Statistics - 02.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan = pd.read_csv(\"C://Users//classroom2-DTP//Downloads//loan.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Loan_ID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Married</th>\n",
       "      <th>Dependents</th>\n",
       "      <th>Education</th>\n",
       "      <th>Self_Employed</th>\n",
       "      <th>ApplicantIncome</th>\n",
       "      <th>CoapplicantIncome</th>\n",
       "      <th>LoanAmount</th>\n",
       "      <th>Loan_Amount_Term</th>\n",
       "      <th>Credit_History</th>\n",
       "      <th>Property_Area</th>\n",
       "      <th>Loan_Status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>LP001002</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>5849</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>LP001003</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>4583</td>\n",
       "      <td>1508.0</td>\n",
       "      <td>128.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Rural</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>LP001005</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>Yes</td>\n",
       "      <td>3000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>LP001006</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>2583</td>\n",
       "      <td>2358.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>LP001008</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>6000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>141.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>LP001011</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>Yes</td>\n",
       "      <td>5417</td>\n",
       "      <td>4196.0</td>\n",
       "      <td>267.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>LP001013</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>2333</td>\n",
       "      <td>1516.0</td>\n",
       "      <td>95.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>LP001014</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>3+</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3036</td>\n",
       "      <td>2504.0</td>\n",
       "      <td>158.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>LP001018</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>4006</td>\n",
       "      <td>1526.0</td>\n",
       "      <td>168.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>LP001020</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>12841</td>\n",
       "      <td>10968.0</td>\n",
       "      <td>349.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>LP001024</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3200</td>\n",
       "      <td>700.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>LP001027</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2500</td>\n",
       "      <td>1840.0</td>\n",
       "      <td>109.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>LP001028</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3073</td>\n",
       "      <td>8106.0</td>\n",
       "      <td>200.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>LP001029</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>1853</td>\n",
       "      <td>2840.0</td>\n",
       "      <td>114.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Rural</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>LP001030</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>1299</td>\n",
       "      <td>1086.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>LP001032</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>4950</td>\n",
       "      <td>0.0</td>\n",
       "      <td>125.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>LP001034</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>1</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3596</td>\n",
       "      <td>0.0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>LP001036</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3510</td>\n",
       "      <td>0.0</td>\n",
       "      <td>76.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>LP001038</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>4887</td>\n",
       "      <td>0.0</td>\n",
       "      <td>133.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Rural</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>LP001041</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2600</td>\n",
       "      <td>3500.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>LP001043</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>7660</td>\n",
       "      <td>0.0</td>\n",
       "      <td>104.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>LP001046</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>5955</td>\n",
       "      <td>5625.0</td>\n",
       "      <td>315.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>LP001047</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>2600</td>\n",
       "      <td>1911.0</td>\n",
       "      <td>116.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>LP001050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3365</td>\n",
       "      <td>1917.0</td>\n",
       "      <td>112.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Rural</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>LP001052</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3717</td>\n",
       "      <td>2925.0</td>\n",
       "      <td>151.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>LP001066</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>Yes</td>\n",
       "      <td>9560</td>\n",
       "      <td>0.0</td>\n",
       "      <td>191.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>LP001068</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>2799</td>\n",
       "      <td>2253.0</td>\n",
       "      <td>122.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>LP001073</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>4226</td>\n",
       "      <td>1040.0</td>\n",
       "      <td>110.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>LP001086</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>1442</td>\n",
       "      <td>0.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>LP001087</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3750</td>\n",
       "      <td>2083.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>LP001243</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3208</td>\n",
       "      <td>3066.0</td>\n",
       "      <td>172.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>LP001245</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1875</td>\n",
       "      <td>1875.0</td>\n",
       "      <td>97.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>LP001248</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>300.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>LP001250</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>3+</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>4755</td>\n",
       "      <td>0.0</td>\n",
       "      <td>95.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>LP001253</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>3+</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>Yes</td>\n",
       "      <td>5266</td>\n",
       "      <td>1774.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>LP001255</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3750</td>\n",
       "      <td>0.0</td>\n",
       "      <td>113.0</td>\n",
       "      <td>480.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>LP001256</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3750</td>\n",
       "      <td>4750.0</td>\n",
       "      <td>176.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>LP001259</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1000</td>\n",
       "      <td>3022.0</td>\n",
       "      <td>110.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>LP001263</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>3+</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3167</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>300.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>LP001264</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>3+</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>Yes</td>\n",
       "      <td>3333</td>\n",
       "      <td>2166.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>LP001265</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3846</td>\n",
       "      <td>0.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>LP001266</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2395</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>LP001267</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>1378</td>\n",
       "      <td>1881.0</td>\n",
       "      <td>167.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>LP001273</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>6000</td>\n",
       "      <td>2250.0</td>\n",
       "      <td>265.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>LP001275</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3988</td>\n",
       "      <td>0.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>LP001279</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>2366</td>\n",
       "      <td>2531.0</td>\n",
       "      <td>136.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>LP001280</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3333</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>99.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>LP001282</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>2500</td>\n",
       "      <td>2118.0</td>\n",
       "      <td>104.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>LP001289</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>8566</td>\n",
       "      <td>0.0</td>\n",
       "      <td>210.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>LP001310</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>5695</td>\n",
       "      <td>4167.0</td>\n",
       "      <td>175.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>LP001316</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>2958</td>\n",
       "      <td>2900.0</td>\n",
       "      <td>131.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>LP001318</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>6250</td>\n",
       "      <td>5654.0</td>\n",
       "      <td>188.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>LP001319</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>2</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3273</td>\n",
       "      <td>1820.0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Urban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>LP001322</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>4133</td>\n",
       "      <td>0.0</td>\n",
       "      <td>122.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>LP001325</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>3620</td>\n",
       "      <td>0.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>LP001326</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6782</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>360.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Urban</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>LP001327</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>2484</td>\n",
       "      <td>2302.0</td>\n",
       "      <td>137.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>LP001333</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>1977</td>\n",
       "      <td>997.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>LP001334</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Not Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>4188</td>\n",
       "      <td>0.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>LP001343</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>1759</td>\n",
       "      <td>3541.0</td>\n",
       "      <td>131.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Semiurban</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Loan_ID  Gender Married Dependents     Education Self_Employed  \\\n",
       "0   LP001002    Male      No          0      Graduate            No   \n",
       "1   LP001003    Male     Yes          1      Graduate            No   \n",
       "2   LP001005    Male     Yes          0      Graduate           Yes   \n",
       "3   LP001006    Male     Yes          0  Not Graduate            No   \n",
       "4   LP001008    Male      No          0      Graduate            No   \n",
       "5   LP001011    Male     Yes          2      Graduate           Yes   \n",
       "6   LP001013    Male     Yes          0  Not Graduate            No   \n",
       "7   LP001014    Male     Yes         3+      Graduate            No   \n",
       "8   LP001018    Male     Yes          2      Graduate            No   \n",
       "9   LP001020    Male     Yes          1      Graduate            No   \n",
       "10  LP001024    Male     Yes          2      Graduate            No   \n",
       "11  LP001027    Male     Yes          2      Graduate           NaN   \n",
       "12  LP001028    Male     Yes          2      Graduate            No   \n",
       "13  LP001029    Male      No          0      Graduate            No   \n",
       "14  LP001030    Male     Yes          2      Graduate            No   \n",
       "15  LP001032    Male      No          0      Graduate            No   \n",
       "16  LP001034    Male      No          1  Not Graduate            No   \n",
       "17  LP001036  Female      No          0      Graduate            No   \n",
       "18  LP001038    Male     Yes          0  Not Graduate            No   \n",
       "19  LP001041    Male     Yes          0      Graduate           NaN   \n",
       "20  LP001043    Male     Yes          0  Not Graduate            No   \n",
       "21  LP001046    Male     Yes          1      Graduate            No   \n",
       "22  LP001047    Male     Yes          0  Not Graduate            No   \n",
       "23  LP001050     NaN     Yes          2  Not Graduate            No   \n",
       "24  LP001052    Male     Yes          1      Graduate           NaN   \n",
       "25  LP001066    Male     Yes          0      Graduate           Yes   \n",
       "26  LP001068    Male     Yes          0      Graduate            No   \n",
       "27  LP001073    Male     Yes          2  Not Graduate            No   \n",
       "28  LP001086    Male      No          0  Not Graduate            No   \n",
       "29  LP001087  Female      No          2      Graduate           NaN   \n",
       "..       ...     ...     ...        ...           ...           ...   \n",
       "70  LP001243    Male     Yes          0      Graduate            No   \n",
       "71  LP001245    Male     Yes          2  Not Graduate           Yes   \n",
       "72  LP001248    Male      No          0      Graduate            No   \n",
       "73  LP001250    Male     Yes         3+  Not Graduate            No   \n",
       "74  LP001253    Male     Yes         3+      Graduate           Yes   \n",
       "75  LP001255    Male      No          0      Graduate            No   \n",
       "76  LP001256    Male      No          0      Graduate            No   \n",
       "77  LP001259    Male     Yes          1      Graduate           Yes   \n",
       "78  LP001263    Male     Yes         3+      Graduate            No   \n",
       "79  LP001264    Male     Yes         3+  Not Graduate           Yes   \n",
       "80  LP001265  Female      No          0      Graduate            No   \n",
       "81  LP001266    Male     Yes          1      Graduate           Yes   \n",
       "82  LP001267  Female     Yes          2      Graduate            No   \n",
       "83  LP001273    Male     Yes          0      Graduate            No   \n",
       "84  LP001275    Male     Yes          1      Graduate            No   \n",
       "85  LP001279    Male      No          0      Graduate            No   \n",
       "86  LP001280    Male     Yes          2  Not Graduate            No   \n",
       "87  LP001282    Male     Yes          0      Graduate            No   \n",
       "88  LP001289    Male      No          0      Graduate            No   \n",
       "89  LP001310    Male     Yes          0      Graduate            No   \n",
       "90  LP001316    Male     Yes          0      Graduate            No   \n",
       "91  LP001318    Male     Yes          2      Graduate            No   \n",
       "92  LP001319    Male     Yes          2  Not Graduate            No   \n",
       "93  LP001322    Male      No          0      Graduate            No   \n",
       "94  LP001325    Male      No          0  Not Graduate            No   \n",
       "95  LP001326    Male      No          0      Graduate           NaN   \n",
       "96  LP001327  Female     Yes          0      Graduate            No   \n",
       "97  LP001333    Male     Yes          0      Graduate            No   \n",
       "98  LP001334    Male     Yes          0  Not Graduate            No   \n",
       "99  LP001343    Male     Yes          0      Graduate            No   \n",
       "\n",
       "    ApplicantIncome  CoapplicantIncome  LoanAmount  Loan_Amount_Term  \\\n",
       "0              5849                0.0         NaN             360.0   \n",
       "1              4583             1508.0       128.0             360.0   \n",
       "2              3000                0.0        66.0             360.0   \n",
       "3              2583             2358.0       120.0             360.0   \n",
       "4              6000                0.0       141.0             360.0   \n",
       "5              5417             4196.0       267.0             360.0   \n",
       "6              2333             1516.0        95.0             360.0   \n",
       "7              3036             2504.0       158.0             360.0   \n",
       "8              4006             1526.0       168.0             360.0   \n",
       "9             12841            10968.0       349.0             360.0   \n",
       "10             3200              700.0        70.0             360.0   \n",
       "11             2500             1840.0       109.0             360.0   \n",
       "12             3073             8106.0       200.0             360.0   \n",
       "13             1853             2840.0       114.0             360.0   \n",
       "14             1299             1086.0        17.0             120.0   \n",
       "15             4950                0.0       125.0             360.0   \n",
       "16             3596                0.0       100.0             240.0   \n",
       "17             3510                0.0        76.0             360.0   \n",
       "18             4887                0.0       133.0             360.0   \n",
       "19             2600             3500.0       115.0               NaN   \n",
       "20             7660                0.0       104.0             360.0   \n",
       "21             5955             5625.0       315.0             360.0   \n",
       "22             2600             1911.0       116.0             360.0   \n",
       "23             3365             1917.0       112.0             360.0   \n",
       "24             3717             2925.0       151.0             360.0   \n",
       "25             9560                0.0       191.0             360.0   \n",
       "26             2799             2253.0       122.0             360.0   \n",
       "27             4226             1040.0       110.0             360.0   \n",
       "28             1442                0.0        35.0             360.0   \n",
       "29             3750             2083.0       120.0             360.0   \n",
       "..              ...                ...         ...               ...   \n",
       "70             3208             3066.0       172.0             360.0   \n",
       "71             1875             1875.0        97.0             360.0   \n",
       "72             3500                0.0        81.0             300.0   \n",
       "73             4755                0.0        95.0               NaN   \n",
       "74             5266             1774.0       187.0             360.0   \n",
       "75             3750                0.0       113.0             480.0   \n",
       "76             3750             4750.0       176.0             360.0   \n",
       "77             1000             3022.0       110.0             360.0   \n",
       "78             3167             4000.0       180.0             300.0   \n",
       "79             3333             2166.0       130.0             360.0   \n",
       "80             3846                0.0       111.0             360.0   \n",
       "81             2395                0.0         NaN             360.0   \n",
       "82             1378             1881.0       167.0             360.0   \n",
       "83             6000             2250.0       265.0             360.0   \n",
       "84             3988                0.0        50.0             240.0   \n",
       "85             2366             2531.0       136.0             360.0   \n",
       "86             3333             2000.0        99.0             360.0   \n",
       "87             2500             2118.0       104.0             360.0   \n",
       "88             8566                0.0       210.0             360.0   \n",
       "89             5695             4167.0       175.0             360.0   \n",
       "90             2958             2900.0       131.0             360.0   \n",
       "91             6250             5654.0       188.0             180.0   \n",
       "92             3273             1820.0        81.0             360.0   \n",
       "93             4133                0.0       122.0             360.0   \n",
       "94             3620                0.0        25.0             120.0   \n",
       "95             6782                0.0         NaN             360.0   \n",
       "96             2484             2302.0       137.0             360.0   \n",
       "97             1977              997.0        50.0             360.0   \n",
       "98             4188                0.0       115.0             180.0   \n",
       "99             1759             3541.0       131.0             360.0   \n",
       "\n",
       "    Credit_History Property_Area  Loan_Status  \n",
       "0              1.0         Urban            1  \n",
       "1              1.0         Rural            0  \n",
       "2              1.0         Urban            1  \n",
       "3              1.0         Urban            1  \n",
       "4              1.0         Urban            1  \n",
       "5              1.0         Urban            1  \n",
       "6              1.0         Urban            1  \n",
       "7              0.0     Semiurban            0  \n",
       "8              1.0         Urban            1  \n",
       "9              1.0     Semiurban            0  \n",
       "10             1.0         Urban            1  \n",
       "11             1.0         Urban            1  \n",
       "12             1.0         Urban            1  \n",
       "13             1.0         Rural            0  \n",
       "14             1.0         Urban            1  \n",
       "15             1.0         Urban            1  \n",
       "16             NaN         Urban            1  \n",
       "17             0.0         Urban            0  \n",
       "18             1.0         Rural            0  \n",
       "19             1.0         Urban            1  \n",
       "20             0.0         Urban            0  \n",
       "21             1.0         Urban            1  \n",
       "22             0.0     Semiurban            0  \n",
       "23             0.0         Rural            0  \n",
       "24             NaN     Semiurban            0  \n",
       "25             1.0     Semiurban            1  \n",
       "26             1.0     Semiurban            1  \n",
       "27             1.0         Urban            1  \n",
       "28             1.0         Urban            0  \n",
       "29             1.0     Semiurban            1  \n",
       "..             ...           ...          ...  \n",
       "70             1.0         Urban            1  \n",
       "71             1.0     Semiurban            1  \n",
       "72             1.0     Semiurban            1  \n",
       "73             0.0     Semiurban            0  \n",
       "74             1.0     Semiurban            1  \n",
       "75             1.0         Urban            0  \n",
       "76             1.0         Urban            0  \n",
       "77             1.0         Urban            0  \n",
       "78             0.0     Semiurban            0  \n",
       "79             NaN     Semiurban            1  \n",
       "80             1.0     Semiurban            1  \n",
       "81             1.0     Semiurban            1  \n",
       "82             1.0         Urban            0  \n",
       "83             NaN     Semiurban            0  \n",
       "84             1.0         Urban            1  \n",
       "85             1.0     Semiurban            1  \n",
       "86             NaN     Semiurban            1  \n",
       "87             1.0     Semiurban            1  \n",
       "88             1.0         Urban            1  \n",
       "89             1.0     Semiurban            1  \n",
       "90             1.0     Semiurban            1  \n",
       "91             1.0     Semiurban            1  \n",
       "92             1.0         Urban            1  \n",
       "93             1.0     Semiurban            1  \n",
       "94             1.0     Semiurban            1  \n",
       "95             NaN         Urban            0  \n",
       "96             1.0     Semiurban            1  \n",
       "97             1.0     Semiurban            1  \n",
       "98             1.0     Semiurban            1  \n",
       "99             1.0     Semiurban            1  \n",
       "\n",
       "[100 rows x 13 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan.head(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some Probability Questions on Loan Data\n",
    "1. What is the Probability of Applicant's Income being more than 25000\n",
    "\n",
    "\n",
    "2. Find the Probability of Loan Status(0) where the Credit Rating of the Customer is 1\n",
    "\n",
    "\n",
    "3. What is the probability of Graduates not getting the Loans\n",
    "\n",
    "4. If the Property is Urban, what is the probability of Applicant's Income More than Mean Ans -28%\n",
    "\n",
    "P(A and B) = P(A) * P(B|A) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0006687888219636395"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Prob#1\n",
    "# Mew and Sigma\n",
    "from scipy.stats import norm\n",
    "mu = loan.ApplicantIncome.mean()\n",
    "sd = loan.ApplicantIncome.std()\n",
    "\n",
    "# find the z score\n",
    "z = (25000-mu)/sd\n",
    "1-norm.cdf(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0    525\n",
       "0.0     89\n",
       "Name: Credit_History, dtype: int64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan.Credit_History.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan.Credit_History = loan.Credit_History.fillna(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    415\n",
       "0    110\n",
       "Name: Loan_Status, dtype: int64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the Dataset where the Crdit History is 1\n",
    "loan[loan.Credit_History==1][\"Loan_Status\"].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.17915309446254074"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#loan[loan.Credit_History==1].shape # 525\n",
    "(525/614)*(110/525) # P(Loan.Stats = 0 | Credit Rating =1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If the Property is Urban, \n",
    "# what is the probability of Applicant's Income More than Mean\n",
    "d = loan[loan.Property_Area==\"Urban\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Loan_ID', 'Gender', 'Married', 'Dependents', 'Education',\n",
       "       'Self_Employed', 'ApplicantIncome', 'CoapplicantIncome', 'LoanAmount',\n",
       "       'Loan_Amount_Term', 'Credit_History', 'Property_Area', 'Loan_Status'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Loan_ID              101\n",
       "Gender                98\n",
       "Married              100\n",
       "Dependents            95\n",
       "Education            101\n",
       "Self_Employed         94\n",
       "ApplicantIncome      101\n",
       "CoapplicantIncome    101\n",
       "LoanAmount            97\n",
       "Loan_Amount_Term      99\n",
       "Credit_History       101\n",
       "Property_Area        101\n",
       "Loan_Status          101\n",
       "dtype: int64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[d.ApplicantIncome>d.ApplicantIncome.median()].count() # 58"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Prob\n",
    "(101/d.shape[0])*100 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Loan_ID              58\n",
       "Gender               56\n",
       "Married              58\n",
       "Dependents           56\n",
       "Education            58\n",
       "Self_Employed        54\n",
       "ApplicantIncome      58\n",
       "CoapplicantIncome    58\n",
       "LoanAmount           55\n",
       "Loan_Amount_Term     57\n",
       "Credit_History       58\n",
       "Property_Area        58\n",
       "Loan_Status          58\n",
       "dtype: int64"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan[(loan.Property_Area==\"Urban\") & \n",
    "     (loan.ApplicantIncome>loan.ApplicantIncome.mean())].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 614 entries, 0 to 613\n",
      "Data columns (total 13 columns):\n",
      "Loan_ID              614 non-null object\n",
      "Gender               601 non-null object\n",
      "Married              611 non-null object\n",
      "Dependents           599 non-null object\n",
      "Education            614 non-null object\n",
      "Self_Employed        582 non-null object\n",
      "ApplicantIncome      614 non-null int64\n",
      "CoapplicantIncome    614 non-null float64\n",
      "LoanAmount           592 non-null float64\n",
      "Loan_Amount_Term     600 non-null float64\n",
      "Credit_History       564 non-null float64\n",
      "Property_Area        614 non-null object\n",
      "Loan_Status          614 non-null int64\n",
      "dtypes: float64(4), int64(2), object(7)\n",
      "memory usage: 62.4+ KB\n"
     ]
    }
   ],
   "source": [
    "# Missing Values in data\n",
    "loan.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Loan_ID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Married</th>\n",
       "      <th>Dependents</th>\n",
       "      <th>Education</th>\n",
       "      <th>Self_Employed</th>\n",
       "      <th>Property_Area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>614</td>\n",
       "      <td>601</td>\n",
       "      <td>611</td>\n",
       "      <td>599</td>\n",
       "      <td>614</td>\n",
       "      <td>582</td>\n",
       "      <td>614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>614</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>LP001754</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0</td>\n",
       "      <td>Graduate</td>\n",
       "      <td>No</td>\n",
       "      <td>Semiurban</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>1</td>\n",
       "      <td>489</td>\n",
       "      <td>398</td>\n",
       "      <td>345</td>\n",
       "      <td>480</td>\n",
       "      <td>500</td>\n",
       "      <td>233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Loan_ID Gender Married Dependents Education Self_Employed  \\\n",
       "count        614    601     611        599       614           582   \n",
       "unique       614      2       2          4         2             2   \n",
       "top     LP001754   Male     Yes          0  Graduate            No   \n",
       "freq           1    489     398        345       480           500   \n",
       "\n",
       "       Property_Area  \n",
       "count            614  \n",
       "unique             3  \n",
       "top        Semiurban  \n",
       "freq             233  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan.describe(include = \"object\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Male      502\n",
       "Female    112\n",
       "Name: Gender, dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan.Gender.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use Male to impute Missin Value in Gender\n",
    "loan.Gender = loan.Gender.fillna(\"Male\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(614, 13)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\classroom2-DTP\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x15f13eceba8>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.distplot(np.log(loan[loan.LoanAmount.notnull()][\"LoanAmount\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    592.000000\n",
       "mean     146.412162\n",
       "std       85.587325\n",
       "min        9.000000\n",
       "25%      100.000000\n",
       "50%      128.000000\n",
       "75%      168.000000\n",
       "max      700.000000\n",
       "Name: LoanAmount, dtype: float64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan.LoanAmount.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan.LoanAmount = loan.LoanAmount.fillna(128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    592.000000\n",
       "mean       4.857444\n",
       "std        0.505142\n",
       "min        2.197225\n",
       "25%        4.605170\n",
       "50%        4.852030\n",
       "75%        5.123964\n",
       "max        6.551080\n",
       "Name: LoanAmount, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(loan[loan.LoanAmount.notnull()][\"LoanAmount\"]).describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Poisson Example\n",
    "\n",
    "1. On average, a household receives 9.5 telemarketing phone calls per week. Using the Poisson probability distribution formula, find the probability that a randomly selected household receives exactly 6 telemarketing phone calls during a given week.  Ans: 0.0764\n",
    "\n",
    "\n",
    "2. The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution, with a mean of 2.5 work-related injuries a month. What is the probability that in a given month, a) No work related injuries occur? b) At least one work-related injury occurs?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07642079604012611"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson.pmf(k =6, mu = 9.5 ) # here mu = lambda/avg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0820849986238988"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Case a mu  = 2.5, k = 0\n",
    "poisson.pmf(0, 2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9179150013761012"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Case 2\n",
    "1-poisson.pmf(0, 2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Cynthia’s Mail Order Company provides free examination of its products for 7 days. If not completely satisfied, a customer can return the product within that period and get a full re- fund. According to past records of the company, an average of 2 of every 10 products sold by this company are returned for a refund. Find the probability that exactly 6 of the 40 products sold by this company on a given day will be returned for a refund. Ans: 0.1221\n",
    "\n",
    "\n",
    "\n",
    "4. A Life Insurance agent sells on the average 3 life insurance policies per week. Use the Poisson law to calculate the probability that in a given week, he will sell  2 or more but less than 5 policies?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00033546, 0.0026837 , 0.0107348 , 0.02862614, 0.05725229,\n",
       "       0.09160366, 0.12213822, 0.13958653, 0.13958653])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What is lambda here...mu = 8, k = 6\n",
    "poisson.pmf(np.arange(0,9),8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25fe03847f0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.plot(np.arange(0,25),poisson.pmf(np.arange(0,25),8), \"o-\", color = \"m\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Continuous Random variable - Normal Distribution\n",
    "\n",
    "1. Calculate the prob by finding the area under the curve.\n",
    "\n",
    "A survey on use of smart phones in India was conducted and it is observed the smart phone users spend 68 minutes in a day on average in sending messages and the corresponding standard deviation is 12 minutes.\n",
    "\n",
    "Assume that the time spent in sending messages follows a normal distribution.\n",
    "What proportion of the smart phone users are spending more than 90 minutes in sending messages daily?\n",
    "What proportion of customers are spending less than 20 minutes?\n",
    "What proportion of customers are spending between 50 minutes and 100 minutes?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the library\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 1 Identify the Mu and Sigma\n",
    "mu = 68\n",
    "sigma = 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 02: Rather convert it into standard normal using Z Score Formula\n",
    "z = (90 - mu)/sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03337650758481725"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 3 Find the Probability following the normal distribution\n",
    "1 - norm.cdf(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Probability appears to be 0.0000317\n"
     ]
    }
   ],
   "source": [
    "# What proportion of customers are spending less than 20 minutes? \n",
    "z = (20-mu)/sigma\n",
    "print(\"The Probability appears to be %1.7f\" %norm.cdf(z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9293624181635521"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What proportion of customers are spending between 50 minutes \n",
    "# and 100 minutes?\n",
    "z1 = (50-mu)/sigma\n",
    "z2 = (100-mu)/sigma\n",
    "\n",
    "norm.cdf(z2) - norm.cdf(z1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean salaries of Data Scientists working in Chennai, India is calculated to be 7,00,000 INR with a standard deviation of 90,000 INR. The random variable salary of Data Scientists follows a normal distribution.\n",
    "\n",
    "What is the probability that a Data Scientist in Chennai has a salary more than 10,00,000 INR? Ans - 0.0004\n",
    "\n",
    "What is the probability that a Data Scientist in Chennai has a salary between 6,00,000 & 9,00,000 INR? Ans - 0.8536\n",
    "\n",
    "What is the probability that a Data Scientist in Chennai has a salary less than 4,00,000 INR? Ans - 0.0004\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0004"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Case 1\n",
    "mu = 700000\n",
    "sd = 90000\n",
    "z = (400000-mu)/sd\n",
    "round(norm.cdf(z), 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8536055914064735"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Case 2\n",
    "z1 = (600000-mu)/sd\n",
    "z2 = (900000-mu)/sd\n",
    "norm.cdf(z2)-norm.cdf(z1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis Testing\n",
    "\n",
    "### A principal of a college claims that the Avg IQ of the Students is above average.\n",
    "\n",
    "A random sample of 100 students' IQ had a mean score of 115. The Population mean IQ is 100 with a SD of 15. Is there sufficient evidence to support the claim? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats # stats library"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step1 - Define the Ho & H1\n",
    "\n",
    "H0: mu = 100 | Null Hypothesis\n",
    "H1: mu > 100 | Alternate Hypothesis\n",
    "\n",
    "\n",
    "### Step 2 : Choose the Alpha level.\n",
    "here we select the alpha = 0.05 and n >30.\n",
    "\n",
    "### Step 3: Identify the Test\n",
    "Population SD is given and n >30. Hence we will follow the Z-test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the test statistic\n",
    "xbar = 115\n",
    "mu = 100\n",
    "sd = 15\n",
    "n = 100\n",
    "ztest_val = (xbar-mu)/(sd/np.sqrt(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ztest_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reject the Null Hypothesis\n"
     ]
    }
   ],
   "source": [
    "if (ztest_val>1.96):\n",
    "    print(\"Reject the Null Hypothesis\")\n",
    "else:\n",
    "    print(\"Fail to Reject the H0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "\n",
    "Claim is Incorrect that the Student's Avg IQ is above average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the Required Library\n",
    "#import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.96"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Finding the Critical value\n",
    "round(stats.norm.isf(0.025),2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mayor of a large city claims that the average net worth of families living in this city is at least 300,000. A random sample of 25 families selected from this city produced a mean net worth of 288,000. \n",
    "\n",
    "Assume that the net worth of all families in this city have a normal distribution with the population standard deviation of 80,000.\n",
    "Using the 2.5% significance level, can you conclude that the mayor’s claim is false?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Null \n",
    "mu = 300000 # Null Hypothesis\n",
    "xbar = 288000\n",
    "sd = 80000\n",
    "alpha = 0.025\n",
    "\n",
    "# H1 - mu < 300000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find the Z Test Statistic\n",
    "ztest = (xbar-mu)/(sd/np.sqrt(25))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.75\n"
     ]
    }
   ],
   "source": [
    "print(ztest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fail to Reject the H0\n"
     ]
    }
   ],
   "source": [
    "if (ztest>stats.norm.isf(alpha)):\n",
    "    print(\"Reject the Null Hypothesis\")\n",
    "else:\n",
    "    print(\"Fail to Reject the H0\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At Canon Food Corporation, it used to take an average of 90 minutes for new workers to learn a food processing job. Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean time taken by new workers to learn the food processing procedure on this new machine is different from 90 minutes.\n",
    "\n",
    "A sample of 20 workers showed that it took, on average, 85 minutes for them to learn the food processing procedure on the new machine.\n",
    "\n",
    "It is known that the learning times for all new workers are normally distributed with a population standard deviation of 7 minutes. \n",
    "\n",
    "Find the p-value for the test that the mean learning time for the food processing procedure on the new machine is different from 90 minutes. What will your conclusion be if alpha=0.01?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Null Hypothesis\n",
    "mu = 90\n",
    "xbar = 85\n",
    "sd = 7\n",
    "# Alternate Hypothesis - mu !=90 | Two Tail Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find the Z Test Statistic\n",
    "ztest = (xbar-mu)/(sd/np.sqrt(20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.1943828249996997\n"
     ]
    }
   ],
   "source": [
    "print(ztest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Since the Z Test Statistic is less than -1.96 (CV). hence it is falling in Rejection Region."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Case Study - Internet Mobile Time\n",
    "\n",
    "Experience marketing Services reported that the typical American spend a mean of 144 minutes(2.4 hours) per day accessing the internet via mobile device. In order to test the validity of the statement, you select a sample of 30 friends and family. The resut for the time spent per day accessing the Internet via mobile device (in minutes) are stored.\n",
    "\n",
    "# is there enough evidence that Pop Mean time spent per day accessing the internet via mobile device is different from 144 minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Two Tail Test\n",
    "mobile = pd.read_csv(\"C://Users//classroom2-DTP//Downloads//InternetMobileTime.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Minutes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Minutes\n",
       "0       72\n",
       "1      144\n",
       "2       48\n",
       "3       72\n",
       "4       36"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mobile.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Null = mu = 144\n",
    "xbar = mobile.Minutes.mean()\n",
    "sample_sd = mobile.Minutes.std()\n",
    "mu = 144\n",
    "n = len(mobile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the test statistic\n",
    "teststats = (xbar-mu)/(sample_sd/np.sqrt(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2246743653638934"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "teststats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculation of P Value basis the t test\n",
    "p = 1-stats.t.cdf(teststats, n-1) # substracting 1 so that it can give me P value (Rejection Region)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11527663441491875"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p <0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Since the p value is greater than 0.05, hence we fail to reject the Null Hypothesis.\n",
    "\n",
    "Ground Rule - If the p value <0.05, then we reject the H0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Case Study - Body Temperature\n",
    "\n",
    "Suppose a doctor claims that 17 year old have an avg body temp that is higher than the commonly accepted average human temperature of 98.6 F. Sample carries the age of 17.\n",
    "\n",
    "Find out if the statement is True.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Two Tail Test\n",
    "temp = pd.read_csv(\"C://Users//classroom2-DTP//Downloads//Temperature.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Null Hypothesis\n",
    "mu = 98.6\n",
    "# Alternate Hypothesis - mu > 98.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-0.006668602694974534, pvalue=0.9947343867528586)"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(temp.Temperature, 98.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two Sample T Test Case Study\n",
    "\n",
    "Two Unrelated Samples are provided. Data was collected on the weight loss of 16 women and 20 men enrolled in weight reduction program. At Alpha = 0.05 test whether the weight loss of these two samples are different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.69, 4.12, 4.65, 3.19, 4.34, 3.68, 4.12, 4.5 , 3.7 , 3.09, 3.65,\n",
       "       4.73, 3.93, 3.46, 3.28, 4.43, 4.13, 3.62, 3.71, 2.92])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Null Hyp - mu(men) = mu(women) | mu(men) - mu(women) = 0\n",
    "# Alt Hyp : mu(men) != mu(women)\n",
    "\n",
    "wt = pd.read_csv(\"C://Users//classroom2-DTP//Downloads//Weight.csv\")\n",
    "\n",
    "np.array(wt.Weight_Male)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.99, 1.8 , 3.79, 4.12, 1.76, 3.5 , 3.61, 2.32, 3.67, 4.26, 4.57,\n",
       "       3.01, 3.82, 4.33, 3.4 , 3.86])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(wt.Weight_Female.dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-1.827188295981286, pvalue=0.0764604205335295)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test of Significance\n",
    "stats.ttest_ind(np.array(wt.Weight_Female.dropna()), np.array(wt.Weight_Male))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion - Since, the pvalue > 0.05 (LOS) hence we fail to reject the null hypothesis. There is no significance difference in the weight loss of males and females"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Case Study of Students\n",
    "25 students score in their final practice exam before and after. At 5% level of significance, find if the coaching really had an impact on performance. This is a related sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "marks_before = [52, 56, 51, 47, 58, 52, 56, 60, 52, 46, 51, 62, 54, 50, 48, 59, 56, 51, 52, \n",
    "                44, 52, 45, 57, 60, 45]\n",
    "\n",
    "marks_after = [62, 54, 40, 65, 76, 82, 53, 68, 77, 60, 69, 34, 69, 73, 67, \n",
    "               82, 62, 49, 44, 43, 77, 61, 67, 67, 54]\n",
    "\n",
    "# Tip use stats.tttest_rel because the samples are RELATED."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=-3.5504295712891536, pvalue=0.0016259982497311876)"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Null Hyp mean(scores_before) = mean(scores_after)\n",
    "# Alt Hyp: mean(scores_before) != mean(scores_after)\n",
    "stats.ttest_rel(marks_before, marks_after)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion - Since, the pvalue < 0.05 (LOS) hence we Reject the Null Hypothesis. There is significance impact of the mentoring on students. The Scores are different"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case Study - Finding if Love Break Up has effect on alcohol consumption\n",
    "\n",
    "Conduct a paired t test to check whether the alcohol consumption is more after the break up.\n",
    "\n",
    "LOS = 5%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "alc_cons_before = np.array([470, 354, 496, 351, 349, 449, 378, 359, 469, 329, 389, 497, \n",
    "                    493, 268, 445, 287, 338, 271, 412, 335])\n",
    "\n",
    "alc_cons_after = np.array([408, 439, 321, 437, 335, 344, 318, 492, 531, 417, 358,\n",
    "                   391, 398, 394, 508, 399, 345, 341, 326, 467])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=0.5375404241815105, pvalue=0.5971346738292477)"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Null Hyp : alc.cons.after = alc.con.before\n",
    "# Alt Hyp : alc.cons.after != alc.con.before\n",
    "stats.ttest_rel(alc_cons_after, alc_cons_before)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion - Since, the pvalue > 0.05 (LOS) hence we Fail to Reject the Null Hypothesis. There is No change in the drinking pattern irrespective of whatsoever and whosoever."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case Study - Check if new therapy leads to change in weight\n",
    "\n",
    "here is the weight of 25 people before they started a new therapy and then again 6 months later the weight was captured. Find if there is a significant difference\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "wt_before = [76,76,72,73,64,63,75,75,71,76,71,76,78,73,76,70,71,82,84,68,70,68,66,67,74]\n",
    "wt_after =  [63,72,67,69,58,59,70,71,70,71,68,71,72,69,92,67,67,78,79,62,67,63,61,63,69]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=4.19760052735678, pvalue=0.0003194442840568375)"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Null Hyp: wt_before.mean() = wt_after.mean()\n",
    "# Alt Hyp: wt_before.mean() != wt_after.mean()\n",
    "stats.ttest_rel(wt_before, wt_after)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Home Assignment\n",
    "\n",
    "The delivery time of Pizza from Zomato and local restaurant is captured. At 5% LOS, is the mean delivery time for Zomato is less than from Local Restaurant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "Zomato_Delivery = [16.8, 11.7, 15.6, 16.7, 17.5, 18.1, 14.1, 21.8, 13.9, 20.8]\n",
    "Local_Rest_Delivery = [22.0, 15.2, 18.7, 15.6, 20.8, 19.5, 17.0, 19.5, 16.5, 24.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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