D29 用機率分佈描述亂中有序的世界－連續型分配 作業.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 作業:\n",
    "作業目標，讓大家熟悉連續型分配的語法，\n",
    "以及怎麼透過 python 語法進行常態分配的機率運算。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q1:計算標準常態分配，小於1的機率有多大?\n",
    "![](Q1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1558,
     "status": "ok",
     "timestamp": 1578021044012,
     "user": {
      "displayName": "Mora chen",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mB40f7sDArbZ5_DYq02nNcnLD0Ryaf7AhsASSQeLQ=s64",
      "userId": "03171203089166907199"
     },
     "user_tz": -480
    },
    "id": "yz28_IgkYdBW",
    "outputId": "a12f486c-18b3-4fb5-d06c-f162aebd9444"
   },
   "outputs": [],
   "source": [
    "# library\n",
    "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",
    "import seaborn as sns\n",
    "\n",
    "'''\n",
    "標準常態的特性：資料點都集中在中心點的兩旁\n",
    "\n",
    "68.3% 的數值，落在平均數 ±1 個標準差間；\n",
    "95.4% 的數值，落在平均數 ±2 個標準差間；\n",
    "99.7% 的數值，落在平均數 ±3 個標準差間。\n",
    "'''\n",
    "import math\n",
    "import pylab\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "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",
    "## Q1\n",
    "#  提示: 用 cdf 來算\n",
    "\n",
    "stats.norm 中的 loc,scale 分別代表\n",
    "loc=mu\n",
    "scale=sigma\n",
    "\n",
    "mu=0\n",
    "sigma=1\n",
    "x=np.linspace(-4, 4, 500)\n",
    "\n",
    "\n",
    "y = stats.norm.cdf(x,mu, sigma)\n",
    "plt.plot(x, y, \"b-\", linewidth=2)\n",
    "\n",
    "plt.title('pdf of Norma(0,1)')\n",
    "plt.show()\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(Z<1)= 0.8413447460685429\n"
     ]
    }
   ],
   "source": [
    "## Q1\n",
    "## 常態分配的計算\n",
    "# 計算標準常態分配記Ｘ　介於 1,-1的比例\n",
    "# 用解答\n",
    "\n",
    "mu=0\n",
    "sigma=1\n",
    "b=  stats.norm.cdf(1,mu, sigma)\n",
    "print(\"P(Z<1)=\",b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q2:計算標準常態分配，大於1，小於 -1 的機率有多大?\n",
    "![](Q2.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(Z>1 or Z<-1)= 0.31731050786291415\n"
     ]
    }
   ],
   "source": [
    "## Q2\n",
    "## 先算 p(<-1X<1)，再算  P(X>1 or X<-1)\n",
    "mu=0\n",
    "sigma=1\n",
    "b=  stats.norm.cdf(1,mu, sigma)\n",
    "a=  stats.norm.cdf(-1,mu, sigma)\n",
    "print(\"P(Z>1 or Z<-1)=\",1-(b-a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q3:X~N(2,4),x 服從常態分配，平均數為2,變異數為 4，計算 X小於 6 的機率有多大?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(Z<2)= 0.9772498680518208\n"
     ]
    }
   ],
   "source": [
    "## Q3\n",
    "#算法1\n",
    "\n",
    "mu=0\n",
    "sigma=1\n",
    "b=  stats.norm.cdf(2,mu, sigma)\n",
    "print(\"P(Z<2)=\",b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "Day33.YOLO 細節理解 - 網路輸出的後處理_HW.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}