04_Inf_Stat_Dist_binom.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Inferential Statistics**"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Binomial Distributions**"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Que: What is the probability that a table of four will leave a tip of `20%` or more on their bill at this restaurant?**\n",
    "\n",
    "To answer this question, we can use the `binomial theorem`, which allows us to calculate the probability of a certain number of successes in a fixed number of trials. In this case, the `success` is leaving a tip of `20%` or more, and the `trial` is a table of four."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>total_bill</th>\n",
       "      <th>tip</th>\n",
       "      <th>sex</th>\n",
       "      <th>smoker</th>\n",
       "      <th>day</th>\n",
       "      <th>time</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16.99</td>\n",
       "      <td>1.01</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.34</td>\n",
       "      <td>1.66</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.01</td>\n",
       "      <td>3.50</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.68</td>\n",
       "      <td>3.31</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24.59</td>\n",
       "      <td>3.61</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>4</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>239</th>\n",
       "      <td>29.03</td>\n",
       "      <td>5.92</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>240</th>\n",
       "      <td>27.18</td>\n",
       "      <td>2.00</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>241</th>\n",
       "      <td>22.67</td>\n",
       "      <td>2.00</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>242</th>\n",
       "      <td>17.82</td>\n",
       "      <td>1.75</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>18.78</td>\n",
       "      <td>3.00</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Thur</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>244 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     total_bill   tip     sex smoker   day    time  size\n",
       "0         16.99  1.01  Female     No   Sun  Dinner     2\n",
       "1         10.34  1.66    Male     No   Sun  Dinner     3\n",
       "2         21.01  3.50    Male     No   Sun  Dinner     3\n",
       "3         23.68  3.31    Male     No   Sun  Dinner     2\n",
       "4         24.59  3.61  Female     No   Sun  Dinner     4\n",
       "..          ...   ...     ...    ...   ...     ...   ...\n",
       "239       29.03  5.92    Male     No   Sat  Dinner     3\n",
       "240       27.18  2.00  Female    Yes   Sat  Dinner     2\n",
       "241       22.67  2.00    Male    Yes   Sat  Dinner     2\n",
       "242       17.82  1.75    Male     No   Sat  Dinner     2\n",
       "243       18.78  3.00  Female     No  Thur  Dinner     2\n",
       "\n",
       "[244 rows x 7 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tips = sns.load_dataset('tips')\n",
    "tips"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Next, we need to calculate the proportion of tables that leave a tip of `10%` or more.\n",
    "\n",
    "- We can do this by creating a new column in the dataframe that indicates whether the tip percentage is 20% or greater, and then taking the mean of that column:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>total_bill</th>\n",
       "      <th>tip</th>\n",
       "      <th>sex</th>\n",
       "      <th>smoker</th>\n",
       "      <th>day</th>\n",
       "      <th>time</th>\n",
       "      <th>size</th>\n",
       "      <th>tip_pct</th>\n",
       "      <th>tip_10plus</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16.99</td>\n",
       "      <td>1.01</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "      <td>0.059447</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.34</td>\n",
       "      <td>1.66</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "      <td>0.160542</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.01</td>\n",
       "      <td>3.50</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "      <td>0.166587</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.68</td>\n",
       "      <td>3.31</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "      <td>0.139780</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24.59</td>\n",
       "      <td>3.61</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>4</td>\n",
       "      <td>0.146808</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
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       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>239</th>\n",
       "      <td>29.03</td>\n",
       "      <td>5.92</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "      <td>0.203927</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>240</th>\n",
       "      <td>27.18</td>\n",
       "      <td>2.00</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "      <td>0.073584</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>241</th>\n",
       "      <td>22.67</td>\n",
       "      <td>2.00</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "      <td>0.088222</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>242</th>\n",
       "      <td>17.82</td>\n",
       "      <td>1.75</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "      <td>0.098204</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>18.78</td>\n",
       "      <td>3.00</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Thur</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "      <td>0.159744</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>244 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     total_bill   tip     sex smoker   day    time  size   tip_pct  tip_10plus\n",
       "0         16.99  1.01  Female     No   Sun  Dinner     2  0.059447           0\n",
       "1         10.34  1.66    Male     No   Sun  Dinner     3  0.160542           1\n",
       "2         21.01  3.50    Male     No   Sun  Dinner     3  0.166587           1\n",
       "3         23.68  3.31    Male     No   Sun  Dinner     2  0.139780           1\n",
       "4         24.59  3.61  Female     No   Sun  Dinner     4  0.146808           1\n",
       "..          ...   ...     ...    ...   ...     ...   ...       ...         ...\n",
       "239       29.03  5.92    Male     No   Sat  Dinner     3  0.203927           1\n",
       "240       27.18  2.00  Female    Yes   Sat  Dinner     2  0.073584           0\n",
       "241       22.67  2.00    Male    Yes   Sat  Dinner     2  0.088222           0\n",
       "242       17.82  1.75    Male     No   Sat  Dinner     2  0.098204           0\n",
       "243       18.78  3.00  Female     No  Thur  Dinner     2  0.159744           1\n",
       "\n",
       "[244 rows x 9 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 0.889344262295082\n"
     ]
    }
   ],
   "source": [
    "# Creating the New Column\n",
    "tips['tip_pct'] = tips['tip'] / tips['total_bill']\n",
    "tips['tip_10plus'] = np.where(tips['tip_pct'] >= 0.1, 1, 0)\n",
    "\n",
    "# Displaying the dataSet\n",
    "display(tips)\n",
    "\n",
    "# calculating the mean\n",
    "prop_10plus = tips['tip_10plus'].mean()\n",
    "print(f\"Mean: {prop_20plus}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use the binomial theorem to calculate the probability of a table of four leaving a tip of 20% or more.\n",
    "\n",
    "- We know that there are `4` people at the table, and the probability of a single person leaving a tip of 20% or more is prop_20plus.\n",
    "- The probability of exactly `k` people at the table leaving a tip of `20%` or more can be calculated as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 4\n",
    "k = 4\n",
    "\n",
    "# Calculating the Porbablity using the Binomial theorem\n",
    "prob = np.math.comb(n, k) * (prop_10plus ** k) * ((1 - prop_10plus) ** (n - k))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `np.math.comb(n, k)` function calculates the number of ways to choose `k` items from a set of `n` items, which in this case is the number of ways to choose `4` people from a table of `4`. The `(prop_20plus ** k) * ((1 - prop_20plus) ** (n - k))` term calculates the probability of getting exactly `k` successes in `n` trials.\n",
    "\n",
    "Finally, we can print out the probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of a table of four leaving a tip of 10% or more is: 62.56 percent\n"
     ]
    }
   ],
   "source": [
    "print(f'The probability of a table of four leaving a tip of 10% or more is: {\"{:.2f}\".format(prob*100)} percent')\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example of how we can use `scipy.stats` to calculate the probability of a table of four leaving a certain number of tips of `10%` or more, and to plot the binomial distribution for this scenario:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`10%`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of a table of four leaving 2 or more tips of 10% or more is: 0.9950300156356519\n"
     ]
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import binom\n",
    "\n",
    "tips = sns.load_dataset('tips')\n",
    "\n",
    "# Calculate the proportion of tables that leave a tip of 10% or more\n",
    "tips['tip_pct'] = tips['tip'] / tips['total_bill']\n",
    "tips['tip_10plus'] = np.where(tips['tip_pct'] >= 0.1, 1, 0)\n",
    "prop_10plus = tips['tip_10plus'].mean()\n",
    "\n",
    "# Calculate the probability of a table of four leaving exactly 0, 1, 2, 3, or 4 tips of 20% or more\n",
    "n = 4\n",
    "k_values = np.arange(n+1)\n",
    "probs = binom.pmf(k_values, n, prop_10plus)\n",
    "\n",
    "# Plot the binomial distribution\n",
    "sns.barplot(x=k_values, y=probs)\n",
    "plt.xlabel('Number of people leaving a tip of 10% or more')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Binomial Distribution of Tip Percentage for a Table of Four')\n",
    "plt.show()\n",
    "\n",
    "# Calculate the probability of a table of four leaving 2 or more tips of 10% or more\n",
    "prob_2plus = binom.sf(1, n, prop_10plus)\n",
    "print('The probability of a table of four leaving 2 or more tips of 10% or more is:', prob_2plus)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example of how we can use `scipy.stats` to calculate the probability of a table of four leaving a certain number of tips of `10%` or more, and to plot the binomial distribution for this scenario:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`20%`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of a table of four leaving 2 or more tips of 20% or more is: 0.1225760599676647\n"
     ]
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import binom\n",
    "\n",
    "tips = sns.load_dataset('tips')\n",
    "\n",
    "# Calculate the proportion of tables that leave a tip of 20% or more\n",
    "tips['tip_pct'] = tips['tip'] / tips['total_bill']\n",
    "tips['tip_20plus'] = np.where(tips['tip_pct'] >= 0.2, 1, 0)\n",
    "prop_20plus = tips['tip_20plus'].mean()\n",
    "\n",
    "# Calculate the probability of a table of four leaving exactly 0, 1, 2, 3, or 4 tips of 20% or more\n",
    "n = 4\n",
    "k_values = np.arange(n+1)\n",
    "probs = binom.pmf(k_values, n, prop_20plus)\n",
    "\n",
    "# Plot the binomial distribution\n",
    "sns.barplot(x=k_values, y=probs)\n",
    "plt.xlabel('Number of people leaving a tip of 20% or more')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Binomial Distribution of Tip Percentage for a Table of Four')\n",
    "plt.show()\n",
    "\n",
    "# Calculate the probability of a table of four leaving 2 or more tips of 20% or more\n",
    "prob_2plus = binom.sf(1, n, prop_20plus)\n",
    "print('The probability of a table of four leaving 2 or more tips of 20% or more is:', prob_2plus)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Wine Dataset**"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the proportion of `Class=3` , `wines` with high alcohol content?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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>Wine</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic.acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Acl</th>\n",
       "      <th>Mg</th>\n",
       "      <th>Phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid.phenols</th>\n",
       "      <th>Proanth</th>\n",
       "      <th>Color.int</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735</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",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>3</td>\n",
       "      <td>13.71</td>\n",
       "      <td>5.65</td>\n",
       "      <td>2.45</td>\n",
       "      <td>20.5</td>\n",
       "      <td>95</td>\n",
       "      <td>1.68</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.52</td>\n",
       "      <td>1.06</td>\n",
       "      <td>7.70</td>\n",
       "      <td>0.64</td>\n",
       "      <td>1.74</td>\n",
       "      <td>740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>3</td>\n",
       "      <td>13.40</td>\n",
       "      <td>3.91</td>\n",
       "      <td>2.48</td>\n",
       "      <td>23.0</td>\n",
       "      <td>102</td>\n",
       "      <td>1.80</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.43</td>\n",
       "      <td>1.41</td>\n",
       "      <td>7.30</td>\n",
       "      <td>0.70</td>\n",
       "      <td>1.56</td>\n",
       "      <td>750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>3</td>\n",
       "      <td>13.27</td>\n",
       "      <td>4.28</td>\n",
       "      <td>2.26</td>\n",
       "      <td>20.0</td>\n",
       "      <td>120</td>\n",
       "      <td>1.59</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.43</td>\n",
       "      <td>1.35</td>\n",
       "      <td>10.20</td>\n",
       "      <td>0.59</td>\n",
       "      <td>1.56</td>\n",
       "      <td>835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>3</td>\n",
       "      <td>13.17</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.37</td>\n",
       "      <td>20.0</td>\n",
       "      <td>120</td>\n",
       "      <td>1.65</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.53</td>\n",
       "      <td>1.46</td>\n",
       "      <td>9.30</td>\n",
       "      <td>0.60</td>\n",
       "      <td>1.62</td>\n",
       "      <td>840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>3</td>\n",
       "      <td>14.13</td>\n",
       "      <td>4.10</td>\n",
       "      <td>2.74</td>\n",
       "      <td>24.5</td>\n",
       "      <td>96</td>\n",
       "      <td>2.05</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.56</td>\n",
       "      <td>1.35</td>\n",
       "      <td>9.20</td>\n",
       "      <td>0.61</td>\n",
       "      <td>1.60</td>\n",
       "      <td>560</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>178 rows × 14 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Wine  Alcohol  Malic.acid   Ash   Acl   Mg  Phenols  Flavanoids  \\\n",
       "0       1    14.23        1.71  2.43  15.6  127     2.80        3.06   \n",
       "1       1    13.20        1.78  2.14  11.2  100     2.65        2.76   \n",
       "2       1    13.16        2.36  2.67  18.6  101     2.80        3.24   \n",
       "3       1    14.37        1.95  2.50  16.8  113     3.85        3.49   \n",
       "4       1    13.24        2.59  2.87  21.0  118     2.80        2.69   \n",
       "..    ...      ...         ...   ...   ...  ...      ...         ...   \n",
       "173     3    13.71        5.65  2.45  20.5   95     1.68        0.61   \n",
       "174     3    13.40        3.91  2.48  23.0  102     1.80        0.75   \n",
       "175     3    13.27        4.28  2.26  20.0  120     1.59        0.69   \n",
       "176     3    13.17        2.59  2.37  20.0  120     1.65        0.68   \n",
       "177     3    14.13        4.10  2.74  24.5   96     2.05        0.76   \n",
       "\n",
       "     Nonflavanoid.phenols  Proanth  Color.int   Hue    OD  Proline  \n",
       "0                    0.28     2.29       5.64  1.04  3.92     1065  \n",
       "1                    0.26     1.28       4.38  1.05  3.40     1050  \n",
       "2                    0.30     2.81       5.68  1.03  3.17     1185  \n",
       "3                    0.24     2.18       7.80  0.86  3.45     1480  \n",
       "4                    0.39     1.82       4.32  1.04  2.93      735  \n",
       "..                    ...      ...        ...   ...   ...      ...  \n",
       "173                  0.52     1.06       7.70  0.64  1.74      740  \n",
       "174                  0.43     1.41       7.30  0.70  1.56      750  \n",
       "175                  0.43     1.35      10.20  0.59  1.56      835  \n",
       "176                  0.53     1.46       9.30  0.60  1.62      840  \n",
       "177                  0.56     1.35       9.20  0.61  1.60      560  \n",
       "\n",
       "[178 rows x 14 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "url = 'https://gist.githubusercontent.com/tijptjik/9408623/raw/b237fa5848349a14a14e5d4107dc7897c21951f5/wine.csv'\n",
    "# Load the wine dataset using Pandas' read_csv function\n",
    "wine = pd.read_csv(url)\n",
    "\n",
    "wine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.countplot(x = wine['Wine'])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(close=None, block=None)>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=wine['Alcohol'])\n",
    "plt.grid()\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Filter the data for Class 3 wines\n",
    "class3 = wine[wine['Wine'] == 3]\n",
    "\n",
    "# Calculate the proportion of Class 3 wines with high alcohol content (above 14%)\n",
    "high_alcohol = (class3['Alcohol'] > 14).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an array of possible number of successes (i.e. number of wines with high alcohol content) in 10 trials\n",
    "n = 10\n",
    "k_values = np.arange(n+1)\n",
    "\n",
    "# Calculate the probability of each possible number of successes\n",
    "probs = np.array([np.math.comb(n, k) * (high_alcohol ** k) *((1 - high_alcohol) ** (n - k)) for k in k_values])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the binomial distribution\n",
    "sns.barplot(x=k_values, y=probs)\n",
    "plt.xlabel('Number of Class 3 wines with high alcohol content')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Binomial Distribution of High Alcohol Content for Class 3 Wines')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "url = 'https://gist.githubusercontent.com/tijptjik/9408623/raw/b237fa5848349a14a14e5d4107dc7897c21951f5/wine.csv'\n",
    "# Load the wine dataset using Pandas' read_csv function\n",
    "wine = pd.read_csv(url)\n",
    "\n",
    "# Filter the data for Class 3 wines\n",
    "class3 = wine[wine['Wine'] == 3]\n",
    "\n",
    "# Calculate the proportion of Class 3 wines with high alcohol content (above 14%)\n",
    "high_alcohol = (class3['Alcohol'] > 14).mean()\n",
    "\n",
    "# Create an array of possible number of successes (i.e. number of wines with high alcohol content) in 10 trials\n",
    "n = 10\n",
    "k_values = np.arange(n+1)\n",
    "\n",
    "# Calculate the probability of each possible number of successes\n",
    "probs = np.array([np.math.comb(n, k) * (high_alcohol ** k) *\n",
    "                 ((1 - high_alcohol) ** (n - k)) for k in k_values])\n",
    "\n",
    "# Plot the binomial distribution\n",
    "sns.barplot(x=k_values, y=probs)\n",
    "plt.xlabel('Number of Class 3 wines with high alcohol content')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Binomial Distribution of High Alcohol Content for Class 3 Wines')\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the probability mass function (PMF) to describe the probability distribution of a discrete random variable. The PMF gives the probability of each possible value that the random variable can take, which allows us to calculate the probabilities of different events or outcomes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n = 10  # number of trials\n",
    "p = 0.5  # probability of success\n",
    "k_values = range(n+1)  # possible number of successes\n",
    "\n",
    "# Calculate the binomial PMF for each value of k\n",
    "pmf_values = [binom.pmf(k, n, p) for k in k_values]\n",
    "\n",
    "# Plot the binomial PMF\n",
    "plt.bar(k_values, pmf_values)\n",
    "plt.xlabel('Number of successes')\n",
    "plt.ylabel('Probability')\n",
    "plt.title(f'Binomial PMF (n={n}, p={p})')\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `scipy.stats.binom`"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p align='center'>\n",
    "  <a href=\"#\"><img src='https://chrispiech.github.io/probabilityForComputerScientists/img/chapters/binEquation2.png' width=35%></a>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import binom\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n, p = 5, 0.4\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "mean, var, skew, kurt = binom.stats(n, p, moments='mvsk')\n",
    "\n",
    "x = np.arange(binom.ppf(0.01, n, p), binom.ppf(0.99, n, p))\n",
    "ax.plot(x, binom.pmf(x, n, p), 'bo', ms=8, label='binom pmf')\n",
    "ax.vlines(x, 0, binom.pmf(x, n, p), colors='b', lw=5, alpha=0.5)\n",
    "\n",
    "rv = binom(n, p)\n",
    "ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, label='frozen pmf')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Methods                   | Description\n",
    "-------------------------|---------------------------------------------------\n",
    "`rvs(n, p, loc, size)`    | Random variates\n",
    "`pmf(k, n, p, loc)`       | Probability mass function\n",
    "`logpmf(k, n, p, loc)`    | Log of the probability mass function\n",
    "`cdf(k, n, p, loc)`       | Cumulative distribution function\n",
    "`logcdf(k, n, p, loc)`    | Log of the cumulative distribution function\n",
    "`stats(n, p, loc, mom)`   | Mean, variance, skewness, and/or kurtosis\n",
    "`entropy(n, p, loc)`      | (Differential) entropy of the RV\n",
    "`median(n, p, loc)`       | Median of the RV\n",
    "`mean(n, p, loc)`         | Mean of the RV\n",
    "`var(n, p, loc)`          | Variance of the RV\n",
    "`std(n, p, loc)`          | Standard deviation of the RV\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.9.13"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}