Homework/Day_29_HW.ipynb

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    "## 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"
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   "source": [
    "# library\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",
    "import matplotlib.pyplot as plt"
   ]
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   "source": [
    "### Q1: 計算標準常態分配，小於1的機率有多大?\n",
    "![](Day_29_Image_Q1.png)"
   ]
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     "text": [
      "P(Z<1) = 0.8413447460685429\n"
     ]
    }
   ],
   "source": [
    "mu = 0     # 平均值\n",
    "sigma = 1  # 標準差\n",
    "\n",
    "prob = stats.norm.cdf( 1, mu, sigma )\n",
    "print( 'P(Z<1) =', prob )"
   ]
  },
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   "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",
    "![](Day_29_Image_Q2.png)\n"
   ]
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     "text": [
      "P(Z<-1 or Z>1) = 0.31731050786291415\n"
     ]
    }
   ],
   "source": [
    "mu = 0     # 平均值\n",
    "sigma = 1  # 標準差\n",
    "\n",
    "prod = 2*stats.norm.cdf( -1, mu, sigma )\n",
    "print( 'P(Z<-1 or Z>1) =', prod )"
   ]
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   "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?\n",
    "\n",
    "- Hint: [Standardizing](https://www.mathsisfun.com/data/standard-normal-distribution.html)"
   ]
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     "text": [
      "P(X<6) = P(Z<2) =  0.9772498680518208\n"
     ]
    }
   ],
   "source": [
    "mu = 0     # 平均值\n",
    "sigma = 1  # 標準差\n",
    "\n",
    "prod = stats.norm.cdf( (6-2)/math.sqrt(4), mu, sigma )\n",
    "print( 'P(X<6) = P(Z<2) = ', prod )"
   ]
  }
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