D28 用機率分布描述亂中有序的世界－ 離散型分配 (2) 作業.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 作業:\n",
    "今天學到五種分配，包含，   \n",
    "離散均勻分配( Discrete Uniform Distribution )   \n",
    "伯努利分配( Bernoulli Distribution )   \n",
    "二項分配(Binomial Distribution)  \n",
    "負二項分配(Negative Binomial Distribution)  \n",
    "超幾何分配(Hypergeometric Distribution)   \n",
    "今天我們透過作業中的問題，回想今天的內容吧!  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q1: 大樂透的頭獎，你必須從49個挑選出 6 個號碼，\n",
    "### 且這六個號碼與頭獎的六個號碼一致，頭獎的機率是屬於哪一種分配?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "''''\n",
    "超幾何分配\n",
    "''''\n",
    "'''\n",
    "可以想像成，大樂透中有49個號碼，6個是屬於開獎抽出的數字那一群，43個是不屬於開獎抽出的數字那一群，  \n",
    "那你挑的六組號碼，有多少個是落在開獎抽出的數字那一群?\n",
    "所以是屬於 超幾何分配.\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q2: 運用範例的 python 程式碼，計算大樂透的中頭獎機率?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "中頭獎的機率為== 7.151123842018523e-08\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "import math\n",
    "import statistics\n",
    "\n",
    "'''\n",
    "X: HG(49,6,6)\n",
    "p(X=6) 的機率就是中頭獎的機率\n",
    "'''\n",
    "probs = stats.hypergeom.pmf(6,49,6,6)\n",
    "print(\"中頭獎的機率為==\",probs)\n",
    "\n",
    "#...用解答"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6]\n",
      "[4.35964976e-01 4.13019450e-01 1.32378029e-01 1.76504039e-02\n",
      " 9.68619724e-04 1.84498995e-05 7.15112384e-08]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''錯了\n",
    "# 1.定義超幾何分配的基本資訊\n",
    "\n",
    "N：共布幾個物件，N = 0,1,...\n",
    "K：N個物件中，有K個是你關心的物件類型個數，K=0,1,2,...,N \n",
    "n：K個物件，要抽出n個物件，n=0,1,...,N\n",
    "\n",
    "N=49\n",
    "K=6\n",
    "n=6\n",
    "\n",
    "#產生一個同樣間隔的序列\n",
    "r = np.arange(0, min(n+1,K+1)) #產出 x 對應點\n",
    "print(r)\n",
    "\n",
    "# 2.計算機率質量函數 (probability mass function)\n",
    "# P(X=x) --> 是機率\n",
    "probs = stats.hypergeom.pmf(r, N,K,n)\n",
    "print(probs)\n",
    "print(type(probs))\n",
    "\n",
    "plt.bar(r, probs)\n",
    "plt.ylabel('P(X=x)')\n",
    "plt.xlabel('x')\n",
    "plt.title('pmf of Hypergeometric(N=49,K=6,n=6)')\n",
    "plt.show()\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q3: 你覺得電腦簽注的中獎機率，和人腦簽注相比，哪一個機率高?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "''''\n",
    "實驗結果都不高 ---> 兩者一樣高\n",
    "''''"
   ]
  }
 ],
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