{
 "cells": [
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "12局中4局以上で高い一致率（10%で発生とする）を示す確率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "r   = 0.1\n",
    "num = 12\n",
    "lim = 3\n",
    "s   = 1.0 - scipy.stats.binom.cdf(lim, num, r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5637470165\n"
     ]
    }
   ],
   "source": [
    "print(100 * s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "42局中に、一致率の4局を含む12局が現れる確率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "num_ext  = 42\n",
    "num_iter = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(20170226)\n",
    "res = np.zeros(num_iter)\n",
    "for ii in range(num_iter):\n",
    "    samp = np.random.choice([0, 1], num_ext, replace=True, p=[1.0-r, r])\n",
    "    seq  = pd.Series(samp).rolling(window=num).sum()\n",
    "    res[ii] = seq.max()\n",
    "s = (res > lim).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.79\n"
     ]
    }
   ],
   "source": [
    "print(100 * s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "念のため他のseedも試す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(20170227)\n",
    "res = np.zeros(num_iter)\n",
    "for ii in range(num_iter):\n",
    "    samp = np.random.choice([0, 1], 42, replace=True, p=[0.9, 0.1])\n",
    "    seq  = pd.Series(samp).rolling(window=12).sum()\n",
    "    res[ii] = seq.max()\n",
    "s = (res > 3).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.48\n"
     ]
    }
   ],
   "source": [
    "print(100 * s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
 ],
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