDIQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x840ca50>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u3053\u306e\u5206\u5e03\u306f\u8868\u306e\u51fa\u308b\u78ba\u7387 $\\theta$ \u304c\u3069\u306e\u5024\u3067\u3042\u308b\u304b\u306b\u3064\u3044\u3066\u306e\u4fe1\u5ff5\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\n",
      "\n",
      "$$ P(0.4\\leq \\theta \\leq 0.6) = \\int_{0.4}^{0.6}6\\theta(1-\\theta)\\mathrm{d}\\theta = 0.2 $$\n",
      "\n",
      "\u306a\u306e\u3067\u3001\u3053\u306e\u4eba\u306f20%\u306e\u78ba\u7387\u3067\u8868\u304c\u51fa\u308b\u78ba\u7387\u306f $0.4\\leq \\theta \\leq 0.6$ \u3060\u308d\u3046\u3068\u4fe1\u3058\u3066\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u3055\u3066\u3001\u3053\u306e\u300c\u30b3\u30a4\u30f3\u30924\u56de\u6295\u3052\u305f\u3089\u5168\u3066\u8868\u304c\u51fa\u305f\u300d\u3068\u3044\u3046\u30c7\u30fc\u30bf $I$ \u304c\u65b0\u305f\u306b\u5f97\u3089\u308c\u305f\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u3088\u308a\u3001\u4e8b\u5f8c\u5206\u5e03\u306f\n",
      "\n",
      "$$ \\pi(\\theta | I) \\propto P(I|\\theta)\\pi(\\theta) = \\theta^4\\times 6\\theta(1-\\theta) \\propto \\theta^5(1-\\theta) $$\n",
      "\n",
      "\u306b\u306a\u308a\u307e\u3059\u3002\u6bd4\u4f8b\u4fc2\u6570\u306f\n",
      "\n",
      "$$\\int_0^1 \\theta^5(1-\\theta)\\mathrm{d}\\theta = \\frac{1}{42}$$\n",
      "\n",
      "\u306a\u306e\u3067\u3001$42$ \u3064\u307e\u308a\n",
      "\n",
      "$$ \\pi(\\theta | I) = 42\\theta^5(1-\\theta) $$\n",
      "\n",
      "\u3067\u3059\u3002\u4e8b\u524d\u5206\u5e03 $\\pi(\\theta)$ \u3068\u4e8b\u5f8c\u5206\u5e03 $\\pi(\\theta|I)$ \u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u30024\u56de\u9023\u7d9a\u3067\u8868\u304c\u51fa\u305f\u3068\u3044\u3046\u7d50\u679c\u3092\u53d7\u3051\u3066\u3001\u3053\u306e\u4eba\u306f\u300c\u3082\u3057\u304b\u3057\u3066\u8868\u306e\u65b9\u304c\u51fa\u3084\u3059\u3044\u30b3\u30a4\u30f3\u306a\u3093\u3058\u3083\u306a\u3044\u304b\uff1f\u300d\u3068\u4fe1\u5ff5\u3092\u6539\u3081\u305f\u3068\u3044\u3046\u308f\u3051\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 1)\n",
      "plot(x, 6*x*(1-x), label='prior')\n",
      "plot(x, 42*x**5*(1-x), label='posterior')\n",
      "legend(loc=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<matplotlib.legend.Legend at 0x87a2a10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ttOIBZQIlsQsbOHhQjWZs1AiqVlUJfcgQ6apoS5duXWLk5pFMbDrRJotTu7mp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\nAxRlcOwyxR7fAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8688bd0>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u3053\u306e\u30c7\u30fc\u30bf $I$ \u306eKL\u60c5\u5831\u91cf\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "$$ \\mathrm{D}_{\\mathrm{KL}}(\\pi(\\theta|I)||\\pi(\\theta)) = \\int_0^1 \\pi(\\theta|I)\\log \\frac{\\pi(\\theta|I)}{\\pi(\\theta)}\\mathrm{d}\\theta = \\int_0^1 42\\theta^5(1-\\theta)\\log\\frac{42\\theta^5(1-\\theta)}{6\\theta(1-\\theta)}\\mathrm{d}\\theta = 42\\int_0^1\\theta^5(1-\\theta)\\log (7\\theta^4)\\mathrm{d}\\theta = 0.67$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u5225\u306e\u5834\u5408\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4e8b\u524d\u5206\u5e03\u306f\u540c\u3058\u3068\u3057\u3066\u300c\uff15\u56de\u30b3\u30a4\u30f3\u3092\u6295\u3052\u305f\u3089\u8868\u3001\u8868\u3001\u88cf\u3001\u8868\u3001\u88cf\u306e\u9806\u306b\u51fa\u305f\u300d\u3068\u3044\u3046\u30c7\u30fc\u30bf $J$ \u306eKL\u60c5\u5831\u91cf\u3092\u6e2c\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u5148\u307b\u3069\u3068\u540c\u69d8\u306b\u3057\u3066\n",
      "\n",
      "$$\\pi(\\theta|J)\\propto \\theta^3(1-\\theta)^2\\times 6\\theta(1-\\theta) \\propto \\theta^4(1-\\theta)^3$$\n",
      "\n",
      "\u53ca\u3073\n",
      "\n",
      "$$ \\int_0^1 \\theta^4(1-\\theta)^3\\mathrm{d}\\theta = \\frac{1}{280} $$\n",
      "\n",
      "\u3088\u308a\n",
      "\n",
      "$$\\pi(\\theta|J) = 280\\theta^4(1-\\theta)^3$$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u56f3\u793a\u3057\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 1)\n",
      "plot(x, 6*x*(1-x), label='prior')\n",
      "plot(x, 280*x**4*(1-x)**3, label='posterior')\n",
      "legend(loc=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.legend.Legend at 0x8b19290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oW6wtWVJlMd9JhG5cXGDoUFi3Tg2R7NkTnj+PfznSiWpZktjtSFiY2uzis89U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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6e43410>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "KL\u60c5\u5831\u91cf\u306f\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002\n",
      "\n",
      "$$\\mathrm{D}_{\\mathrm{KL}}(\\pi(\\theta|J)||\\pi(\\theta)) = \\int_0^1280\\theta^4(1-\\theta)^3\\log\\frac{280\\theta^4(1-\\theta)^3}{6\\theta(1-\\theta)}\\mathrm{d}\\theta = 0.17$$\n",
      "\n",
      "\u5148\u307b\u3069\u306e0.67\u3088\u308a\u3082\u5927\u5206\u5c0f\u3055\u3044\u5024\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u8003\u3048\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\n",
      "\n",
      "1. \u300c4\u56de\u9023\u7d9a\u8868\u300d\u3068\u3044\u3046\u30c7\u30fc\u30bf $I$ \u306f\u4e88\u60f3\u5916\u3060\u3063\u305f\u306e\u3067\u3001\u4fe1\u5ff5\u3092\u5927\u304d\u304f\u6539\u8a02\u3059\u308b\u5fc5\u8981\u304c\u3042\u3063\u305f\u3002\n",
      "2. \u300c\u8868\u3001\u8868\u3001\u88cf\u3001\u8868\u3001\u88cf\u300d\u3068\u3044\u3046\u30c7\u30fc\u30bf $J$ \u306f\u3088\u304f\u3042\u308a\u305d\u3046\u306a\u4e88\u60f3\u3067\u304d\u308b\u7d50\u679c\u306a\u306e\u3067\u3001\u4fe1\u5ff5\u306f\u3042\u307e\u308a\u5927\u304d\u304f\u6539\u8a02\u3055\u308c\u306a\u304b\u3063\u305f"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}

【分散共分散行列】のところですが、以下のようではないでしょうか？なにぶん初心者のため、よくわからないんですが。

平均が$\mu=E[X]$である$n$次元確率変数 $X$ に対して, 各成分が以下で定義される $n$ 次正方行列を分散共分散行列(variance-covariance matrix)と呼ぶ。

$$E_{ij}=E[(X_i-E[X_i])(X_j-E[X_j])]$$

つまり、$ \sum_{ij} =V[X_i],\sum_{ij}=Cov[X_i,X_j] ;;; (i\neq j)$である。

これは以下のように書き表す事ができる為、分散の多次元分布への一般化とみなす事が出来ます。

$$\sum =E[(X-\mu)(X-\mu)^T] =\sum = E[XX^T]-E[X]E[X]^T $$

また、分散共分散行列 $\Sigma$ は必ず半正定値対称行列になります。対称行列であるのは定義より明らかで、任意のベクトル $a$ に対して

$$a^T\sum a=a^T E[XX^T]a-a^T E[X]E[X]^T a =E[(a^T X)(a^T X)^T]-E[a^T X]^2=V[a^TX] \geq 0$$

となるからです。