h8a.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ハンバーガー統計学 + Python (第８章)\n",
    "\n",
    "* [アイスクリーム統計学・第１章〜第３章（散布図と相関、相関係数、無相関検定）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%93%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第４章〜第６章（単回帰、偏相関、重回帰）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%94%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%96%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第７章〜第９章（相関行列、因子分析1、因子分析2）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%97%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%99%E7%AB%A0.ipynb)\n",
    "* [アイスクリーム統計学・第１０章（主成分分析とクラスター分析）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%82%A2%E3%82%A4%E3%82%B9%E3%82%AF%E3%83%AA%E3%83%BC%E3%83%A0%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%EF%BC%90%E7%AB%A0.ipynb)\n",
    "* [ハンバーガー統計学・第１章〜第２章（平均と分散、信頼区間）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%83%8F%E3%83%B3%E3%83%8F%E3%82%99%E3%83%BC%E3%82%AB%E3%82%99%E3%83%BC%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%91%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%92%E7%AB%A0.ipynb)\n",
    "* [ハンバーガー統計学・第３章〜第５章（カイ２乗検定、t検定 （対応なし・対応あり））](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%83%8F%E3%83%B3%E3%83%8F%E3%82%99%E3%83%BC%E3%82%AB%E3%82%99%E3%83%BC%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%93%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%95%E7%AB%A0.ipynb)\n",
    "* [ハンバーガー統計学・第６章〜第７章（分散分析 (１要因、２要因) ）](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%83%8F%E3%83%B3%E3%83%8F%E3%82%99%E3%83%BC%E3%82%AB%E3%82%99%E3%83%BC%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%96%E7%AB%A0%E3%80%9C%E7%AC%AC%EF%BC%97%E7%AB%A0.ipynb)\n",
    "* [ハンバーガー統計学・第８章 (分布と仮説検定)](http://nbviewer.jupyter.org/github/maskot1977/ipython_notebook/blob/master/%E3%83%8F%E3%83%B3%E3%83%8F%E3%82%99%E3%83%BC%E3%82%AB%E3%82%99%E3%83%BC%E7%B5%B1%E8%A8%88%E5%AD%A6%E3%83%BB%E7%AC%AC%EF%BC%98%E7%AB%A0.ipynb)\n",
    "\n",
    "### Jupyter Notebook (IPython Notebook) とは\n",
    "* Python という名のプログラミング言語が使えるプログラミング環境。計算コードと計算結果を同じ場所に時系列で保存できるので、実験系における実験ノートのように、いつどんな処理を行って何を得たのか記録して再現するのに便利。\n",
    "* [当学演習室での Jupyter Notebook の起動方法](https://raw.githubusercontent.com/maskot1977/-/master/%E6%BC%94%E7%BF%92%E5%AE%A4.txt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.　分布と仮説検定\n",
    "ここから先は、今までの総復習になります。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.1 [データの種類に関する理解](http://qiita.com/ynakayama/items/93157f4c3ae4b23cb748#%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E7%A8%AE%E9%A1%9E%E3%81%AB%E9%96%A2%E3%81%99%E3%82%8B%E7%90%86%E8%A7%A3)\n",
    "上記リンクのページを読んで、以下の用語の意味を理解してください。\n",
    "\n",
    "* 離散変数 (discrete variable) と 連続変数 (continuous variable)\n",
    "* 名義尺度、順序尺度、間隔尺度、比例尺度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.2 [標本抽出法](http://qiita.com/ynakayama/items/d7f6989a4e17ed8a05ec)\n",
    "上記リンクのページを読んで、以下の用語の意味を理解してください。\n",
    "\n",
    "* 標本調査\n",
    "* 無作為抽出法、有意抽出法\n",
    "* 母平均、母比率、極限定理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.3 [標本抽出と推定・検定](http://qiita.com/ynakayama/items/09b8a09f79ebaff24ea8)\n",
    "上記リンクのページを読んで、以下の用語の意味を理解してください。\n",
    "\n",
    "* 母集団 (population)\n",
    "* 推定 (estimation)、区間推定 (interval estimation)、不偏推定量 (unbiased estimator)\n",
    "* 検定"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.4 [データ分析と統計処理の基本的な手順の整理](http://qiita.com/ynakayama/items/1d0530f83b6dabd7b2fa#_reference-d1fd49cac38e75700d6f)\n",
    "上記リンクのページを読んで、以下の用語の意味と統計処理の流れを理解してください。\n",
    "\n",
    "* 記述統計と推測統計\n",
    "* 散布図、回帰分析\n",
    "* 標準誤差と t 値\n",
    "* 重回帰分析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.5 [統計量と区間推定](http://qiita.com/ynakayama/items/5a955c7e29c295292502)\n",
    "上記リンクのページを読んで、以下の用語の意味を理解してください。\n",
    "\n",
    "* 平均値、中央値、分散、標準偏差\n",
    "* 復元抽出と非復元抽出\n",
    "* 標本の期待値と分散\n",
    "* 信頼区間"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.6 [仮説検定と確率分布](http://qiita.com/ynakayama/items/e41f592ad7fe02f23c1c#_reference-641569ed3919a0a008da)\n",
    "上記リンクのページを読んで、以下の用語の意味を理解してください。\n",
    "\n",
    "* 仮説検定\n",
    "* 連続型の確率分布 ... 正規分布、指数分布など\n",
    "* 離散型の確率分布 ... ポアソン分布など\n",
    "* カイ二乗検定、t 検定\n",
    "\n",
    "正規分布に関して、右記のリンク先も読んでください。→ [正規分布](https://ja.wikipedia.org/wiki/%E6%AD%A3%E8%A6%8F%E5%88%86%E5%B8%83)\n",
    "\n",
    "その他の分布に関して、右記のリンク先も読んでください。→[連続型確率分布](http://qiita.com/ynakayama/items/42ece37f040c45863d9a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__ランダムな数字__：\n",
    "以下のコードを実行してください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 図やグラフを図示するためのライブラリをインポートする。\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 乱数を扱うためのライブラリをインポートする。\n",
    "import random\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 一様乱数を１０個発生させて data というリストに格納する。\n",
    "data = []\n",
    "for n in range(10):\n",
    "    data.append(random.random())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.6883771030302529,\n",
       " 0.1135319243359828,\n",
       " 0.7476411620572164,\n",
       " 0.1689763373266342,\n",
       " 0.05641014134913169,\n",
       " 0.6621040379081664,\n",
       " 0.960254021927889,\n",
       " 0.5935874814597817,\n",
       " 0.08967766002174016,\n",
       " 0.41134892395100797]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# data の中身を確認する。\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSWrMyEtSY0Zekhoz8pLUmJGXpMb+D0ts45NuKG1OAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c5e2390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ヒストグラムを描く。\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__課題8.6__：以下の問いに答えてください。\n",
    "* 一様乱数を 10回、100回、1000回、10000回発生させて、それぞれヒストグラムを描いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PKjL9YpI3AA8DDwG/NK08q8j0/zaZZp5V5np1kjcBh1nYV6+Zdaaq2pvkBuAuFn7q76qq\nL84y02joK4EbquqhaWVZZaZ3AB9c9KeDf1DT+wU2NNOzgb9JcoSFv5D69WnlOSrJtcAccFqSr7Fw\nELyZH36exrro1IuhJKkx//d/ktSYJS9JjVnyktSYJS9JjVnyktSYJS9JjVnyktSYJS9Jjf0fyboB\nQtlPR0UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea26cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(10):\n",
    "    data.append(random.random())\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2aRHx3aaDZTBOeT8l6fVrPj5h8Ln12/zYiG02g5K5kO3TJF0l6cKI2OhPpsxK5uJnJH3S\ntrW6tnmR7Rcj4oYZZZyVkrl4UtL+iPiepO/Z/qKkn9Lq+vBmUjIXl0n6oCRFxCO2vyHpVElfmUnC\n+TJ2d46zbNKT9BO2d9jeJukSSesffDdIerd06MzM70TE8hi3kcXIubD9ekmfkfSuiHikgYyzMnIu\nIuLkweUkra5779qExS2VPUb+UdI5tg+z3dbqk1Ob8byJkrl4TNL5kjRY3z1F0qMzTTlb1vC/Osfu\nzuIj7xhyso7t31z9clwVETfafpvthyU9p9XfrJtOyVxI+oCk10r6y8ER54sRcWZzqetROBcvGTLz\nkDNS+Bh5yPa/SrpH0vclXRURDzQYuxaF94s/lvS3a14+9wcR8e2GItfK9rWSdkr6EduPS9otaZsq\ndCcn6QBAQrwNGgAkRHkDQEKUNwAkRHkDQEKUNwAkRHkDQEKUNwAkRHkDQEL/B4SR9/c4hyuOAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f09c2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(100):\n",
    "    data.append(random.random())\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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x3r8DnwPeMOu6Z3hObABuBZ4xePy0Wdc9w7a4DHj3gXYA7gXWz7r2CbXHK4AzgZuP8POh\nc7OvK/UuNyKdD/wDQFV9BdiQZKGn48+TNduiqq6vqvsHD6+nzfH9XW9O+2Pg08Dd0yxuyrq0xZuB\nz1TVXQBVdc+Ua5yWLm1RwFMG808B7q2qn0+xxqmpqi8BP1pllaFzs69Q73Ij0qHr3HWYdVow7E1Z\nbwX+baIVzcaa7ZDkV4ELqurvmNX4r+nock6cBjw1yXVJbkjylqlVN11d2uKDwK8n+T/g68A7plTb\nPBo6N6dy85EOL8mrgItYfgl2LPprYGWfasvBvpb1wIuBVwMnAl9O8uWqumO2Zc3Ea4Ebq+rVSZ4L\nfCHJC6rqgVkXdjToK9S73Ih0F/DMNdZpQaebspK8ALgSOLeqVnv5dbTq0g4vAT6RJCz3nZ6X5OGq\n2jmlGqelS1v8ALinqn4G/CzJfwAvZLn/uSVd2uIi4N0AVfXtJN8FzgC+OpUK58vQudlX98sNwK8l\nOSXJE4E3Aof+Ye4E/gAgycuAH1fVUk/HnydrtkWSZwGfAd5SVd+eQY3TsGY7VNVzBtOzWe5X/6MG\nAx26/X3sAF6R5LgkJ7D8pliL9310aYt9wDkAg/7j04DvTLXK6QpHfpU6dG72cqVeR7gRKckfLv+4\nrqyqzyd5XZI7gJ+y/GzcnC5tAfw58FTgbwdXqQ9X1Vmzq7p/HdvhFzaZepFT0vHv4/Yk1wA3A48A\nV1bVN2dY9kR0PC/+ArhqxTC/P6uq+2ZU8kQl+TiwCPxyku8BlwNPZIzc9OYjSWqIX2cnSQ0x1CWp\nIYa6JDXEUJekhhjqktQQQ12SGmKoS1JDDHVJasj/A+7c58cToA6VAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef6ab50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(1000):\n",
    "    data.append(random.random())\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3cd5d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(10000):\n",
    "    data.append(random.random())\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "* __random.normalvariate(mu, sigma)__ は正規分布に従う乱数を発生させる関数です（mu は平均で、sigma は標準偏差）。平均０、標準偏差1の正規分布に従う乱数を 10回、100回、1000回、10000回発生させて、それぞれヒストグラムを描いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f6c89d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(10):\n",
    "    data.append(random.normalvariate(0, 1))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEACAYAAABMEua6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAEE1JREFUeJzt3X+MXNV5xvHnMeanKQRHxdvGYQ1JSdpIiKIIqEDNCJri\npEqMlLSQtE0gEq3UpJC2ohCo5P2rTSJVKVXEH1EJIihWpJA2MaEoDqI3FU0XUmxjMIa6ijA/vQkt\nWEqMLGK//WMu1mqZ3Zm5987cmdffjzTyndlz73nnePzs9ZmZcx0RAgDksKrtAgAAzSHUASARQh0A\nEiHUASARQh0AEiHUASCRvqFu+w7bC7Z39fjZX9k+YnvtaMoDAAxjkDP1OyVdsfRB2+slvV/SvqaL\nAgBU0zfUI+IhSa/0+NGXJN3YeEUAgMoqzanb/rCk5yLi8YbrAQDUsHrYHWyfLOkWdadejj7cWEUA\ngMqGDnVJ75C0QdJjti1pvaRHbV8YET9Z2tg2i8sAQAURMfQJ86DTLy5viognImImIs6JiLMlPS/p\nN3sF+qLCJuq2efPm1muYhpomtS5qoqZjoa6qBvlI4xZJP5R0ru1nbV+7NLPF9AsATIS+0y8R8fE+\nPz+nuXIAAHUck98o7XQ6bZfwJpNYkzSZdVHTYKhpcJNaVxWuM3czUAd2jLoPAMjGtmKEb5QCAKYA\noQ4AiRDqAJAIoQ4AiRDqAJAIoQ4AiRDqAJAIoQ4AiRDqAJAIoQ4AiRDqOGbNzGyQ7Uq3mZkNbZcP\n9MTaLzhmda/xUvW16VprXgP9sPYLAIBQB4BMCHUASIRQB4BECHUASIRQB4BECHUASIRQB4BECHUA\nSKRvqNu+w/aC7V2LHvui7T22d9r+lu3TRlsmAGAQg5yp3ynpiiWPbZP0nog4X9JeSZ9rujAAwPD6\nhnpEPCTplSWPPRARR8q785LWj6A2AMCQmphT/5Sk+xs4DgCgptV1drZ9q6TXI2LLSu3m5uaObnc6\nHXU6nTrdAkA6RVGoKIraxxlo6V3bs5LujYjzFj12jaTrJF0WEYdW2JeldzGRWHoXk6zq0ruDnqm7\nvL3R2UZJN0r67ZUCHQAwXn3P1G1vkdSR9FZJC5I2S7pF0gmS/rdsNh8Rf7bM/pypYyJxpo5JVvVM\nnSsf4ZhFqGOSceUjAAChDgCZEOoAkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoA\nkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoAkEjf\nULd9h+0F27sWPXaG7W22n7b9Pdunj7ZMAMAgBjlTv1PSFUseu1nSAxHxLkkPSvpc04UBAIbXN9Qj\n4iFJryx5eJOku8rtuyRd2XBdAIAKqs6pnxkRC5IUEfslndlcSQCAqlY3dJxY6Ydzc3NHtzudjjqd\nTkPdAkAORVGoKIrax3HEinncbWTPSro3Is4r7++R1ImIBdszkv4tIn59mX1jkD6AcbOtPucjK+0t\nXtcYJduKCA+736DTLy5vb9gq6Zpy+5OSvjNsxwCA5vU9U7e9RVJH0lslLUjaLOnbkr4p6e2S9kn6\ng4h4dZn9OVPHROJMHZOs6pn6QNMvdRDqmFSEOibZqKdfAABTgFAHgEQIdQBIhFAHgEQIdQBIhFAH\ngEQIdQBIhFAHgEQIdQBIhFAHgEQIdQBIhFBPYmZmg2xXus3MbKDuoZ04pXUjOxb0SmJaF6dqs+66\nfU/jeGN6sKAXAIBQB4BMCHUASIRQB4BECHUASIRQB4BECHUASIRQB4BECHUASIRQB4BEaoW67b+w\n/YTtXba/bvuEpgoDAAyvcqjb/lVJfy7pgog4T9JqSVc3VRgAYHira+5/nKQ1to9IOkXSi/VLAgBU\nVflMPSJelPT3kp6V9IKkVyPigaYKAwAMr/KZuu23SNokaVbSAUn32P54RGxZ2nZubu7odqfTUafT\nqdotAKRUFIWKoqh9nMrrqdv+qKQrIuK68v4fS7ooIj6zpB3rqY8B66mPv+9pHG9MjzbWU39W0sW2\nT3L3X8flkvbUOB4AoKY6c+qPSLpH0g5Jj6l76vKVhuoCAFTA5eySYPpl/H1P43hjenA5OwAAoQ4A\nmRDqAJAIoQ4AiRDqAJAIoQ4AiRDqAJAIoQ4AiRDqAJAIoQ4AiRDqAJBI3SsfAS06sVy/BcAbCHVM\nsUOqvqiW1F2UC8iF6RcASIRQB4BECHUASIRQB4BECHUASIRQB4BECHUASIRQB4BECHUASIRQB4BE\naoW67dNtf9P2Htu7bV/UVGEAgOHVXfvlNkn/GhG/b3u1pFMaqAkAUJEjqi2IZPs0STsi4h192kXV\nPjC47mqFVcfZauvvqG7d9Rf0aqPv9sYb08O2ImLoVefqTL+cLell23fa3m77K7ZPrnE8AEBNdaZf\nVku6QNKnI+K/bP+DpJslbV7acG5u7uh2p9NRp9Op0e1ozcxs0MLCvkr7rls3q/37n2m2oLGoty75\nqlWn6MiRgw3Wg5Ucm6/R/IqiUFEUtY9TZ/plnaT/jIhzyvuXSropIj60pN1UTb8wjTHu/Y/Nuuu8\nTqb1NYrhjH36JSIWJD1n+9zyocslPVn1eACA+up++uV6SV+3fbykH0u6tn5JAICqKk+/DNwB0y9j\nwfTLNPXN9Av6a+PTLwCACUOoA0AihDoAJEKoA0AihDoAJEKoA0AihDoAJEKoA0AihDoAJEKoA0Ai\nddd+adzhw4d199136+DBaku5rl27VldddVWtpWQBYFpN3Nov8/Pz6nQ2yf5Ipf4OH/6a9u7drdnZ\n2Ur7T+u6Gqz9Mk19nyTpUMV93zB9r1EMp+raLxN3pi5JJ510tg4cuL3SvmvW3NdwNUDTDqn+LyOg\nN+bUASARQh0AEiHUASARQh0AEiHUASARQh0AEiHUASARQh0AEiHUASARQh0AEqkd6rZX2d5ue2sT\nBQEAqmviTP0GSU82cBwAQE21Qt32ekkflPRPzZQDAKij7pn6lyTdqHpLzgEAGlJ56V3bvydpISJ2\n2u5ohfVA5+bmjm53Oh11Op2q3U64E2tdnGPVqlN05Ei1i4MAg6n+Gl23blb79z/TbDk4qigKFUVR\n+ziVL5Jh+28l/ZGkX0g6WdIvSfrniPjEknZDXyRj48bP6sCB+Up1rVkzq927/721i2RM50UbqHt6\n9m2zby6wMU5VL5JRefolIm6JiLMi4hxJV0t6cGmgAwDGi8+pA0AijVzOLiJ+IOkHTRwLAFAdZ+oA\nkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoAkAihDgCJEOoAkEjKUH/vey+V7Uo3\nAJhmjSzoNWlefvl51VtvGgCmU8ozdQA4VhHqAJAIoQ4AiRDqAJAIoQ4AiRDqAJAIoQ4AiRDqAJAI\noQ4AiRDqAJBI5VC3vd72g7Z3237c9vVNFgYAGF6dtV9+IekvI2Kn7VMlPWp7W0Q81VBtAIAhVT5T\nj4j9EbGz3P6ZpD2S3tZUYQCA4TUyp257g6TzJT3cxPEAANXUXnq3nHq5R9IN5Rn7m8zNzR3d7nQ6\n6nQ6dbsFgFSKolBRFLWP44iq645LtldL+q6k+yPitmXaxDB9zM/Pa+PGz+rAgflKNa1ZM6uf//xZ\n1VtPvY192+ybuqdn3zb7turkBYZjWxEx9AUe6k6/fFXSk8sFOgBgvOp8pPESSX8o6TLbO2xvt72x\nudIAAMOqPKceEf8h6bgGawEA1MQ3SgEgEUIdABIh1AEgEUIdABIh1AEgEUIdABIh1AEgEUIdABIh\n1AEgEUIdABIh1AEgEUIdwIBOlO3Kt+OOW9PKvjMzG2o965mZDa31XUXti2QAOFYcUp114I8cqb6W\ne519FxaGXpJ8yf77Wuu7Cs7UASARQh0AEiHUASARQh0AEiHUASARQh0AEiHUASARQh0AEiHUASCR\nWqFue6Ptp2z/t+2bmioKAFBN5VC3vUrSlyVdIek9kj5m+91NFTZaRdsF9FC0XcAyirYL6KFou4Ae\nirYL6KFou4AeirYL6KkoirZLaEydM/ULJe2NiH0R8bqkb0ja1ExZo1a0XUAPRdsFLKNou4AeirYL\n6KFou4AeirYL6KFou4CeCPWut0l6btH958vHAAAtmbhVGo8//ni99tpTOu20D1Xa/+DBnzZcEQBM\nD0dUW1LS9sWS5iJiY3n/ZkkREV9Y0q76Wp0AcAyLiKHX7q0T6sdJelrS5ZJekvSIpI9FxJ5KBwQA\n1FZ5+iUiDtv+jKRt6s7N30GgA0C7Kp+pAwAmT+PfKLX9Rdt7bO+0/S3bpy3TbmxfXLL9UdtP2D5s\n+4IV2j1j+zHbO2w/MiE1jXOczrC9zfbTtr9n+/Rl2o18nAZ53rb/0fbe8rV2/ijqGLYu2++z/art\n7eXtb0Zczx22F2zvWqHNWMepX03jHqOyz/W2H7S92/bjtq9fpt24x6pvXUOPV0Q0epP0O5JWlduf\nl/R3PdqskvQ/kmYlHS9pp6R3N13Lov7eJenXJD0o6YIV2v1Y0hmjqmPYmloYpy9I+uty+yZJn29j\nnAZ53pI+IOm+cvsiSfNj+DsbpK73Sdo6jtdQ2d+lks6XtGuZn7cxTv1qGusYlX3OSDq/3D5V3fcD\nJ+E1NUhdQ41X42fqEfFARBwp785LWt+j2Vi/uBQRT0fEXkn93km2xrQezoA1jfsLXpsk3VVu3yXp\nymXajXqcBnnemyR9TZIi4mFJp9teN8KaBq1L6v86a0xEPCTplRWajH2cBqhJGuMYSVJE7I+IneX2\nzyTt0Zu/V9PGWA1SlzTEeI06wD4l6f4ej0/qF5dC0vdt/8j2dW0Xo/GP05kRsSB1X2ySzlym3ajH\naZDnvbTNCz3atFGXJP1W+d/3+2z/xohr6qeNcRpEa2Nke4O6/5N4eMmPWh2rFeqShhivSp9+sf19\nSYt/g1ndf+i3RsS9ZZtbJb0eEVuq9DGKmgZwSUS8ZPuX1Q2tPeVZR5s1NWqFmnrN0y33Lnqj45TM\no5LOioiDtj8g6duSzm25pknT2hjZPlXSPZJuKM+MJ0KfuoYar0qhHhHv71PgNZI+KOmyZZq8IOms\nRffXl49V1q+mAY/xUvnnT23/i7r/3a4cVg3UNNZxKt/cWhcRC7ZnJP1kmWM0Ok49DPK8X5D09j5t\nmta3rsX/ICPiftu3214bEf834tqW08Y4raitMbK9Wt3gvDsivtOjSStj1a+uYcdrFJ9+2SjpRkkf\njohDyzT7kaR32p61fYKkqyVtbbqW5Urs+aB9SvnbUrbXSPpdSU+0WZPGP05bJV1Tbn9S0pteYGMa\np0Ge91ZJnyjruFjSq29MHY1Q37oWz8HavlDdjw2POtCt5V9DbYzTijW1NEaS9FVJT0bEbcv8vK2x\nWrGuocdrBO/m7pW0T9L28nZ7+fivSPruonYb1X2nd6+km0f17nLZ15XqzpW9pu63X+9fWpOks9X9\nNMMOSY9PQk0tjNNaSQ+U/W2T9Ja2xqnX85b0p5L+ZFGbL6v7aZTHtMKnmsZZl6RPq/tLboekH0q6\naMT1bJH0oqRDkp6VdG3b49SvpnGPUdnnJZIOL3rtbi//Ltseq751DTtefPkIABLhcnYAkAihDgCJ\nEOoAkAihDgCJEOoAkAihDgCJEOoAkAihDgCJ/D8YlNtWLl3m7QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f7e6190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(100):\n",
    "    data.append(random.normalvariate(0, 1))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGu6R1xHvSjMp7y+ikvLfM\ntPqthxon7bceahz0ayVvvLeMJG1ghrskNchwl7QBjD9Xv97n6Z1zX2fm5razsHB4rD6nnPIDvPji\n/5twi7M+n7oe5nzXQ42T9lsPNU7abzbn6Tufc09yeZJvJvlfST6+WtvZaAbBXmO9BsE+Xp/JdiBJ\ns2LTavzQJKcA/x54J/BnwJeT3FVV31yN7a3UCy+8wKc//WmefvppvvOd73DuueeO3Pe9730vF154\n4djbnGQEPlv6QK/jGpbqM5s1zaI+s/m76nVcw0v1+316vV7XZUxkVcIduBQ4VFWHAZLcAVwFzGS4\nf+tb3+L66+d59tkPAf8bOHvEnn/Mt7/95+zZc8vY2/zrEfgo5ocvGHy9nAV9Zm1HnN2aZlGf2fxd\n9TquYbEtvP3tbx+719at53D06OPTL2dMqxXuZwNHFr3/UwaBP7O2bHktzz77b3hpkC7nFuDrq1WS\npE49A+xm9DwYWFiYjQHYaoX7urJp0ya+//0nOe20n+b73z/Iq1/9JyP1e/bZx9m8+R2rXJ0kjW9V\nzpZJ8lZgvqouH77fCVRV3bRoHY/YSdIERjlbZrXC/VXAQQYHVP8ceAR4f1UdmPrGJEkvsyrTMlX1\nQpJfBu5jcLrlrQa7JK2dzi5ikiStnk5vP5Bkd5I/TfKV4evyLutZLMnHkryY5IdnoJZfTfK1JF9N\n8sUkc13XBJDk5iQHkjya5A+SnDYDNf1Mkq8neSHJJR3XMlMX8iW5NclCkse6ruWYJNuSPJDkG0n2\nJfmVGahpS5IvDfe3fUl2d13TMUlOGWbl3cutOwv3lvmNqrpk+Ppi18XA4A8OeBcwK1cZ3VxVb66q\ntwD/hcH5WbPgPuCiqroYOATs6rgegH3APwL+W5dFLLqQ7zLgIuD9Sd7YZU3AnmE9s+R54KNVdRHw\nE8CHuv49VdUzwNuH+9vFwBVJZuVU7o8A+0dZcRbCfTZOCn2pTwHXd13EMVX1vUVvfxB4sataFquq\nvVV1rJaHgW1d1gNQVQer6hDd/10dv5Cvqp4Djl3I15mqegh4qssalqqqo1X16HD5e8ABRr+KcNVU\n1bGbMW1hcGyy8/nr4aDzPcBnRll/FsL9l4df6z+T5PSui0lyJXCkqvZ1XctiSX4tyRPAzwL/uut6\nTuCDwH/tuogZcqIL+ToPrVmWZDuDkfKXuq3k+PTHV4GjwP1V9eWua+KvB50j/UOz6hcxJbkf2Lq4\niUFxn2BwieevVlUl+TXgN4B/1mFNnwRuYDAls/izVfdKv6eq+kJVfRL45HDu9sOMe9ncKtU1XOcT\nwHNVdfus1KT1JckPAZ8HPrLkm2onht9I3zI8jvRHSS6sqpGmQ1ZDkp8CFqrq0SQ9RsilVQ/3qnrX\n8msB8B+ANdkxT1ZTkr8DbAe+lsEz5rYBf5Lk0qr6iy5qOoHbgXtYo3Bfrq4k1zL4qrhml+qO8bvq\n0pPA6xa93zZs0xJJNjEI9t+tqru6rmexqvq/SR4ELmfEue5V8jbgyiTvAU4FXpPks1X1Cyfr0PXZ\nMovP+vjHdHyjlqr6elXNVdXrq+pcBl+l37Lawb6cJOctens1g3nJzg3PbroeuHJ4EGrWdDnv/mXg\nvCTnJNkMvA9Y9gyHNRC6Px6x1O8A+6vqN7suBCDJa49NESc5lcE3+U5velhVN1TV66rq9Qz+lh54\npWCH7u8tc3OSixkcIHwc+OfdlvMyxWzsCDcmOZ/B7+kw8C86rueY3wI2A/cPvujwcFVd12VBSa4e\n1vVa4D8nebSqrljrOmbxQr4ktzO47eKZw+M3u6tqT8c1vQ34OWDfcI67gBs6PnPubwG3Dc94OgX4\n/aq6p8N6JuJFTJLUoFk4W0aSNGWGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDfr/Mbnm\n3JNd+xUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fa39c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(1000):\n",
    "    data.append(random.normalvariate(0, 1))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fB+4Hbmy6fRK4r9neDdyQ5IwkFwOXAvsG3b8kafEGXt45hduBXUluAg7RO2OHqjqQZBe9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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f5fc950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(10000):\n",
    "    data.append(random.normalvariate(0, 1))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* __random.expovariate(lambd)__は指数分布に従う乱数を発生させる関数です（lambd は平均にしたい値の逆数）。平均1の指数分布に従う乱数を 10回、100回、1000回、10000回発生させて、それぞれヒストグラムを描いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f22e9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(10):\n",
    "    data.append(random.expovariate(1))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEACAYAAABMEua6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKHUASOR/AcqBww5jrgFFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f6f2790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(100):\n",
    "    data.append(random.expovariate(1))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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q6gdJ/j2wN8kL/OvJ58l/c0+SNLWpgr6qftD985+S/C9gAzCbZGVVzSZZBbzy5nvYMbI+\n0y2SpLMGgwGDwWCqfaRqsgF3krcDy6rqRJJ3AHuBncAHgFer6oEkfwxcWVVbztG/Jh3sJ9uo+gzT\nfVjIFP2n6Tv9sSf9dybp0peEqhrr9LtpRvQrgb8YBjbLgS9X1d4kfwfsTnIX8CKwaYpjSJKmNHHQ\nV9X/Bdafo/1V4IPTFCVJWjheGXvJmfyqWq+slZamac+60QU3+VW14JW10lLkiF6SGmfQS1LjDHpJ\napxBL0mNM+glqXEGvSQ1zqCXpMYZ9JLUOINekhpn0C853kJBWmq8BcKS4y0UpKXGEb0kNc6gl6TG\nGfSS1DiDXpIaZ9BrTJOfteMZO1I/DHqN6exZO+Mvs7PHPbVT6sGiBX2SW5L8Q5L/k+SPF+s4upRM\n/iYxfKN4sYeapUvfogR9kmXAfwU+BLwX+O0kv7wYx2rDoO8CLiKD8zy3tC72GgwGfZdw0fC1mM5i\njeg3AIer6sWqOgU8CmxcpGM1YNB3AReRwXmeW1qfCAy31/laTGexgn41cHTk8ctdm9Qjv0jW0tTr\nLRDe+c7fnKjfyZP/wMmTC1yMloDJb/8wO/tWkslv/7Bs2ds5c+a1sfvt3Llz4r5nrVx5DcePH5m4\n/1K1atW1U30KvJhe91RNft+TN91p8mvAjqq6pXu8BaiqemBkm4U/sCQtAVU11qhjsYL+LcALwAeA\nHwDPAL9dVYcW/GCSpPNalKmbqvqXJPcAexl+D/AFQ16S+rEoI3pJ0sWjlytjvZhqKMmaJPuTfDfJ\ngSSf6LumPiVZluTZJHv6rqVvSVYk+VqSQ91/H7/ad019SfKHSb6T5NtJvpzksr5rulCSfCHJbJJv\nj7RdmWRvkheSPJlkxVz7ueBB78VUP+M08Mmqei/w68DvL+HXAuBe4GDfRVwkPg98o6rWAf8BWJJT\nn0l+AfgD4Maq+hWG082b+63qgnqEYVaO2gLsq6rrgf3A1rl20seI3oupOlV1vKqe79ZPMPyfeUle\nb5BkDfBh4OG+a+lbkncC/7mqHgGoqtNV9ZOey+rTW4B3JFkOvB34x57ruWCq6pvAD9/QvBHY1a3v\nAm6faz99BL0XU51DkmuB9cDT/VbSmz8B/ohpfuewHWuBf07ySDeV9adJ3tZ3UX2oqn8EPge8BBwD\nflRV+/qtqndXVdUsDAeLwFVzdfDulReBJFcAjwH3diP7JSXJbwCz3aebdMtSthy4EfhvVXUj8BrD\nj+tLTpJ/x3AEew3wC8AVST7Sb1UXnTkHR30E/THg3SOP13RtS1L3cfQx4EtV9Xjf9fTkJuC2JN8H\n/gfw/iR/3nNNfXoZOFpVf9c9foxh8C9FHwS+X1WvVtW/AP8T+E8919S32SQrAZKsAl6Zq0MfQf8t\n4Lok13Tfnm8GlvJZFl8EDlbV5/supC9VdV9Vvbuq3sPwv4f9VfW7fdfVl+5j+dEkv9Q1fYCl+yX1\nS8CvJXlrhveg+ABL74vpN37K3QPc2a3fAcw5QLzg97rxYqrXJbkJ+ChwIMlzDD+C3VdVT/RbmS4C\nnwC+nOTfAN8Hfq/nenpRVc8keQx4DjjV/fNP+63qwknyFWAGeFeSl4DtwGeBryW5C3gR2DTnfrxg\nSpLa5pexktQ4g16SGmfQS1LjDHpJapxBL0mNM+glqXEGvSQ1zqCXpMb9fxCVg603wkTNAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea91a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(1000):\n",
    "    data.append(random.expovariate(1))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rkywDTqyqzU2/e/rGSJIWyGzX9E+pqnGAqtoDnNK0Lwd29vXb3bQtB3b1te9q2iRJC2jx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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f07c250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(10000):\n",
    "    data.append(random.expovariate(1))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* __np.random.binomial(n=10, p=0.5)__ は、二項分布に従う乱数を発生させる numpy の関数です（確率pで表が出るコインをn回投げたときに、表が出る個数を返します）。p=0.5の二項分布に従う乱数を 10回、100回、1000回、10000回発生させて、それぞれヒストグラムを描いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea780d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(10):\n",
    "    data.append(np.random.binomial(n=10, p=0.5))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/Bh6qqs/ON9Wavgy8NMkZSU5ldYfo6cdawBIHuqGUq4CLuz3y3qmqR6rqBcAu4MVJfmne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\nS1ySGmaJS1LDLHFJapglLkkN+392RELmfT1k2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f87bbd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(100):\n",
    "    data.append(np.random.binomial(n=10, p=0.5))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f0242d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(1000):\n",
    "    data.append(np.random.binomial(n=10, p=0.5))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f058250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(10000):\n",
    "    data.append(np.random.binomial(n=10, p=0.5))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 同様に、p=0.2, p=0.8 の二項分布に従う乱数を10000回発生させて、それぞれヒストグラムを描いてください。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f622210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(1000):\n",
    "    data.append(np.random.binomial(n=10, p=0.2))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f8c9a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = []\n",
    "for n in range(1000):\n",
    "    data.append(np.random.binomial(n=10, p=0.8))\n",
    "plt.hist(data, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.7 [分布の適合度を検定する](http://qiita.com/ynakayama/items/5ab69d6d06d61148a689#_reference-b3cc8224722bc23a82f2)\n",
    "上記リンクのページを読んで、以下のトピックの意味を理解してください。\n",
    "\n",
    "* 検定によってわかること\n",
    "* 分布の適合度の検定\n",
    "* ポアソン分布と極限定理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 8.8 [t検定](http://www.geisya.or.jp/~mwm48961/statistics/bunsan1.htm)\n",
    "上記リンクのページを読んでt検定の概要を理解してください。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "下記は、t検定を行うPythonプログラムの例です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[68, 75, 80, 71, 73, 79, 69, 65]\n",
      "[86, 83, 76, 81, 75, 82, 87, 75]\n",
      "t 値は -2.99232037543\n",
      "確率は 0.0201600161737\n",
      "有意な差があります\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy import stats\n",
    "\n",
    "X = [68, 75, 80, 71, 73, 79, 69, 65]\n",
    "Y = [86, 83, 76, 81, 75, 82, 87, 75]\n",
    "\n",
    "print(X)\n",
    "print(Y)\n",
    "\n",
    "t, p = stats.ttest_rel(X, Y)\n",
    "\n",
    "print( \"t 値は %(t)s\" %locals() )\n",
    "print( \"確率は %(p)s\" %locals() )\n",
    "\n",
    "if p < 0.05:\n",
    "    print(\"有意な差があります\")\n",
    "else:\n",
    "    print(\"有意な差がありません\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.9 [カイ二乗検定 (Chi-squared test)](http://stat.biopapyrus.net/statistic/chisqtest.html)\n",
    "カイ二乗検定は、観測データの分布が理論値の分布に従うかどうかを検定する手法である。例えば、サイコロを60回ふったとき、各目が出る回数は次のようになったとき、理論値の分布に従うかどうかを検定する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "chi2 値は 3.02600126762\n",
      "確率は 0.0296994592035\n",
      "有意な差があります\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "o = [17, 10, 6, 7, 15, 5] # 実測値\n",
    "e = [10, 10, 10, 10, 10, 10] # 理論値\n",
    "\n",
    "chi2, p = stats.chisquare(o, f_exp = e)\n",
    "\n",
    "print( \"chi2 値は %(t)s\" %locals() )\n",
    "print( \"確率は %(p)s\" %locals() )\n",
    "\n",
    "if p < 0.05:\n",
    "    print(\"有意な差があります\")\n",
    "else:\n",
    "    print(\"有意な差がありません\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__今日の課題提出__：計算結果を.ipynb ファイル（または.jsonファイル）として保存し、指定したアドレスまでメールしてください。メールタイトルは「__ハンバーガー統計学8__」とし、メール本文に学籍番号と氏名を明記のこと。また、感想も書いてくれると喜びます。今後の講義の改善につながるかも知れません。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# お疲れ様でした。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これで統計学の勉強は一通り終了です。忘れてしまっても、また必要になったときに思い出して復習してください。ここから先、統計についての理解を深めるには、言葉の定義や数式の意味をインターネット等を通じて調べてよく考えてみるのも良いですし、以下のような総説を読んでみるのも良いと思います。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [ダメな統計学](http://id.fnshr.info/2014/12/17/stats-done-wrong-toc/)\n",
    "* [グラフでウソをつく方法――統計リテラシーのための基礎文献](http://bylines.news.yahoo.co.jp/soichiromatsutani/20150216-00043032/)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}