Machine learning math application.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1b9246f0",
   "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>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>classs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)   \n",
       "0                  5.1               3.5                1.4               0.2  \\\n",
       "1                  4.9               3.0                1.4               0.2   \n",
       "2                  4.7               3.2                1.3               0.2   \n",
       "3                  4.6               3.1                1.5               0.2   \n",
       "4                  5.0               3.6                1.4               0.2   \n",
       "..                 ...               ...                ...               ...   \n",
       "145                6.7               3.0                5.2               2.3   \n",
       "146                6.3               2.5                5.0               1.9   \n",
       "147                6.5               3.0                5.2               2.0   \n",
       "148                6.2               3.4                5.4               2.3   \n",
       "149                5.9               3.0                5.1               1.8   \n",
       "\n",
       "     classs  \n",
       "0         0  \n",
       "1         0  \n",
       "2         0  \n",
       "3         0  \n",
       "4         0  \n",
       "..      ...  \n",
       "145       2  \n",
       "146       2  \n",
       "147       2  \n",
       "148       2  \n",
       "149       2  \n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_iris\n",
    "import pandas as pd\n",
    "from copy import copy\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "from scipy.stats import rv_discrete\n",
    "import scipy.integrate as spi\n",
    "from scipy.stats import entropy\n",
    "import math\n",
    "import scipy.stats as stats\n",
    "from scipy.stats import ttest_1samp\n",
    "\n",
    "\n",
    "iris = load_iris()\n",
    "\n",
    "dataset = pd.DataFrame(data=iris.data, columns=iris.feature_names)\n",
    "dataset['classs'] = iris.target\n",
    "\n",
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c9e78f22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class_freq = dataset[\"classs\"].value_counts()\n",
    "\n",
    "class_freq_df = pd.DataFrame({\n",
    "    \"classs\": class_freq.index,\n",
    "    \"freq\": class_freq.values\n",
    "})\n",
    "\n",
    "prob = class_freq_df[\"freq\"] / len(dataset)\n",
    "\n",
    "class_freq_df[\"prob\"] = prob\n",
    "\n",
    "plt.bar(class_freq_df[\"classs\"].values, class_freq_df[\"prob\"].values)\n",
    "plt.xticks(range(len(class_freq_df)), class_freq_df[\"classs\"].values)\n",
    "plt.xlabel(\"Class\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.title(\"Probability Mass Function of Iris Dataset\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "12b584fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "CDF = class_freq_df.cumsum()\n",
    "CDF[\"classs\"] = class_freq_df[\"classs\"]\n",
    "CDF[\"freq\"] = class_freq_df[\"freq\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "431e0f8a",
   "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>classs</th>\n",
       "      <th>freq</th>\n",
       "      <th>prob</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>50</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>50</td>\n",
       "      <td>0.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>50</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   classs  freq      prob\n",
       "0       0    50  0.333333\n",
       "1       1    50  0.666667\n",
       "2       2    50  1.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "83dc939d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(CDF[\"classs\"].values, CDF[\"prob\"].values)\n",
    "plt.xticks(range(len(CDF)), CDF[\"classs\"].values)\n",
    "plt.xlabel(\"Class\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.title(\"Probabilty Cumulative Function \")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "eb1f7b2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.scatter(x, y, s=None, c=None, marker=None, cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, *, edgecolors=None, plotnonfinite=False, data=None, **kwargs)>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.scatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7c2f7825",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimation of PDF')"
      ]
     },
     "execution_count": 7,
     "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": [
    "plt.hist(dataset['sepal length (cm)'], bins=30, density=True)\n",
    "plt.xlabel(\"sapal length cm)\")\n",
    "plt.ylabel(\"probablities\")\n",
    "plt.title(\"Estimation of PDF\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8e214ad",
   "metadata": {},
   "source": [
    "## Dot Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "622ee13f",
   "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>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>classs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)   \n",
       "0                  5.1               3.5                1.4               0.2  \\\n",
       "1                  4.9               3.0                1.4               0.2   \n",
       "2                  4.7               3.2                1.3               0.2   \n",
       "3                  4.6               3.1                1.5               0.2   \n",
       "4                  5.0               3.6                1.4               0.2   \n",
       "..                 ...               ...                ...               ...   \n",
       "145                6.7               3.0                5.2               2.3   \n",
       "146                6.3               2.5                5.0               1.9   \n",
       "147                6.5               3.0                5.2               2.0   \n",
       "148                6.2               3.4                5.4               2.3   \n",
       "149                5.9               3.0                5.1               1.8   \n",
       "\n",
       "     classs  \n",
       "0         0  \n",
       "1         0  \n",
       "2         0  \n",
       "3         0  \n",
       "4         0  \n",
       "..      ...  \n",
       "145       2  \n",
       "146       2  \n",
       "147       2  \n",
       "148       2  \n",
       "149       2  \n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1c650335",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1128.14"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset[\"sepal length (cm)\"].dot(dataset[\"petal width (cm)\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83de81e1",
   "metadata": {},
   "source": [
    "## Vector simple operation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "63514b58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      5.3\n",
       "1      5.1\n",
       "2      4.9\n",
       "3      4.8\n",
       "4      5.2\n",
       "      ... \n",
       "145    9.0\n",
       "146    8.2\n",
       "147    8.5\n",
       "148    8.5\n",
       "149    7.7\n",
       "Length: 150, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset[\"sepal length (cm)\"].add(dataset[\"petal width (cm)\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "339eb724",
   "metadata": {},
   "source": [
    "## Visualizing vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f02148eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.FancyArrow at 0x1f9ee4d2940>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiwAAAGdCAYAAAAxCSikAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAA4YUlEQVR4nO3deXiV1bn38W8ShCBCFNEgGgUODkdGBYzUuaaAtVasKCAtk0NVpGAcsRVsaw/OooJirQpKma3UWsUhFtTKICCO9VQ99gWHMKgkEIRAst8/VpNtKiAJJM/eO9/Pde1L9s2TzZ104Oe617OetFgsFkOSJCmBpUfdgCRJ0ncxsEiSpIRnYJEkSQnPwCJJkhKegUWSJCU8A4skSUp4BhZJkpTwDCySJCnhNYi6gT2hvLyczz77jKZNm5KWlhZ1O5IkaRfEYjE2bNhAq1atSE/f+RpKSgSWzz77jJycnKjbkCRJNbBq1SoOOeSQnV6TEoGladOmQPiGmzVrFnE3kiRpVxQXF5OTk1P59/jOpERgqRgDNWvWzMAiSVKS2ZXtHG66lSRJCc/AIkmSEp6BRZIkJTwDiyRJSngGFkmSlPAMLJIkKeEZWCRJUsIzsEiSpIRnYJEkSQnPwCJJkhKegUWSJCU8A4skSUp4BhZJkuq5Vatg27aou9i5lHhasyRJqpk//QnOPRcaNoROneD446Fbt/A66ijIyIi6w8DAIklSPfbxx5CeDqWlsHQpvPkmTJgQfi8zE445BnJz4Ve/gv33j65PR0KSJNVzaWnxX2/dGv/15s2wcCGMHw9PPFHnbVVhYJEkqR77ZljZkX33hb59a72VnapRYJk4cSKtW7cmMzOT3NxclixZssNrH3roIU466ST2228/9ttvP/Ly8r51fSwWY8yYMRx00EE0btyYvLw8Pvjgg5q0JkmSqmFXAsvtt0Pz5rXfy85UO7DMnDmT/Px8xo4dy/Lly+ncuTO9evVizZo1271+/vz5DBgwgL/97W8sXLiQnJwcevbsyaefflp5zW233ca9997LpEmTWLx4MU2aNKFXr15s3ry55t+ZJEnaLRkZYQ/LsGFRdwJpsVgsVp0vyM3NpXv37kz4946c8vJycnJyGDFiBNdff/13fn1ZWRn77bcfEyZMYNCgQcRiMVq1asVVV13F1VdfDUBRURHZ2dlMnjyZ/v37f+dnFhcXk5WVRVFREc2aNavOtyNJUr02fjxcfTWUlW3/9xcvhuOOq50/uzp/f1drhaW0tJRly5aRl5cX/4D0dPLy8li4cOEufcamTZvYunUrzf+9tvTxxx9TWFhY5TOzsrLIzc3d5c+UJEnVV14Ob78N21u6yMgIKyu1FVaqq1q3Na9bt46ysjKys7Or1LOzs3n//fd36TOuu+46WrVqVRlQCgsLKz/jPz+z4vf+05YtW9iyZUvl++Li4l3+HiRJEqxeDRdcAC+9tP3fb9wYxo2r2552pk7vErrllluYMWMGTz75JJmZmTX+nHHjxpGVlVX5ysnJ2YNdSpKU2l58Edq3j4eVRo2+fc3//A8ceGDd9rUz1QosLVq0ICMjg9WrV1epr169mpYtW+70a++44w5uueUWnn/+eTp16lRZr/i66nzm6NGjKSoqqnytWrWqOt+GJEn10rZt8MtfQs+e8MUXoZaRUfXslYwM+O//hssui6bHHalWYGnYsCFdu3aloKCgslZeXk5BQQE9evTY4dfddttt/Pa3v2XevHl069atyu+1adOGli1bVvnM4uJiFi9evMPPbNSoEc2aNavykiRJO7ZqFZx8clg5qdiz8tOfwm9+U/W6sjKYNAkaJNhZ+NUeCeXn5/PQQw8xZcoU/vGPf3DZZZdRUlLC0KFDARg0aBCjR4+uvP7WW2/lxhtv5JFHHqF169YUFhZSWFjIxo0bAUhLS2PUqFHcfPPNPPXUU7z99tsMGjSIVq1a0adPnz3zXUqSVI/95S/QsWM4tRbCkfuTJ8Pjj8M++8Svy8iA/v1DsEk01c5P/fr1Y+3atYwZM4bCwkK6dOnCvHnzKjfNrly5kvT0eA564IEHKC0tpe9/HJE3duxYbrrpJgCuvfZaSkpKuOSSS1i/fj0nnngi8+bN2619LpIk1XdbtsB118E998RrRx8djtk/6qjw/psHxzVsCHfeWbc97qpqn8OSiDyHRZKkqj76KDyF+c0347VLL4W77gp3AFWYMAFGjAjB5dZb4Zpr6q7H6vz9nWATKkmStLtmzIALL4RNm8L7Jk3CCGhnzwNq2xZGjqyT9mrEwCJJUorYtCmEjj/8IV479liYMwfatNn+12RlhdWV++8PI6FE5dOaJUlKAe+9F8LJN8NKfn7YaLujsALws5/Bl1+GW50TmSsskiQlsVgMHn0ULr88bLKFsGryxz/CmWfu2mfsu2+ttbfHGFgkSUpSGzbAJZeEPSsVTjgBZs6Egw+Orq/a4EhIkqQktHw5dOoUDytpaXDjjTB/fuqFFXCFRZKkpBKLhVuR8/PDUfsABxwQVlVOOy3a3mqTgUWSpCTx1VcwZAg89VS8lpcX9qsk0oMKa4MjIUmSksBrr0GHDvGwkpERDnp77rnUDyvgCoskSQmtvBxuuy08Zbm8PNQOPjicrXL88dH2VpcMLJIkJajVq2HgQCgoiNfOPjvcxrzfftH1FQVHQpIkJaCXXgojoIqw0qBB2Gz75JP1L6yAgUWSpISybVu4PTkvD9atC7U2bWDJEhg+vOrTlesTR0KSJCWITz6Bfv3CBtsKF1wAkyZB06bR9ZUIXGGRJCkBPP10GAFVhJXMzLBXZepUwwoYWCRJilRpaTgE7qyzoKgo1I46KpxkO2RI/R0B/SdHQpIkReT//g/69oU33ojXLrkExo+Hxo0jayshGVgkSYrArFkwbBiUlIT3TZrAI4/A+edH21eiMrBIklSHvv4aRo2C3/8+XuvSBZ54Atq2jaqrxOceFkmS6sg//gFdu1YNK1deCYsXG1a+iysskiTVslgMpkyByy6DzZtDLSsr3AH0ox9F21uyMLBIklSLNmyASy+FadPite99D2bOhEMOia6vZONISJKkWrJiRdifUhFW0tLCQwwXLDCsVJcrLJIk7WGxGNx/f9ifsnVrqLVoATNmwOmnR9tbsjKwSJK0B331FQwdCn/+c7x2+unwxz9CdnZ0fSU7R0KSJO0hixZBx47xsJKeDuPGwfPPG1Z2lysskiTtpvJyuOMOuOEGKCsLtVatYPbssMFWu8/AIknSbli7FgYOhBdeiNd+/OPw4MLmzaPrK9U4EpIkqYb+9jdo3z4eVho0gHvvhblzDSt7moFFkqRqKiuDMWPCZtq1a0OtdetwYu2IET5huTY4EpIkqRo+/RT694dXX43X+vcPx+03bRpdX6nOFRZJknbRM89Ahw7xsNKoETz8cDgYzrBSuwwskiR9h9JSuOoqOPNMWL8+1I48EpYtg2HDHAHVBUdCkiTtxMcfQ9++sHx5vHbRRXDPPbD33tH1Vd+4wiJJ0g7MmQOdOsXDyt57w/Tp8NBDhpW6ZmCRJOk/bN4Ml10G550HGzeGWufO8OabYYOt6p6BRZKkb3j/fejaFSZNitdGjgy3LLdrF11f9Z17WCRJ+rcpU+DSS8MKC0BWFjz2WDi5VtEysEiS6r2NG8MIaOrUeO3442HWLMjJia4vxTkSkiTVa2++CV26xMNKWlp4iOErrxhWEokrLJKkeikWC/tURo6ErVtDbf/9YcYMyMuLtjd9m4FFklTvrF8fDnx78sl47bTTwom1LVtG1pZ2wpGQJKleWbwYOnaMh5X0dPjd7+DFFw0ricwVFklSvVBeDnfdBddfH562DHDQQTB7NpxwQrS96bsZWCRJKW/tWvjpT+H55+O1H/0o3MbcvHl0fWnXORKSJKW0BQvCE5YrwkqDBjB+PDz1lGElmRhYJEkpqawMfv3rsJl2zZpQO+wwWLgw3BnkE5aTiyMhSVLK+eyz8MyfV16J184/Pzy0sFmz6PpSzbnCIklKKfPmQfv28bDSqFEIKjNmGFaSmYFFkpQStm6Fa66BM84I56wAHHEELF0KF13kCCjZORKSJCW9f/0rjHxefz1eGzYM7rsP9t47sra0BxlYJElJ7U9/giFDYMOG8L5xY3j4YRgwINK2tIc5EpIkJaXNm2H4cDj33HhY6dQJ3nrLsJKKDCySpKTzz39Ct25w//3x2ogRsGQJtGsXXV+qPY6EJElJ5fHH4ZJLwgoLhDt/pkyBPn0ibUu1zMAiSUoKJSVhBDRlSryWmwuzZsGhh0bXl+qGIyFJUsJ76y3o0iUeVtLSwkMMX3nFsFJfuMIiSUpYsRj8/vfwi19AaWmoNW8O06dDz57R9qa6ZWCRJCWkoiK48EJ44ol47dRTQ1hp2TKythQRR0KSpITz+uvQsWM8rKSlwc03w4svGlbqK1dYJEkJIxaDu++G666DbdtCLTsbZs+Gk06KtjdFy8AiSUoI69bBoEHw7LPx2g9/CI89BvvvH11fSgyOhCRJkXv5ZejQIR5WGjQIKy1PP21YUWBgkSRFpqwMfvvbsJl29epQO/RQWLgQRo3yCcuKcyQkSYrE55+HZ/4sWBCv9e0Lf/gDZGVF15cSkysskqQ699xz0L59PKw0bAgPPhhOrTWsaHsMLJKkOrN1azihtndv+OqrUDv8cFi6NDwfyBGQdsSRkCSpTvy//wfnnRfOWKkwdCjcdx80aRJdX0oOrrBIkmrd3LnhILiKsNK4MUydCo88YljRrjGwSJJqzebNcMUVcM45sGFDqHXoACtWwMCBkbamJGNgkSTVig8+gOOOg4kT47Xhw8MqyxFHRNeXklONAsvEiRNp3bo1mZmZ5ObmsmTJkh1e++6773LuuefSunVr0tLSGD9+/Leuuemmm0hLS6vyOuqoo2rSmiQpAUybBp07w9tvh/dNm8Kf/gQTJkBmZrS9KTlVO7DMnDmT/Px8xo4dy/Lly+ncuTO9evVizZo1271+06ZNtG3blltuuYWWO3liVfv27fn8888rX6+++mp1W5MkRaykBIYNC+Oer78Ote7dQ3A555xoe1Nyq3Zgueuuu7j44osZOnQoRx99NJMmTWLvvffmkUce2e713bt35/bbb6d///40atRoh5/boEEDWrZsWflq0aJFdVuTJEXonXfgmGPg0UfjtWuvhb//HQ47LLq+lBqqFVhKS0tZtmwZeXl58Q9ITycvL4+FCxfuViMffPABrVq1om3btgwcOJCVK1fu8NotW7ZQXFxc5SVJikYsBg89BF27hn0rAPvtF54LdOutsNde0fan1FCtwLJu3TrKysrIzs6uUs/OzqawsLDGTeTm5jJ58mTmzZvHAw88wMcff8xJJ53Ehoot5f9h3LhxZGVlVb5ycnJq/GdLkmquuBj69QuHvpWWhtrJJ4fVlt69o+1NqSUh7hI644wzOO+88+jUqRO9evXimWeeYf369cyaNWu7148ePZqioqLK16pVq+q4Y0nS0qXhbJXZs8P7tDT4zW/gpZegVatoe1PqqdZJty1atCAjI4PVFY/U/LfVq1fvdENtde27774cccQRfPjhh9v9/UaNGu10P4wkqfbEYnDPPXDNNbBtW6gdeGAILiefHG1vSl3VWmFp2LAhXbt2paCgoLJWXl5OQUEBPXr02GNNbdy4kY8++oiDDjpoj32mJGn3ffEFnHUWXHllPKz07g3vvmtYUe2q9rOE8vPzGTx4MN26deO4445j/PjxlJSUMHToUAAGDRrEwQcfzLhx44CwUfe9996r/PWnn37KihUr2GeffWjXrh0AV199NWeddRaHHXYYn332GWPHjiUjI4MBAwbsqe9TkrSbXn01PAuoYstiRgbcdhuMGgXpCbHBQKms2oGlX79+rF27ljFjxlBYWEiXLl2YN29e5UbclStXkv6N/+Z+9tlnHHPMMZXv77jjDu644w5OOeUU5s+fD8Ann3zCgAED+OKLLzjggAM48cQTWbRoEQcccMBufnuSpN1VVga33AJjxkB5eajl5MCcOeEkW6kupMVisVjUTeyu4uJisrKyKCoqolmzZlG3I0kpo7AQLrgA/va3eO3cc+HhhyErK7q+lBqq8/e3i3iSpO164QVo3z4eVvbaCyZNCptrDSuqawYWSVIV27bB6NHQqxd8+WWotWsXbmP++c/D7ctSXav2HhZJUupauRLOPx8WL47XBg0KT1zeZ5/o+pJcYZEkAfDUU+EguIqwkpkJjz0GU6YYVhQ9A4sk1XNbtsAvfgFnnx2O2oewd2XFCvjZzyJtTarkSEiS6rEPPwx3/bz1Vrx22WVw111hhUVKFAYWSaqnpk+Hiy6CTZvC+332gcmTQ4CREo2BRZLqmU2bwgjo4Yfjta5dw+3KbdpE15e0M+5hkaR65N134dhjq4aVq6+GhQsNK0psrrBIUj0Qi4WQcsUVYZMtwL77wrRpcMYZkbYm7RIDiySluOJiuPhimDUrXjvpJJgxA1q1iq4vqTocCUlSClu2DDp1ioeVtDQYOzYct29YUTJxhUWSUlAsBvfdB1ddFY7aBzjggBBcTj010takGjGwSFKK+fJLGDIE/vKXeK1nT5g6NYQWKRk5EpKkFPL3v0OHDvGwkpEBt98Ozz5rWFFyc4VFklJAeTnceiv86lfh1wCHHAJz5kBubrS9SXuCgUWSktzq1XDBBfDSS/HaOefAI4+EW5elVOBISJKS2IsvhgcVVoSVvfaCiRPhiScMK0otBhZJSkLbtsEvfxk2037xRai1bQtLlsDll4fbl6VU4khIkpLMqlXQr184Tr/CT38KDzwQHmAopSJXWCQpifzlL9CxYzysZGaGJyw//rhhRanNwCJJSaC0FEaNgh//GIqKQu3oo+GNN2Dw4Ehbk+qEIyFJSnAffQR9+8KKFfHaz38Od98NjRtH1pZUpwwskpTAZs6EYcNg06bwvkkTePRROO+8aPuS6pqBRZIS0KZNMHIk/OEP8dqxx4aD4Nq0ia4vKSruYZGkBPPeeyGcfDOs5OeHjbaGFdVXrrBIUoKIxcK45/LLYcuWUNt33/DQwjPPjLQ1KXIGFklKABs2hI2006fHayecADNmhGcCSfWdIyFJitgbb0DnzvGwkpYGN94I8+cbVqQKrrBIUkRiMZgwIexP2bYt1A44INwZdNpp0fYmJRoDiyRF4KuvYMgQeOqpeC0vD/74RzjwwMjakhKWIyFJqmMLF0KHDvGwkp4Ot94Kzz1nWJF2xBUWSaoj5eVw++1www3h1wAHHwyzZ0OPHtH2JiU6A4sk1YE1a2DgQHjxxXjt7LPDbcz77RddX1KycCQkSbXspZegfft4WGnQIGy2ffJJw4q0qwwsklRLtm0Ltyfn5cG6daHWpg0sWQLDh4fblyXtGkdCklQLPvkE+vWD116L1wYMgAcfhKZNo+tLSlausEjSHvbXv4a7gCrCSmYmPPJIuGXZsCLVjIFFkvaQ0tJwCNyPfgRFRaF21FGwfDkMHeoISNodjoQkaQ/4v/+Dvn3DMfsVLrkExo+Hxo0ja0tKGQYWSdpNs2bBsGFQUhLeN2kSRkDnnx9tX1IqMbBIUg19/TWMGgW//3281qULPPEEtG0bVVdSanIPiyTVwPvvQ9euVcPKqFGweLFhRaoNrrBIUjVNmQKXXgqbN4f3WVkwdWrYbCupdhhYJGkXbdgAl10Wbk+u8L3vwcyZcMgh0fUl1QeOhCRpF6xYEfanVISVtDT45S9hwQLDilQXXGGRpJ2IxeD+++HKK2Hr1lDbf/+wqnL66dH2JtUnBhZJ2oH168OBb3Pnxmunnx5WWbKzo+pKqp8cCUnSdixaFI7Xrwgr6ekwbhw8/7xhRYqCKyyS9A3l5XDnnTB6NJSVhVqrVjB7dthgKykaBhZJ+re1a2HgQHjhhXjtrLNg8mRo3jyytiThSEiSAJg/H9q3j4eVBg3g3nvhz382rEiJwMAiqV4rK4OxY+H73w8rLACtW4cTa0eM8AnLUqJwJCSp3vr0U+jfH159NV7r3z8ct9+0aXR9Sfo2V1gk1UvPPhvuAqoIK40awcMPw7RphhUpERlYJNUrpaVw9dXwwx+Gc1YAjjwSli2DYcMcAUmJypGQpHrj44+hb19Yvjxeu+giuOce2Hvv6PqS9N0MLJLqhSeegCFDYOPG8H7vvcMIqH//SNuStIscCUlKaZs3hycs9+0bDyudO8ObbxpWpGRiYJGUst5/H7p2hUmT4rWRI8Mty+3aRdeXpOpzJCQpJT32GPz852GFBaBZM3j8cfjxj6PtS1LNGFgkpZSNG8MIaOrUeO3442HWLMjJia4vSbvHkZCklPHWW9ClSzyspKXBDTfAK68YVqRk5wqLpKQXi4V9KiNHwtatobb//jBjBuTlRdubpD3DwCIpqa1fHw58e/LJeO2008KJtS1bRtaWpD3MkZCkpLVkCXTsGA8r6enwu9/Biy8aVqRU4wqLpKRTXg533w3XXReetgxw0EFhY+2JJ0bbm6TaYWCRlFTWrYOf/hSeey5e+9GPYMoUaN48ur4k1S5HQpKSxoIF0L59PKw0aADjx8NTTxlWpFRnYJGU8MrK4Ne/Dptp16wJtcMOg4ULw51BPmFZSn2OhCQltM8+gwED4OWX47Xzz4eHHgqn10qqH2q0wjJx4kRat25NZmYmubm5LFmyZIfXvvvuu5x77rm0bt2atLQ0xo8fv9ufKal+mDcPOnSIh5VGjUJQmTHDsCLVN9UOLDNnziQ/P5+xY8eyfPlyOnfuTK9evVhTsU77HzZt2kTbtm255ZZbaLmD+wyr+5mSUtvWrXDttXDGGfDVV6F2xBGwdClcdJEjIKk+SovFYrHqfEFubi7du3dnwoQJAJSXl5OTk8OIESO4/vrrd/q1rVu3ZtSoUYwaNWqPfSZAcXExWVlZFBUV0cx/7ZKS2r/+FUY+r78erw0bBvfdB3vvHVlbkmpBdf7+rtYKS2lpKcuWLSPvG2ddp6enk5eXx8KFC2vUbE0+c8uWLRQXF1d5SUp+f/oTdOoUDyuNG8Mf/wgPP2xYkeq7agWWdevWUVZWRnZ2dpV6dnY2hYWFNWqgJp85btw4srKyKl85PtVMSmqbN8Pw4XDuubBhQ6h17AhvvgkXXBBtb5ISQ1Le1jx69GiKiooqX6tWrYq6JUk19M9/QvfucP/98dqIEWGV5fDDo+tLUmKp1m3NLVq0ICMjg9WrV1epr169eocbamvjMxs1akSjRo1q9OdJShxTp8LFF4cVFgh3/kyZAn36RNqWpARUrRWWhg0b0rVrVwoKCipr5eXlFBQU0KNHjxo1UBufKSmxlZTAkCHws5/Fw0puLrz9tmFF0vZV++C4/Px8Bg8eTLdu3TjuuOMYP348JSUlDB06FIBBgwZx8MEHM27cOCBsqn3vvfcqf/3pp5+yYsUK9tlnH9q1a7dLnykpdbz1Vtir8uGH8dr118NvfgN77RVdX5ISW7UDS79+/Vi7di1jxoyhsLCQLl26MG/evMpNsytXriQ9Pb5w89lnn3HMMcdUvr/jjju44447OOWUU5g/f/4ufaak5BeLwe9/D7/4BZSWhlrz5jB9OvTsGW1vkhJftc9hSUSewyIltqKicODbnDnx2qmnwrRpcNBBkbUlKWK1dg6LJFXX66+Hs1UqwkpaGtx8M7z4omFF0q7z4YeSakUsBnffDdddB9u2hVp2NsyeDSedFG1vkpKPgUXSHrduHQwaBM8+G6/98IfhluUWLaLrS1LyciQkaY965ZXwhOWKsNKgAdx1Fzz9tGFFUs0ZWCTtEWVlYW/KKadAxTmQhx4Kr70GV17pE5Yl7R5HQpJ22+efw4ABsGBBvNa3L/zhD5CVFV1fklKHKyySdstzz4URUEVYadgQHnwQZs0yrEjacwwskmpk69ZwQm3v3vDll6HWrh0sXQqXXOIISNKe5UhIUrX9v/8H550XzlipMGQITJgATZpE1pakFOYKi6RqmTsXOnaMh5XGjcNTlx991LAiqfYYWCTtki1bYMQIOOcc2LAh1Dp0gBUrYODASFuTVA8YWCR9pw8+gO7dw8inwvDhYZXliCOi60tS/eEeFkk7NW1aeHDh11+H902bwuTJ8JOfRNqWpHrGwCJpu0pKwgjo0Ufjte7dw+3KrVtH1pakesqRkKRveecdOPbYqmHl2mvh7383rEiKhisskirFYuF02iuugNLSUNtvvzAW6t072t4k1W8GFkkAFBeHvSqzZ8drJ58M06dDq1bR9SVJ4EhIEuF02o4d42ElLQ1+/Wt46SXDiqTE4AqLVI/FYnDPPXDNNbBtW6gdeGDYWHvKKdH2JknfZGCR6qkvvgjH6T/9dLzWuzc8/ji0aBFZW5K0XY6EpHro1VfDKbUVYSUjA+68E/76V8OKpMRkYJHqkbIy+N3vwrinsDDUcnLgtdcgPx/S/X8ESQnKkZBUTxQWwgUXwN/+Fq/95Cfw8MOw776RtSVJu8R/n5LqgRdegPbt42Flr73ggQdgzhzDiqTkYGCRUti2bXDDDdCrF3z5Zai1axduY7700nD7siQlA0dCUopatQrOPx8WLYrXBg2CiRNhn32i60uSasIVFikFPfVUuAuoIqxkZsJjj8GUKYYVScnJwCKlkC1bYORIOPvscNQ+wNFHw4oV8LOfRdqaJO0WR0JSivjwQzj3XHjrrXjtssvgrrvCCoskJTMDi5QCZsyACy+ETZvC+332gcmTQ4CRpFRgYJGS2KZN8ItfhLNUKnTtGh5i2KZNdH1J0p7mHhYpSb37Lhx7bNWwcvXVsHChYUVS6nGFRUoysRg88ggMHx422UI4/G3aNDjjjEhbk6RaY2CRkkhxMVxyCcycGa+ddBJMnw4HHxxdX5JU2xwJSUli+XLo3DkeVtLS4KabwnH7hhVJqc4VFinBxWJw331w1VXhqH2AAw6AWbPg1FMjbU2S6oyBRUpgX34JQ4bAX/4Sr/XsCVOnhtAiSfWFIyEpQb32WjhevyKsZGTA7bfDs88aViTVPwYWKcGUl8O4cWEz7eefh9ohh8Df/x5uW073f7WS6iFHQlICWb0aBg6EgoJ47Zxzwm3M++4bWVuSFDn/XU1KEAUFYQRUEVb22gsmToQnnjCsSJKBRYrYtm3wy1/CD34A69aFWtu2sGQJXH55uH1Zkuo7R0JShD75BM4/PxynX2HgQJg0KTzAUJIUuMIiReQvfwkjoIqwkpkZnrA8daphRZL+k4FFqmOlpXDllfDjH0NRUagdfTS88QYMHhxtb5KUqBwJSXXoo4+gb19YsSJe+/nP4e67oXHjyNqSpIRnYJHqyMyZMGwYbNoU3jdpAo8+CuedF21fkpQMDCxSLfv6axg5Eh56KF475hiYMyfcDSRJ+m7uYZFq0XvvwbHHVg0r+fmwaJFhRZKqwxUWqRbEYuGOn8svh82bQ23ffcMdQGeeGWVnkpScDCzSHrZhQ9hIO316vHbCCTBjRngmkCSp+hwJSXvQG29A587xsJKWBjfeCPPnG1YkaXe4wiLtAbFYeO7PlVeGo/YBWrQIdwZ9//vR9iZJqcDAIu2mr76CoUPhz3+O1/Ly4I9/hAMPjK4vSUoljoSk3bBwIXTsGA8r6elw663w3HOGFUnak1xhkWqgvBxuvx1uuCH8GqBVq3C2So8e0fYmSanIwCJV05o14YnKL74Yr519dji1dr/9outLklKZIyGpGl56Cdq3j4eVBg3gvvvgyScNK5JUmwws0i7Yti3cnpyXB+vWhVqbNrBkCVxxRbh9WZJUexwJSd/h00+hXz/4+9/jtQED4MEHoWnT6PqSpPrEFRZpJ/761zACqggrmZnwyCPhlmXDiiTVHQOLtB2lpeEhhT/6ERQVhdpRR8GyZeHMFUdAklS3HAlJ/+H//g/69g3H7Fe4+GK45x5o3Di6viSpPjOwSN8we3ZYQSkpCe+bNAkjoPPPj7YvSarvHAlJwNdfw6WXhmBSEVa6dIG33jKsSFIiMLCo3nv/fejWLdz1U2HUKFi8GNq2jawtSdI3OBJSvTZlSlhZ2bw5vM/KgqlTw2ZbSVLiMLCoXtq4MQSVP/4xXvve92DmTDjkkOj6kiRtnyMh1TsrVkDnzvGwkpYGv/wlLFhgWJGkROUKi+qNWAweeCDsT9m6NdT23z+sqpx+eqStSZK+g4FF9cL69TBsWHhIYYXvfx+mTYPs7MjakiTtohqNhCZOnEjr1q3JzMwkNzeXJUuW7PT62bNnc9RRR5GZmUnHjh155plnqvz+kCFDSEtLq/Lq3bt3TVqTvmXRIujQIR5W0tNh3Dh44QXDiiQli2oHlpkzZ5Kfn8/YsWNZvnw5nTt3plevXqxZs2a717/22msMGDCACy+8kDfeeIM+ffrQp08f3nnnnSrX9e7dm88//7zyNX369Jp9R9K/lZfD7bfDiSeGBxgCtGoFr7wC118fgoskKTmkxWKxWHW+IDc3l+7duzNhwgQAysvLycnJYcSIEVx//fXfur5fv36UlJTw9NNPV9aOP/54unTpwqRJk4CwwrJ+/Xrmzp1bo2+iuLiYrKwsioqKaNasWY0+Q6ll7Vr46U/h+efjtbPOgsmToXnzyNqSJH1Ddf7+rta/Y5aWlrJs2TLy8vLiH5CeTl5eHgsXLtzu1yxcuLDK9QC9evX61vXz58/nwAMP5Mgjj+Syyy7jiy++2GEfW7Zsobi4uMpLqjB/fhgBVYSVBg3g3nvhz382rEhSsqpWYFm3bh1lZWVk/8fgPzs7m8LCwu1+TWFh4Xde37t3bx577DEKCgq49dZbWbBgAWeccQZlZWXb/cxx48aRlZVV+crJyanOt6EUVVYGY8eGzbQVE8rWrcOJtSNG+IRlSUpmCXGXUP/+/St/3bFjRzp16sR//dd/MX/+fE7fzv2mo0ePJj8/v/J9cXGxoaWe+/RT6N8fXn01XuvfPxy375RQkpJftVZYWrRoQUZGBqtXr65SX716NS1bttzu17Rs2bJa1wO0bduWFi1a8OGHH2739xs1akSzZs2qvFR/PftsGAFVhJVGjeDhh8Mty/5XQ5JSQ7UCS8OGDenatSsFBQWVtfLycgoKCujRo8d2v6ZHjx5Vrgd44YUXdng9wCeffMIXX3zBQQcdVJ32VM9s3QrXXAM//GE4ZwXgyCNh2bJw5oojIElKHdW+sTM/P5+HHnqIKVOm8I9//IPLLruMkpIShg4dCsCgQYMYPXp05fUjR45k3rx53Hnnnbz//vvcdNNNLF26lCuuuAKAjRs3cs0117Bo0SL+9a9/UVBQwNlnn027du3o1avXHvo2lWr+9S/o0QPuuCNeu+giWL4c2rePrC1JUi2p9h6Wfv36sXbtWsaMGUNhYSFdunRh3rx5lRtrV65cSfo3Drj43ve+x7Rp0/jVr37FDTfcwOGHH87cuXPp0KEDABkZGbz11ltMmTKF9evX06pVK3r27Mlvf/tbGjVqtIe+TaWSJ56AIUPCAwwB9t47jIC+sRVKkpRiqn0OSyLyHJb6YfNmuPJK+PfxPUB4iOGcOdCuXXR9SZJqptbOYZGi8r//C926VQ0rI0eGW5YNK5KU+hLitmZpZx5/HC65JKywQLjz5/HH4cc/jrYvSVLdMbAoYW3cCMOHw2OPxWvHHw8zZ8Khh0bXlySp7jkSUkJ66y3o0iUeVtLSYPTo8OBCw4ok1T+usCihxGLhdNpf/CKcswKw//4wfTr84AfR9iZJio6BRQlj/Xq48EL405/itdNOCyfW7uRgZElSPeBISAlhyRLo2DEeVtLT4Xe/gxdfNKxIklxhUcTKy+Huu+G668LTliEElNmz4cQTo+1NkpQ4DCyKzLp18LOfwbx58dqZZ8KUKWHfiiRJFRwJKRILFoRn/lSElQYNYPx4+MtfDCuSpG8zsKhOlZXBb34TNtOuWRNqhx0GCxeGk2t9wrIkaXscCanOfP55eEDhyy/Ha+efDw89FE6vlSRpR1xhUZ2YNy+MgCrCSsOGIajMmGFYkSR9NwOLatXWrXDttXDGGfDVV6F2xBGwbBlcdJEjIEnSrnEkpFrzr3+Fkc/rr8drw4bBfffB3ntH1pYkKQkZWFQrnnwSBg+GDRvC+8aN4Q9/gAsuiLYvSVJyciSkPWrzZrjiCvjJT+JhpWNHePNNw4okqeYMLNpj/vlP6N4dJk6M1664IoyEDj88ur4kScnPkZD2iKlT4eKLwwoLhDt/pkyBPn0ibUuSlCIMLNotJSVhFWXy5HgtNxdmzYJDD42sLUlSinEkpBp7+2045piqYeX66+GVVwwrkqQ9yxUWVVssFg59GzECSktDrXlzmD4devaMtjdJUmoysKhaiorCgW9z5sRrp5wSwspBB0XXlyQptTkS0i57/XXo1CkeVtLS4Le/hYICw4okqXa5wqLvFIvB+PHhiP1t20ItOxtmz4aTToq0NUlSPWFg0U598QUMGgTPPBOv/fCH4ZblFi2i60uSVL84EtIOvfIKdOgQDysNGsBdd8HTTxtWJEl1y8Cibykrg5tvDptpCwtDLScHXnsNrrzSJyxLkuqeIyFV8fnnMGAALFgQr/XtGx5cmJUVXV+SpPrNFRZVev75MAKqCCsNG8KDD4ZTaw0rkqQoGVjE1q3hhNpeveDLL0OtXTtYuhQuucQRkCQpeo6E6rmVK+H882Hx4nhtyBCYMAGaNImsLUmSqnCFpR6bOxc6doyHlcxMePxxePRRw4okKbEYWOqhLVvCc4DOOQeKi0OtQwd480346U+j7U2SpO0xsNQzH3wAxx0XRj4Vhg8Px+4fcUR0fUmStDPuYalHpk0LDy78+uvwvmlTmDwZfvKTSNuSJOk7GVjqgU2bwgjokUfite7dw+3KrVtH1pYkSbvMkVCKe+cdOOaYqmHlmmvg7383rEiSkocrLCkqFgun015xBZSWhtp++4WxUO/e0fYmSVJ1GVhSUHExXHxxGPlUOPlkmD4dWrWKri9JkmrKkVCKWbYMOnWKh5W0NPj1r+GllwwrkqTk5QpLiojF4N574eqrYdu2UDvwwBBcTjkl2t4kSdpdBpYU8MUX4Tj9p5+O13r3hscegwMOiKwtSZL2GEdCSe7VV8MptRVhJSMD7rwT/vpXw4okKXUYWJJUeTn8z/+EcU9hYajl5MBrr0F+PqT7n6wkKYU4EkpChYVwwQXwt7/Faz/5CTz8MOy7b2RtSZJUa/z38CTz4othBFQRVvbaCx54AObMMaxIklKXgSVJbNsGN9wAPXuGTbYA//Vf4aGFl14abl+WJClVORJKAqtWwfnnw6JF8dqgQTBxIuyzT3R9SZJUV1xhSXBPPQUdO8bDSmZmuF15yhTDiiSp/jCwJKgtW2DkSDj7bCgqCrWjj4YVK+BnP4u0NUmS6pwjoQT00Udw7rnw5pvx2mWXwV13hRUWSZLqGwNLgpkxAy68EDZtCu/32QcmTw4BRpKk+srAkiA2bYJf/CKcpVKha1eYPRvatImuL0mSEoF7WBLAe+/BscdWDStXXw0LFxpWJEkCV1giFYvBo4/C5ZeHTbYQDn+bNg3OOCPS1iRJSigGlohs2ACXXBL2rFQ48cTw/uCDo+tLkqRE5EgoAsuXQ6dO8bCSlgZjx8L8+YYVSZK2xxWWOhSLwX33wVVXhaP2AQ44AGbNglNPjbQ1SZISmoGljnz5JQwdGk6urdCzJ0ydGkKLJEnaMUdCdeC118Lx+hVhJSMDbrsNnn3WsCJJ0q5whaUWlZeHYPLLX4ZfQ9ijMmcOHH98tL1JkpRMDCy1ZPVqGDgQCgritT594JFHYL/9ImtLkqSk5EioFhQUQIcO8bCy114wcSL86U+GFUmSasLAsgdt2wa/+hX84Aewbl2otW0LS5aEw+HS0qLtT5KkZOVIaA/55BPo1y9ssK0wcCBMmhQeYChJkmrOFZY94OmnwwioIqxkZoYnLE+daliRJGlPMLDshtJSuPJKOOssKCoKtf/+73CS7eDB0fYmSVIqcSRUQx99BH37wooV8drPfw533w2NG0fWliRJKcnAUgOzZsGwYVBSEt43aRKeunzeedH2JUlSqqrRSGjixIm0bt2azMxMcnNzWbJkyU6vnz17NkcddRSZmZl07NiRZ555psrvx2IxxowZw0EHHUTjxo3Jy8vjgw8+qElrterrr8MqSr9+8bByzDHw1luGFUmSalO1A8vMmTPJz89n7NixLF++nM6dO9OrVy/WrFmz3etfe+01BgwYwIUXXsgbb7xBnz596NOnD++8807lNbfddhv33nsvkyZNYvHixTRp0oRevXqxefPmmn9ne9g//gFdu8Lvfx+v5efDokXh1mVJklR70mKxWKw6X5Cbm0v37t2ZMGECAOXl5eTk5DBixAiuv/76b13fr18/SkpKePrppytrxx9/PF26dGHSpEnEYjFatWrFVVddxdVXXw1AUVER2dnZTJ48mf79+39nT8XFxWRlZVFUVESzZs2q8+18p1gs3PFz+eVQkZ/23TfcAXTmmXv0j5IkqV6pzt/f1VphKS0tZdmyZeTl5cU/ID2dvLw8Fi5cuN2vWbhwYZXrAXr16lV5/ccff0xhYWGVa7KyssjNzd3hZ9alMWPCfpWKsHLCCfD224YVSZLqUrUCy7p16ygrKyM7O7tKPTs7m8LCwu1+TWFh4U6vr/hndT5zy5YtFBcXV3nVlvfeC/9MS4Mbb4T58+GQQ2rtj5MkSduRlOewjBs3jqysrMpXTk5Orf1ZJ50UAsqLL8JvfgMNvK9KkqQ6V63A0qJFCzIyMli9enWV+urVq2nZsuV2v6Zly5Y7vb7in9X5zNGjR1NUVFT5WrVqVXW+jWoZNQpWroTvf7/W/ghJkvQdqhVYGjZsSNeuXSmoeAwxYdNtQUEBPXr02O7X9OjRo8r1AC+88ELl9W3atKFly5ZVrikuLmbx4sU7/MxGjRrRrFmzKq/a5EMLJUmKVrUHHPn5+QwePJhu3bpx3HHHMX78eEpKShg6dCgAgwYN4uCDD2bcuHEAjBw5klNOOYU777yTM888kxkzZrB06VJ+/+/7g9PS0hg1ahQ333wzhx9+OG3atOHGG2+kVatW9OnTZ899p5IkKWlVO7D069ePtWvXMmbMGAoLC+nSpQvz5s2r3DS7cuVK0tPjCzff+973mDZtGr/61a+44YYbOPzww5k7dy4dOnSovObaa6+lpKSESy65hPXr13PiiScyb948MjMz98C3KEmSkl21z2FJRLV5DoskSaodtXYOiyRJUhQMLJIkKeEZWCRJUsIzsEiSpIRnYJEkSQnPwCJJkhKegUWSJCU8A4skSUp4BhZJkpTwDCySJCnhVftZQomo4ukCxcXFEXciSZJ2VcXf27vylKCUCCwbNmwAICcnJ+JOJElSdW3YsIGsrKydXpMSDz8sLy/ns88+o2nTpqSlpe3Rzy4uLiYnJ4dVq1b5YMU9zJ9t7fDnWnv82dYef7a1J5F/trFYjA0bNtCqVSvS03e+SyUlVljS09M55JBDavXPaNasWcL9B50q/NnWDn+utcefbe3xZ1t7EvVn+10rKxXcdCtJkhKegUWSJCU8A8t3aNSoEWPHjqVRo0ZRt5Jy/NnWDn+utcefbe3xZ1t7UuVnmxKbbiVJUmpzhUWSJCU8A4skSUp4BhZJkpTwDCySJCnhGVi+w8SJE2ndujWZmZnk5uayZMmSqFtKei+//DJnnXUWrVq1Ii0tjblz50bdUkoYN24c3bt3p2nTphx44IH06dOH//3f/426rZTwwAMP0KlTp8qDt3r06MGzzz4bdVsp55ZbbiEtLY1Ro0ZF3UrSu+mmm0hLS6vyOuqoo6Jua7cYWHZi5syZ5OfnM3bsWJYvX07nzp3p1asXa9asibq1pFZSUkLnzp2ZOHFi1K2klAULFjB8+HAWLVrECy+8wNatW+nZsyclJSVRt5b0DjnkEG655RaWLVvG0qVL+f73v8/ZZ5/Nu+++G3VrKeP111/nwQcfpFOnTlG3kjLat2/P559/Xvl69dVXo25pt3hb807k5ubSvXt3JkyYAIRnFuXk5DBixAiuv/76iLtLDWlpaTz55JP06dMn6lZSztq1aznwwANZsGABJ598ctTtpJzmzZtz++23c+GFF0bdStLbuHEjxx57LPfffz8333wzXbp0Yfz48VG3ldRuuukm5s6dy4oVK6JuZY9xhWUHSktLWbZsGXl5eZW19PR08vLyWLhwYYSdSbumqKgICH+xas8pKytjxowZlJSU0KNHj6jbSQnDhw/nzDPPrPL/t9p9H3zwAa1ataJt27YMHDiQlStXRt3SbkmJhx/WhnXr1lFWVkZ2dnaVenZ2Nu+//35EXUm7pry8nFGjRnHCCSfQoUOHqNtJCW+//TY9evRg8+bN7LPPPjz55JMcffTRUbeV9GbMmMHy5ct5/fXXo24lpeTm5jJ58mSOPPJIPv/8c379619z0kkn8c4779C0adOo26sRA4uUgoYPH84777yT9DPrRHLkkUeyYsUKioqKmDNnDoMHD2bBggWGlt2watUqRo4cyQsvvEBmZmbU7aSUM844o/LXnTp1Ijc3l8MOO4xZs2Yl7RjTwLIDLVq0ICMjg9WrV1epr169mpYtW0bUlfTdrrjiCp5++mlefvllDjnkkKjbSRkNGzakXbt2AHTt2pXXX3+de+65hwcffDDizpLXsmXLWLNmDccee2xlraysjJdffpkJEyawZcsWMjIyIuwwdey7774cccQRfPjhh1G3UmPuYdmBhg0b0rVrVwoKCipr5eXlFBQUOLdWQorFYlxxxRU8+eSTvPTSS7Rp0ybqllJaeXk5W7ZsibqNpHb66afz9ttvs2LFispXt27dGDhwICtWrDCs7EEbN27ko48+4qCDDoq6lRpzhWUn8vPzGTx4MN26deO4445j/PjxlJSUMHTo0KhbS2obN26skvI//vhjVqxYQfPmzTn00EMj7Cy5DR8+nGnTpvHnP/+Zpk2bUlhYCEBWVhaNGzeOuLvkNnr0aM444wwOPfRQNmzYwLRp05g/fz7PPfdc1K0ltaZNm35rj1WTJk3Yf//93Xu1m66++mrOOussDjvsMD777DPGjh1LRkYGAwYMiLq1GjOw7ES/fv1Yu3YtY8aMobCwkC5dujBv3rxvbcRV9SxdupTTTjut8n1+fj4AgwcPZvLkyRF1lfweeOABAE499dQq9UcffZQhQ4bUfUMpZM2aNQwaNIjPP/+crKwsOnXqxHPPPccPfvCDqFuTtuuTTz5hwIABfPHFFxxwwAGceOKJLFq0iAMOOCDq1mrMc1gkSVLCcw+LJElKeAYWSZKU8AwskiQp4RlYJElSwjOwSJKkhGdgkSRJCc/AIkmSEp6BRZIkJTwDiyRJSngGFkmSlPAMLJIkKeEZWCRJUsL7/62eJdDxT2LaAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.arrow(0, 0, dataset['sepal length (cm)'][0], dataset['petal width (cm)'][0], head_width=0.01, head_length=0.1, fc='blue', ec='blue')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f510372b",
   "metadata": {},
   "source": [
    "## Simple transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5bcd91cf",
   "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>sepal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>1.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>1.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length (cm)  petal width (cm)\n",
       "0                  5.1               0.2\n",
       "1                  4.9               0.2\n",
       "2                  4.7               0.2\n",
       "3                  4.6               0.2\n",
       "4                  5.0               0.2\n",
       "..                 ...               ...\n",
       "145                6.7               2.3\n",
       "146                6.3               1.9\n",
       "147                6.5               2.0\n",
       "148                6.2               2.3\n",
       "149                5.9               1.8\n",
       "\n",
       "[150 rows x 2 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector = dataset[[\"sepal length (cm)\" ,'petal width (cm)' ]]\n",
    "vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7f5d8d6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.1, 0.2])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector = np.array(vector.iloc[0 , ])\n",
    "vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "634078a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([ 31., -18.])]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_vector = [vector * 10 - 20]\n",
    "new_vector"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "421bb7ad",
   "metadata": {},
   "source": [
    "## Visualizing transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b05d3050",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.FancyArrow at 0x1f9ee7020a0>"
      ]
     },
     "execution_count": 15,
     "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": [
    "fig, ax = plt.subplots()\n",
    "ax.arrow(0, 0, new_vector[0][0], new_vector[0][1], head_width=0.3, head_length=0.5, fc='blue', ec='blue')\n",
    "ax.arrow(0, 0, dataset['sepal length (cm)'][0], dataset['petal width (cm)'][0], head_width=0.5, head_length=0.5, fc='black', ec='black')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "506521ef",
   "metadata": {},
   "source": [
    "## A matrix transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c1835696",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1],\n",
       "       [1, 2]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transform = np.array([[2, 1], [1, 2]])\n",
    "transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "67eb9d0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([10.4,  5.5])]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transformed_vector = [np.matmul(transform, vector)]\n",
    "transformed_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e45ad215",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.FancyArrow at 0x1f9ee49b8b0>"
      ]
     },
     "execution_count": 18,
     "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": [
    "fig, ax = plt.subplots()\n",
    "ax.arrow(0, 0, new_vector[0][0], new_vector[0][1], head_width=0.3, head_length=0.5, fc='blue', ec='blue')\n",
    "ax.arrow(0, 0, dataset['sepal length (cm)'][0], dataset['petal width (cm)'][0], head_width=0.5, head_length=0.5, fc='black', ec='black')\n",
    "ax.arrow(0, 0, transformed_vector[0][0], transformed_vector[0][1], head_width=0.3, head_length=0.5, fc='red', ec='red')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6df2e59",
   "metadata": {},
   "source": [
    "## Determinants "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1a159543",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.FancyArrow at 0x1f9ee8b6400>"
      ]
     },
     "execution_count": 19,
     "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": [
    "fig, ax = plt.subplots()\n",
    "ax.arrow(0, 0, dataset['sepal length (cm)'][0], dataset['petal width (cm)'][0], head_width=0.05, head_length=0.05, fc='black', ec='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6e7426b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03999999999999985"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector = dataset[[\"sepal length (cm)\" ,'petal width (cm)' ]].iloc[0:2 , :]\n",
    "vector\n",
    "determinant = np.linalg.det(vector)\n",
    "determinant"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f4ae675",
   "metadata": {},
   "source": [
    "## Matrix Inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7d907d4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   5. ,   -5. ],\n",
       "       [-122.5,  127.5]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inverse = np.linalg.inv(vector)\n",
    "inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c9cac405",
   "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>sepal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  petal width (cm)\n",
       "0                5.1               0.2\n",
       "1                4.9               0.2"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c6b44096",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e+00, -5.55111512e-18],\n",
       "       [ 6.10622664e-17,  1.00000000e+00]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(np.matmul(vector , inverse))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "399dea38",
   "metadata": {},
   "source": [
    "## Derivatives and integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b9f26267",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{3}$"
      ],
      "text/plain": [
       "x**3"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sp.Symbol('x')\n",
    "y = x**3\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "227bed0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 x^{2}$"
      ],
      "text/plain": [
       "3*x**2"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dy_dx = sp.diff(y, x)\n",
    "dy_dx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "23f52beb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 6 x$"
      ],
      "text/plain": [
       "6*x"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dy_dx2 = sp.diff(y, x ,2)\n",
    "dy_dx2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "cd27a516",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 12$"
      ],
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dy_dx.subs(x, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1659c50c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integral = sp.integrate(dy_dx , (x , 0 , 1))\n",
    "integral"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44cc61bc",
   "metadata": {},
   "source": [
    "## eigenvalues eigenvectors\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "ceb69d51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.1, 0.2],\n",
       "       [4.9, 0.2]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector = np.array(vector)\n",
    "vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "0299f10c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.72059116, -0.03924363],\n",
       "       [ 0.69336021,  0.99922967]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvalues, eigenvectors = np.linalg.eig(vector)\n",
    "eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d293c88e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.29244205, 0.00755795])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7262a4f2",
   "metadata": {},
   "source": [
    "## Expexcted value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1cd2397c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value: 2.4\n"
     ]
    }
   ],
   "source": [
    "pmf = [0.2, 0.3, 0.4, 0.1]\n",
    "values = [1, 2, 3, 4]\n",
    "\n",
    "# Create a discrete random variable object\n",
    "discrete_rv = rv_discrete(values=(values, pmf))\n",
    "\n",
    "expected_value = discrete_rv.mean()\n",
    "\n",
    "print(\"Expected value:\", expected_value)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "9f414c99",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value: 16.0\n"
     ]
    }
   ],
   "source": [
    "def pdf(x):\n",
    "    return 2*x\n",
    "\n",
    "a = 0\n",
    "b = 4\n",
    "\n",
    "expected_value = np.trapz(pdf(np.linspace(a, b, num=100)), np.linspace(a, b, num=100))\n",
    "\n",
    "print(\"Expected value:\", expected_value)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bb32c6d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='classs', ylabel='sepal length (cm)'>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAGwCAYAAABVdURTAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAxHElEQVR4nO3deXQUdcL18VsE6A5IwiJkkQB5BmUXw2qCjuMjGhnE4AKSibKjaBgUXPPOiAhi1BFlUxBBQMEFUcANwqKADPAAAoooCBITliQohoQl3WjS7x+MLZkkmEo6qU7l+zmnzqGrf1V1u23oa1V1leHxeDwCAACwiRpWBwAAAPAlyg0AALAVyg0AALAVyg0AALAVyg0AALAVyg0AALAVyg0AALCVmlYHqGwFBQU6evSo6tWrJ8MwrI4DAABKwePx6OTJkwoPD1eNGhfeN1Ptys3Ro0cVERFhdQwAAFAGhw4dUtOmTS84ptqVm3r16kk69+YEBQVZnAYAAJRGbm6uIiIivN/jF1Ltys1vh6KCgoIoNwAAVDGlOaWEE4oBAICtWFpu8vPz9fjjjysyMlKBgYH605/+pIkTJ+qP7uW5bt06derUSQ6HQy1bttT8+fMrJzAAAPB7lh6WevbZZzVz5kwtWLBA7dq10/bt2zVkyBAFBwdr9OjRxS6Tmpqq3r17a+TIkVq0aJHWrl2r4cOHKywsTLGxsZX8CgAAgL8xPH+0m6QC3XTTTQoJCdHcuXO982677TYFBgZq4cKFxS7z6KOP6uOPP9bXX3/tnTdgwACdOHFCK1eu/MNt5ubmKjg4WDk5OZxzAwBAFWHm+9vSw1IxMTFau3atvvvuO0nSl19+qY0bN6pXr14lLrN582b17Nmz0LzY2Fht3ry52PFut1u5ubmFJgAAYF+WHpZ67LHHlJubq9atWysgIED5+fmaNGmSEhISSlwmMzNTISEhheaFhIQoNzdXeXl5CgwMLPRccnKynnzyyQrJDwAA/I+le24WL16sRYsW6c0339SOHTu0YMECPf/881qwYIHPtpGUlKScnBzvdOjQIZ+tGwAA+B9L99w8/PDDeuyxxzRgwABJUocOHZSWlqbk5GQNGjSo2GVCQ0OVlZVVaF5WVpaCgoKK7LWRJIfDIYfD4fvwAADAL1m65+bMmTNF7g8REBCggoKCEpeJjo7W2rVrC81bvXq1oqOjKyQjAACoWiwtN3369NGkSZP08ccf64cfftDSpUv1wgsv6JZbbvGOSUpK0sCBA72PR44cqYMHD+qRRx7R3r179fLLL2vx4sUaM2aMFS8BAAD4GUsPS02fPl2PP/647rvvPh07dkzh4eG65557NG7cOO+YjIwMpaenex9HRkbq448/1pgxYzR16lQ1bdpUc+bM4Ro3AABAksXXubEC17kBAKDqMfP9Xe1unAkAqB48Ho9cLpflGdxut6RzP3ApzU0fK5LT6bQ8Q2Wg3AAAbMnlcnHKwn9JSUkp9pfFdsNdwQEAgK2w5wYAYEtOp1MpKSmWZnC5XIqLi5MkLV++XE6n09I8Vm+/slBuAAC2ZBiGXx2CcTqdfpXHzjgsBQAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbIVyAwAAbMXSctOiRQsZhlFkSkxMLHb8/Pnzi4x1Op2VnBoAAPizmlZufNu2bcrPz/c+/vrrr3X99derX79+JS4TFBSkffv2eR8bhlGhGQEAQNViablp3LhxocfPPPOM/vSnP+maa64pcRnDMBQaGlrqbbjdbrndbu/j3Nxc80EBAECV4Tfn3Jw9e1YLFy7U0KFDL7g35tSpU2revLkiIiIUFxenPXv2XHC9ycnJCg4O9k4RERG+jg4AAPyI35SbZcuW6cSJExo8eHCJY1q1aqXXXntNy5cv18KFC1VQUKCYmBgdPny4xGWSkpKUk5PjnQ4dOlQB6QEAgL+w9LDU+ebOnatevXopPDy8xDHR0dGKjo72Po6JiVGbNm30yiuvaOLEicUu43A45HA4fJ4XAAD4J78oN2lpaVqzZo3ef/99U8vVqlVLUVFROnDgQAUlAwAAVY1fHJaaN2+emjRpot69e5taLj8/X7t371ZYWFgFJQMAAFWN5eWmoKBA8+bN06BBg1SzZuEdSQMHDlRSUpL38YQJE7Rq1SodPHhQO3bs0J133qm0tDQNHz68smMDAAA/ZflhqTVr1ig9PV1Dhw4t8lx6erpq1Pi9f2VnZ2vEiBHKzMxUgwYN1LlzZ23atElt27atzMgAAMCPGR6Px2N1iMqUm5ur4OBg5eTkKCgoyOo4AAAby8vLU2xsrCQpJSVFgYGBFiequsx8f1t+WAoAAMCXKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWLC03LVq0kGEYRabExMQSl3n33XfVunVrOZ1OdejQQZ988kklJgYAAP7O0nKzbds2ZWRkeKfVq1dLkvr161fs+E2bNik+Pl7Dhg3Tzp071bdvX/Xt21dff/11ZcYGAAB+zPB4PB6rQ/zmgQce0EcffaT9+/fLMIwiz99xxx06ffq0PvroI++8K6+8UldccYVmzZpVqm3k5uYqODhYOTk5CgoK8ll2oDrzeDxyuVyWZ3C73ZIkh8NR7L8hlcnpdFqeAdbLy8tTbGysJCklJUWBgYEWJ6q6zHx/16ykTH/o7NmzWrhwocaOHVviPwibN2/W2LFjC82LjY3VsmXLSlyv2+32/oMnnXtzAPiWy+Xy/gOOc/giA6zjNycUL1u2TCdOnNDgwYNLHJOZmamQkJBC80JCQpSZmVniMsnJyQoODvZOERERvooMAAD8kN/suZk7d6569eql8PBwn643KSmp0N6e3NxcCg7gY06nUykpKZZmcLlciouLkyQtX75cTqfT0jxWbx+ozvyi3KSlpWnNmjV6//33LzguNDRUWVlZheZlZWUpNDS0xGUcDoccDodPcgIonmEYfnUIxul0+lUeAJXLLw5LzZs3T02aNFHv3r0vOC46Olpr164tNG/16tWKjo6uyHgAAKAKsbzcFBQUaN68eRo0aJBq1iy8I2ngwIFKSkryPr7//vu1cuVKTZ48WXv37tX48eO1fft2jRo1qrJjAwAAP2V5uVmzZo3S09M1dOjQIs+lp6crIyPD+zgmJkZvvvmmZs+erY4dO2rJkiVatmyZ2rdvX5mRAQCAH7P8nJsbbrhBJV1qZ926dUXm9evXr8SL/AEAAFhebgAA9uIPF3X0F+e/D7wn51TGBS4pNwAAn+KijsX77VIF1V1lXODS8nNuAAAAfIk9NwCACpPfJ796f9N4JOX/588Bkqrr7cZ+lQI+DKi0zVXnjxwAoKLVFN80tawOUP1wWAoAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANgK5QYAANiKqRvRnzhxQkuXLtXnn3+utLQ0nTlzRo0bN1ZUVJRiY2MVExNTUTkBAABKpVR7bo4eParhw4crLCxMTz31lPLy8nTFFVfouuuuU9OmTfXZZ5/p+uuvV9u2bfXOO+9UdGYAAIASlWrPTVRUlAYNGqQvvvhCbdu2LXZMXl6eli1bpilTpujQoUN66KGHfBoUAACgNEpVbr755hs1atTogmMCAwMVHx+v+Ph4HT9+3CfhAAAAzCrVYak/KjblHQ8AAOArpk4o/s3Ro0e1ceNGHTt2TAUFBYWeGz16tE+CAQAAlIXpcjN//nzdc889ql27tho1aiTDMLzPGYZBuQEAAJYyXW4ef/xxjRs3TklJSapRg8vkAAAA/2K6nZw5c0YDBgyg2AAAAL9kuqEMGzZM7777bkVkAQAAKDfTh6WSk5N10003aeXKlerQoYNq1apV6PkXXnjBZ+EAAADMKlO5SUlJUatWrSSpyAnFAAAAVjJdbiZPnqzXXntNgwcProA4AAAA5WP6nBuHw6EePXpURBYAAIByM11u7r//fk2fPr0isgAAAJSb6cNSW7du1aeffqqPPvpI7dq1K3JC8fvvv++zcAAAAGaZLjf169fXrbfeWhFZAAAAys10uZk3b55PAxw5ckSPPvqoVqxYoTNnzqhly5aaN2+eunTpUuz4devW6dprry0yPyMjQ6GhoT7NBgAAqh7T5SY1NVW//vqrLr300kLz9+/fr1q1aqlFixalXld2drZ69Oiha6+9VitWrFDjxo21f/9+NWjQ4A+X3bdvn4KCgryPmzRpUurtAgAA+zJdbgYPHqyhQ4cWKTf/93//pzlz5mjdunWlXtezzz6riIiIQnuDIiMjS7VskyZNVL9+/VJvCwBQOTwez+8PfrUuB/zIeZ+DQp+PCmK63OzcubPYn4JfeeWVGjVqlKl1ffDBB4qNjVW/fv20fv16XXLJJbrvvvs0YsSIP1z2iiuukNvtVvv27TV+/PgSf57udrvldru9j3Nzc01lBACYc/6/uQEfBliYBP7I7XarTp06FboN0z8FNwxDJ0+eLDI/JydH+fn5ptZ18OBBzZw5U5deeqlSUlJ07733avTo0VqwYEGJy4SFhWnWrFl677339N577ykiIkJ/+ctftGPHjmLHJycnKzg42DtFRESYyggAAKoWw2Ny/1CfPn0UGBiot956SwEB5xp5fn6+7rjjDp0+fVorVqwo9bpq166tLl26aNOmTd55o0eP1rZt27R58+ZSr+eaa65Rs2bN9MYbbxR5rrg9NxEREcrJySl0zg6Aqi0vL0+xsbGSpJSUFAUGBlqcqPo6c+aMbrzxRklSfp/8MhwjgO38+vtevJUrV5Zpz01ubq6Cg4NL9f1t+iP37LPP6s9//rNatWqlq6++WpL0+eefKzc3V59++qmpdYWFhalt27aF5rVp00bvvfeeqfV069ZNGzduLPY5h8Mhh8Nhan0AgLIrdJ/BmqLcoJDKuA+l6cNSbdu21VdffaX+/fvr2LFjOnnypAYOHKi9e/eqffv2ptbVo0cP7du3r9C87777Ts2bNze1nl27diksLMzUMgAAwJ7K1KfDw8P19NNPl3vjY8aMUUxMjJ5++mn1799fW7du1ezZszV79mzvmKSkJB05ckSvv/66JGnKlCmKjIxUu3bt5HK5NGfOHH366adatWpVufMAAICqr1R7btLT002t9MiRI6Ua17VrVy1dulRvvfWW2rdvr4kTJ2rKlClKSEjwjsnIyCi0/bNnz+rBBx9Uhw4ddM011+jLL7/UmjVrdN1115nKCAAA7KlUJxSHhISob9++Gj58uLp27VrsmJycHC1evFhTp07V3XffrdGjR/s8rC+YOSEJQNXBCcX+4/z/Fvm3cEIxdO6E4qXnTigu699Pn59Q/M0332jSpEm6/vrr5XQ61blzZ4WHh8vpdCo7O1vffPON9uzZo06dOum5557TX//6V9OhAQAAfKFUh6UaNWqkF154QRkZGZoxY4YuvfRS/fTTT9q/f78kKSEhQV988YU2b95MsQEAAJYytbMwMDBQt99+u26//faKygMAAFAupn8KDgAA4M8oNwAAwFYoNwAAwFYoNwAAwFYoNwAAwFbKdGml/fv367PPPtOxY8dUUFBQ6Llx48b5JBgAAEBZmC43r776qu69915dfPHFCg0NLXR3T8MwKDdAJfN4PHK5XFbHsNz57wHvxzlOp7NS7sAM+BvT5eapp57SpEmT9Oijj1ZEHgAmuVwu76XucU5cXJzVEfwCt6FAdWX6nJvs7Gz169evIrIAAACUm+k9N/369dOqVas0cuTIisgDoBxe+vMJOQL+8F64tuTxSGf/cwpg7RpSdT0a4843lLihvtUxAEuVqtxMmzbN++eWLVvq8ccf15YtW9ShQwfVqlWr0Fh/vRs4UB04AjxyBlidwjocgJGk6llugfOVqty8+OKLhR5fdNFFWr9+vdavX19ovmEYlBsAAGCpUpWb1NTUis4BAADgE6ZPKJ4wYYLOnDlTZH5eXp4mTJjgk1AAAJv4tZpPv0hy/Wf6xQ/yWDlVItMnFD/55JMaOXKk6tSpU2j+mTNn9OSTT3KdGwCAV8CH1fgkMFjG9J4bj8dT7EWhvvzySzVs2NAnoQAAAMqq1HtuGjRoIMMwZBiGLrvsskIFJz8/X6dOneLn4QAAOZ1OpaSkWB3DL7hcLu9FJZcvXy6n02lxIutVxntQ6nIzZcoUeTweDR06VE8++aSCg4O9z9WuXVstWrRQdHR0hYQEAFQdhmFwZeRiOJ1O3pdKUupyM2jQIElSZGSkYmJiilzfBgAAwB+YPqE4KipKeXl5ysvLKzTfMAw5HA7Vrl3bZ+EAAADMMl1u6tevf8G7zDZt2lSDBw/WE088oRo1TJ+vDAAAUC6my838+fP1j3/8Q4MHD1a3bt0kSVu3btWCBQv0z3/+Uz/++KOef/55ORwO/b//9/98HhgAAOBCTJebBQsWaPLkyerfv793Xp8+fdShQwe98sorWrt2rZo1a6ZJkyZRbgAAQKUzfdxo06ZNioqKKjI/KipKmzdvliRdddVVSk9PL386AAAAk0yXm4iICM2dO7fI/Llz5yoiIkKSdPz4cTVo0KD86QAAAEwyfVjq+eefV79+/bRixQp17dpVkrR9+3bt3btXS5YskSRt27ZNd9xxh2+TAgAAlILpcnPzzTdr7969euWVV/Tdd99Jknr16qVly5apRYsWkqR7773XpyEBAABKy3S5kc5dyO+ZZ57xdRYAAIByK1O5OXHihLZu3apjx46poKCg0HMDBw70STAAAICyMF1uPvzwQyUkJOjUqVMKCgoqdEE/wzAoNwAAwFKmfy314IMPaujQoTp16pROnDih7Oxs7/Tzzz9XREYAAIBSM11ujhw5otGjR6tOnToVkQcAAKBcTJeb2NhYbd++vSKyAAAAlJvpctO7d289/PDDGj9+vN577z198MEHhSazjhw5ojvvvFONGjVSYGCgOnTo8Iflad26derUqZMcDodatmyp+fPnm94uAACwJ9MnFI8YMUKSNGHChCLPGYah/Pz8Uq8rOztbPXr00LXXXqsVK1aocePG2r9//wWvbpyamqrevXtr5MiRWrRokdauXavhw4crLCxMsbGxZl8OAACwGdPl5r9/+l0ezz77rCIiIjRv3jzvvMjIyAsuM2vWLEVGRmry5MmSpDZt2mjjxo168cUXiy03brdbbrfb+zg3N9dH6QEAgD8yfVjqfC6Xq1wb/+CDD9SlSxf169dPTZo0UVRUlF599dULLrN582b17Nmz0LzY2FjvTTv/W3JysoKDg73Tb/e/AgAA9mS63OTn52vixIm65JJLdNFFF+ngwYOSpMcff7zYG2peyMGDBzVz5kxdeumlSklJ0b333qvRo0drwYIFJS6TmZmpkJCQQvNCQkKUm5urvLy8IuOTkpKUk5PjnQ4dOmQqIwAAqFpMl5tJkyZp/vz5eu6551S7dm3v/Pbt22vOnDmm1lVQUKBOnTrp6aefVlRUlO6++26NGDFCs2bNMhurRA6HQ0FBQYUmAABgX6bLzeuvv67Zs2crISFBAQEB3vkdO3bU3r17Ta0rLCxMbdu2LTSvTZs2Sk9PL3GZ0NBQZWVlFZqXlZWloKAgBQYGmto+AACwnzJdxK9ly5ZF5hcUFOiXX34xta4ePXpo3759heZ99913at68eYnLREdHa+3atYXmrV69WtHR0aa2DQAA7Ml0uWnbtq0+//zzIvOXLFmiqKgoU+saM2aMtmzZoqeffloHDhzQm2++qdmzZysxMdE7JikpqdD9qkaOHKmDBw/qkUce0d69e/Xyyy9r8eLFGjNmjNmXAgAAbMj0T8HHjRunQYMG6ciRIyooKND777+vffv26fXXX9dHH31kal1du3bV0qVLlZSUpAkTJigyMlJTpkxRQkKCd0xGRkahw1SRkZH6+OOPNWbMGE2dOlVNmzbVnDlzuMYNAACQVIZyExcXpw8//FATJkxQ3bp1NW7cOHXq1Ekffvihrr/+etMBbrrpJt10000lPl/c1Yf/8pe/aOfOnaa3BQAA7M90uZGkq6++WqtXr/Z1FgBl4PF4vH92l/4C4bCp8z8D5382gOqkTOUGgP84/wrciRtKvnUJqh+32606depYHQOodKUqNw0aNJBhGKVa4c8//1yuQAAAAOVRqnIzZcqUCo4BoKwcDof3zy/9OVuOgAsMhu2583/fg3f+ZwOoTkpVbgYNGlTROQCU0fl7VR0BkpNyg/8o7R53wG7KdeNMAAAAf0O5AQAAtkK5AQAAtkK5AQAAtsJ1bqogj8cjl8tleYbfrq/icDgsP3HR6XRangEA4B9KVW5uvfXWUq/w/fffL3MYlI7L5eJeWv8lJSVFgYGBVscAAPiBUpWb4ODgis4BAADgE6UqN/PmzavoHDDB6XQqJSXF0gwul0txcXGSpOXLl8vpdFqax+rtAwD8B+fcVEGGYfjVIRin0+lXeQAA1VuZys2SJUu0ePFipaen6+zZs4We27Fjh0+CAQAAlIXpn4JPmzZNQ4YMUUhIiHbu3Klu3bqpUaNGOnjwoHr16lURGQEAAErNdLl5+eWXNXv2bE2fPl21a9fWI488otWrV2v06NHKycmpiIwAAAClZrrcpKenKyYmRpIUGBiokydPSpLuuusuvfXWW75NBwAAYJLpchMaGqqff/5ZktSsWTNt2bJFkpSamiqPx+PbdAAAACaZLjf/+7//qw8++ECSNGTIEI0ZM0bXX3+97rjjDt1yyy0+DwgAAGCG6V9LzZ49WwUFBZKkxMRENWrUSJs2bdLNN9+se+65x+cBAQAAzDBdbmrUqKEaNX7f4TNgwAANGDDAp6EAAADKqkzXucnOztbcuXP17bffSpLatm2rIUOGqGHDhj4NBwAAYJbpc242bNigyMhITZs2TdnZ2crOzta0adMUGRmpDRs2VERGAACAUjO95yYxMVH9+/fXzJkzFRAQIEnKz8/Xfffdp8TERO3evdvnIQEAAErL9J6bAwcO6MEHH/QWG0kKCAjQ2LFjdeDAAZ+GAwAAMMt0uenUqZP3XJvzffvtt+rYsaNPQgEAAJSV6cNSo0eP1v33368DBw7oyiuvlCRt2bJFL730kp555hl99dVX3rGXX36575ICAACUgulyEx8fL0l65JFHin3OMAx5PB4ZhqH8/PzyJwRQau58Q1L1vFK4xyOdPXcJLtWuIRmGtXmscu4zAEnyeDxyuVyWZjh/+1ZnkSSn0ymjGvzlMF1uUlNTKyIHAB9I3FDf6giA33C5XIqNjbU6hldcXJzVEZSSkqLAwECrY1Q40+WmefPmFZEDAADAJ8p0Eb833nhDs2bNUmpqqjZv3qzmzZtrypQpioyM9ItmClQnTqdTKSkpVsewnMvl8v77s3z5cjmdTosTWa+6vwf+8HfD4/HI7XZLkhwOh+WHhKrLZ8J0uZk5c6bGjRunBx54QJMmTfKeV1O/fn1NmTKFcgNUMsMwqsVuZjOcTifvCfzm70adOnWsjlDtmP4p+PTp0/Xqq6/qH//4R6Fr3XTp0oUL+AEAAMuZLjepqamKiooqMt/hcOj06dM+CQUAAFBWpstNZGSkdu3aVWT+ypUr1aZNG1PrGj9+vAzDKDS1bt26xPHz588vMr66HD8EAAClY/qcm7FjxyoxMVEul0sej0dbt27VW2+9peTkZM2ZM8d0gHbt2mnNmjW/B6p54UhBQUHat2+f97HVJ2cBAAD/YrrcDB8+XIGBgfrnP/+pM2fO6G9/+5vCw8M1depUDRgwwHyAmjUVGhpa6vGGYZgaDwAAqhfTh6UkKSEhQfv379epU6eUmZmpw4cPa9iwYWUKsH//foWHh+t//ud/lJCQoPT09AuOP3XqlJo3b66IiAjFxcVpz549FxzvdruVm5tbaAIAAPZlutzk5eXpzJkzks79vC0vL09TpkzRqlWrTG+8e/fumj9/vlauXKmZM2cqNTVVV199tU6ePFns+FatWum1117T8uXLtXDhQhUUFCgmJkaHDx8ucRvJyckKDg72ThEREaZzAgCAqsPweDymbkRzww036NZbb9XIkSN14sQJtWrVSrVr19ZPP/2kF154Qffee2+Zw5w4cULNmzfXCy+8UKo9Qb/88ovatGmj+Ph4TZw4sdgxbrfbewElScrNzVVERIRycnIUFBRU5qzVXV5envey5tXlct7wb3wmAXvLzc1VcHBwqb6/Te+52bFjh66++mpJ0pIlSxQaGqq0tDS9/vrrmjZtWtkS/0f9+vV12WWX6cCBA6UaX6tWLUVFRV1wvMPhUFBQUKEJAADYl+lyc+bMGdWrV0+StGrVKt16662qUaOGrrzySqWlpZUrzKlTp/T9998rLCysVOPz8/O1e/fuUo8HAAD2Z7rctGzZUsuWLdOhQ4eUkpKiG264QZJ07Ngx03tFHnroIa1fv14//PCDNm3apFtuuUUBAQGKj4+XJA0cOFBJSUne8RMmTNCqVat08OBB7dixQ3feeafS0tI0fPhwsy8DAADYlOmfgo8bN05/+9vfNGbMGF133XWKjo6WdG4vTnFXLr6Qw4cPKz4+XsePH1fjxo111VVXacuWLWrcuLEkKT09XTVq/N6/srOzNWLECGVmZqpBgwbq3LmzNm3apLZt25p9GQAAwKZMn1AsSZmZmcrIyFDHjh295WPr1q0KCgq64BWG/YGZE5JQMk7ehL/hMwnYm5nvb9N7biQpNDS0yIX0unXrVpZVAQAA+FSZLuIHAADgryg3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVig3AADAVmpaHaCq8Xg8crlcVsew3PnvAe/HOU6nU4ZhWB0DAKo9yo1JLpdLsbGxVsfwK3FxcVZH8AspKSkKDAy0OgYAVHsclgIAALbCnptyON0pQapRTd9Cj0cq+PXcn2vUlKrr4ZiCX1V3xyKrUwAAzlNNv5l9pEZNKaCW1SksVNvqAAAAFMFhKQAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuWlpvx48fLMIxCU+vWrS+4zLvvvqvWrVvL6XSqQ4cO+uSTTyopLQAAqAos33PTrl07ZWRkeKeNGzeWOHbTpk2Kj4/XsGHDtHPnTvXt21d9+/bV119/XYmJAQCAP6tpeYCaNRUaGlqqsVOnTtWNN96ohx9+WJI0ceJErV69WjNmzNCsWbMqMqaXx+P5/UH+L5WyTfix8z4DhT4bAADLWF5u9u/fr/DwcDmdTkVHRys5OVnNmjUrduzmzZs1duzYQvNiY2O1bNmyEtfvdrvldru9j3Nzc8uV9/x11d35ZrnWBXtxu92qU6eO1TEAoNqz9LBU9+7dNX/+fK1cuVIzZ85Uamqqrr76ap08ebLY8ZmZmQoJCSk0LyQkRJmZmSVuIzk5WcHBwd4pIiLCp68BAAD4F0v33PTq1cv758svv1zdu3dX8+bNtXjxYg0bNswn20hKSiq0tyc3N7dcBcfhcHj/fDrqb1JArXLlQxWX/4t3D975nw0AgHUsPyx1vvr16+uyyy7TgQMHin0+NDRUWVlZheZlZWVd8Jwdh8Ph0y8dwzB+fxBQi3IDr0KfDQCAZSz/tdT5Tp06pe+//15hYWHFPh8dHa21a9cWmrd69WpFR0dXRjwAAFAFWFpuHnroIa1fv14//PCDNm3apFtuuUUBAQGKj4+XJA0cOFBJSUne8ffff79WrlypyZMna+/evRo/fry2b9+uUaNGWfUSAAC4oH//+9/q16+f/v3vf1sdpdqwtNwcPnxY8fHxatWqlfr3769GjRppy5Ytaty4sSQpPT1dGRkZ3vExMTF68803NXv2bHXs2FFLlizRsmXL1L59e6teAgAAJXK5XJo8ebKysrI0efJkuVwuqyNVC5aec/P2229f8Pl169YVmdevXz/169evghIBAOA7Cxcu1PHjxyVJx48f16JFi3z2gxmUzK9OKAZQNXk8Hsv/j/T87VudRZKcTicnmVdzhw8f1qJFi7wX+PR4PFq0aJFiY2PVtGlTi9PZG+UGQLm5XC7FxsZaHcMrLi7O6ghKSUlRYGCg1TFgEY/HoxdffLHE+c8//zzltwL51a+lAACwg7S0NG3btk35+fmF5ufn52vbtm1KS0uzKFn1wJ4bAOXmdDqVkpJiaQaPx+O9PYrD4bD8/4qdTqel24e1mjdvrq5du2rHjh2FCk5AQIA6d+6s5s2bW5jO/ig3AMrNMAy/OATDvb3gLwzD0JgxY3TXXXcVO9/q8m13HJYCAKACNG3aVAkJCd4iYxiGEhISdMkll1iczP4oNwAAVJA777xTjRo1kiRdfPHFSkhIsDhR9UC5AQCggjidTj344IMKCQnR2LFjORerknDODQAAFahHjx7q0aOH1TGqFcpNeRT8anUC63g8v7/+GjWl6npyXHX+DACAn6LclEPdHYusjgAAAP4L59wAAABbYc+NSf5wsTJ/4HK5vJe4X758OSfJiYu2AYC/oNyY5C8XK/MnTqeT9wQA4Dc4LAUAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGyFcgMAAGzFb8rNM888I8Mw9MADD5Q4Zv78+TIMo9DkdDorLyQAAPB7Na0OIEnbtm3TK6+8ossvv/wPxwYFBWnfvn3ex4ZhVGQ0AABQxVi+5+bUqVNKSEjQq6++qgYNGvzheMMwFBoa6p1CQkIuON7tdis3N7fQBAAA7MvycpOYmKjevXurZ8+epRp/6tQpNW/eXBEREYqLi9OePXsuOD45OVnBwcHeKSIiwhexAQCAn7K03Lz99tvasWOHkpOTSzW+VatWeu2117R8+XItXLhQBQUFiomJ0eHDh0tcJikpSTk5Od7p0KFDvooPAAD8kGXn3Bw6dEj333+/Vq9eXeqTgqOjoxUdHe19HBMTozZt2uiVV17RxIkTi13G4XDI4XD4JDMAAPB/lpWbL774QseOHVOnTp288/Lz87VhwwbNmDFDbrdbAQEBF1xHrVq1FBUVpQMHDlR0XAAAUEVYVm6uu+467d69u9C8IUOGqHXr1nr00Uf/sNhI58rQ7t279de//rWiYgIAgCrGsnJTr149tW/fvtC8unXrqlGjRt75AwcO1CWXXOI9J2fChAm68sor1bJlS504cUL/+te/lJaWpuHDh1d6fgAA4J/84jo3JUlPT1eNGr+f85ydna0RI0YoMzNTDRo0UOfOnbVp0ya1bdvWwpQAAMCfGB6Px2N1iMqUm5ur4OBg5eTkKCgoyOo4VVZeXp5iY2MlSSkpKQoMDLQ4EQDAzsx8f1t+nRsAAABfotwAAABbodwAAABbodwAAABbodwAAABbodwAAABbodwAAABbodwAAABbodwAAABb8evbL6B4Ho9HLpfL0gznb9/qLJLkdDplGIbVMQAAfoByUwW5XC7vrQ/8QVxcnNURuAUEAMCLw1IAAMBW2HNTBTmdTqWkpFiawePxyO12S5IcDoflh4ScTqel2wcA+A/KTRVkGIZfHIKpU6eO1REAACiCw1IAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWKDcAAMBWqt1dwT0ejyQpNzfX4iQAAKC0fvve/u17/EKqXbk5efKkJCkiIsLiJAAAwKyTJ08qODj4gmMMT2kqkI0UFBTo6NGjqlevngzDsDpOlZabm6uIiAgdOnRIQUFBVscB+EzCL/G59A2Px6OTJ08qPDxcNWpc+KyaarfnpkaNGmratKnVMWwlKCiIv7DwK3wm4Y/4XJbfH+2x+Q0nFAMAAFuh3AAAAFuh3KDMHA6HnnjiCTkcDqujAJL4TMI/8bmsfNXuhGIAAGBv7LkBAAC2QrkBAAC2QrkBAAC2QrkBAAC2QrlBmbz00ktq0aKFnE6nunfvrq1bt1odCdXYhg0b1KdPH4WHh8swDC1btszqSKjmkpOT1bVrV9WrV09NmjRR3759tW/fPqtjVRuUG5j2zjvvaOzYsXriiSe0Y8cOdezYUbGxsTp27JjV0VBNnT59Wh07dtRLL71kdRRAkrR+/XolJiZqy5YtWr16tX755RfdcMMNOn36tNXRqgV+Cg7Tunfvrq5du2rGjBmSzt2vKyIiQn//+9/12GOPWZwO1Z1hGFq6dKn69u1rdRTA68cff1STJk20fv16/fnPf7Y6ju2x5wamnD17Vl988YV69uzpnVejRg317NlTmzdvtjAZAPivnJwcSVLDhg0tTlI9UG5gyk8//aT8/HyFhIQUmh8SEqLMzEyLUgGA/yooKNADDzygHj16qH379lbHqRaq3V3BAQCoTImJifr666+1ceNGq6NUG5QbmHLxxRcrICBAWVlZheZnZWUpNDTUolQA4J9GjRqljz76SBs2bFDTpk2tjlNtcFgKptSuXVudO3fW2rVrvfMKCgq0du1aRUdHW5gMAPyHx+PRqFGjtHTpUn366aeKjIy0OlK1wp4bmDZ27FgNGjRIXbp0Ubdu3TRlyhSdPn1aQ4YMsToaqqlTp07pwIED3sepqanatWuXGjZsqGbNmlmYDNVVYmKi3nzzTS1fvlz16tXznpMYHByswMBAi9PZHz8FR5nMmDFD//rXv5SZmakrrrhC06ZNU/fu3a2OhWpq3bp1uvbaa4vMHzRokObPn1/5gVDtGYZR7Px58+Zp8ODBlRumGqLcAAAAW+GcGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwAAYCuUGwB+64cffpBhGNq1a5fVUQBUIZQbAABgK5QbAABgK5QbAJYrKCjQc889p5YtW8rhcKhZs2aaNGlSkXH5+fkaNmyYIiMjFRgYqFatWmnq1KmFxqxbt07dunVT3bp1Vb9+ffXo0UNpaWmSpC+//FLXXnut6tWrp6CgIHXu3Fnbt2+XJKWlpalPnz5q0KCB6tatq3bt2umTTz6p+BcPwOdqWh0AAJKSkvTqq6/qxRdf1FVXXaWMjAzt3bu3yLiCggI1bdpU7777rho1aqRNmzbp7rvvVlhYmPr3769ff/1Vffv21YgRI/TWW2/p7Nmz2rp1q/cOzQkJCYqKitLMmTMVEBCgXbt2qVatWpKkxMREnT17Vhs2bFDdunX1zTff6KKLLqrU9wGAb3BXcACWOnnypBo3bqwZM2Zo+PDhhZ774YcfFBkZqZ07d+qKK64odvlRo0YpMzNTS5Ys0c8//6xGjRpp3bp1uuaaa4qMDQoK0vTp0zVo0KAiz11++eW67bbb9MQTT/jkdQGwDoelAFjq22+/ldvt1nXXXVeq8S+99JI6d+6sxo0b66KLLtLs2bOVnp4uSWrYsKEGDx6s2NhY9enTR1OnTlVGRoZ32bFjx2r48OHq2bOnnnnmGX3//ffe50aPHq2nnnpKPXr00BNPPKGvvvrKty8UQKWh3ACwVGBgYKnHvv3223rooYc0bNgwrVq1Srt27dKQIUN09uxZ75h58+Zp8+bNiomJ0TvvvKPLLrtMW7ZskSSNHz9ee/bsUe/evfXpp5+qbdu2Wrp0qSRp+PDhOnjwoO666y7t3r1bXbp00fTp0337YgFUCg5LAbCUy+VSw4YNNW3atD88LPX3v/9d33zzjdauXesd07NnT/30008lXgsnOjpaXbt21bRp04o8Fx8fr9OnT+uDDz4o8lxSUpI+/vhj9uAAVRAnFAOwlNPp1KOPPqpHHnlEtWvXVo8ePfTjjz9qz549RQ5VXXrppXr99deVkpKiyMhIvfHGG9q2bZsiIyMlSampqZo9e7ZuvvlmhYeHa9++fdq/f78GDhyovLw8Pfzww7r99tsVGRmpw4cPa9u2bbrtttskSQ888IB69eqlyy67TNnZ2frss8/Upk2bSn8/AJQf5QaA5R5//HHVrFlT48aN09GjRxUWFqaRI0cWGXfPPfdo586duuOOO2QYhuLj43XfffdpxYoVkqQ6depo7969WrBggY4fP66wsDAlJibqnnvu0a+//qrjx49r4MCBysrK0sUXX6xbb71VTz75pKRzPzNPTEzU4cOHFRQUpBtvvFEvvvhipb4PAHyDw1IAAMBWOKEYAADYCuUGAADYCuUGAADYCuUGAADYCuUGAADYCuUGAADYCuUGAADYCuUGAADYCuUGAADYCuUGAADYCuUGAADYyv8HMJRC1OR7J04AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "sns.boxplot(x=dataset['classs'], y=dataset['sepal length (cm)'])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "0fda3fa7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 300 artists>"
      ]
     },
     "execution_count": 35,
     "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": [
    "hist, bin_edges = np.histogram(dataset['sepal length (cm)'], bins=300, density=True)\n",
    "bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2\n",
    "pdf = hist / np.sum(hist)\n",
    "pdf\n",
    "plt.bar(bin_centers, pdf, width=0.1, alpha=0.5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "201ef7bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value of sepal length: 0.07\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jamee\\AppData\\Local\\Temp\\ipykernel_21376\\619184492.py:1: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n",
      "  If increasing the limit yields no improvement it is advised to analyze \n",
      "  the integrand in order to determine the difficulties.  If the position of a \n",
      "  local difficulty can be determined (singularity, discontinuity) one will \n",
      "  probably gain from splitting up the interval and calling the integrator \n",
      "  on the subranges.  Perhaps a special-purpose integrator should be used.\n",
      "  expected_value, _ = spi.quad(lambda x: x * np.interp(x, bin_centers, pdf), bin_centers[0], bin_centers[-1])\n"
     ]
    }
   ],
   "source": [
    "expected_value, _ = spi.quad(lambda x: x * np.interp(x, bin_centers, pdf), bin_centers[0], bin_centers[-1])\n",
    "print(\"Expected value of sepal length: {:.2f}\".format(expected_value))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "6fb59761",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.843333333333334"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.array(dataset['sepal length (cm)']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "9f2cb8a7",
   "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 sepal length between 5 and 6 is 0.42\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "# Fit a normal distribution to the data\n",
    "mu, std = norm.fit(dataset['sepal length (cm)'])\n",
    "\n",
    "# Define the range of values to plot the function\n",
    "x = np.linspace(dataset['sepal length (cm)'].min(), dataset['sepal length (cm)'].max(), 100)\n",
    "\n",
    "# Calculate the PDF using the fitted parameters\n",
    "pdf_fit = norm.pdf(x, mu, std)\n",
    "\n",
    "# Calculate the area under the curve between two values\n",
    "a, b = 5, 6\n",
    "prob = norm.cdf(b, mu, std) - norm.cdf(a, mu, std)\n",
    "\n",
    "# Plot the fitted function and the area under the curve\n",
    "plt.plot(x, pdf_fit, label='Fitted normal distribution')\n",
    "plt.fill_between(x, pdf_fit, where=(x >= a) & (x <= b), color='blue', alpha=0.2)\n",
    "plt.xlabel('sepal length (cm)')\n",
    "plt.ylabel('Probability density')\n",
    "plt.title('Fitted normal distribution')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print(f'The probability of sepal length between {a} and {b} is {prob:.2f}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac1a7fc9",
   "metadata": {},
   "source": [
    "## Markov Chains from scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "572caa60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.2, 0.6, 0.2],\n",
       "       [0.3, 0. , 0.7],\n",
       "       [0.5, 0. , 0.5]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MC = np.array(([0.2 , 0.6 , 0.2] ,\n",
    "             [0.3 , 0 , 0.7],\n",
    "             [0.5 , 0 , 0.5]))\n",
    "MC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "c2836e9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.2, 0.6, 0.2])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_vector = [1 , 0, 0]\n",
    "initial_vector = np.matmul(initial_vector ,  MC)\n",
    "initial_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "4d400dbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.  +0.j       , -0.15+0.3122499j, -0.15-0.3122499j])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Finding the stationary state with eigen vectors and values\n",
    "eigenvalues, eigenvectors = np.linalg.eig(MC)\n",
    "eigenvalues\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "91782aa4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.57735027+0.j        ,  0.70597631+0.j        ,\n",
       "         0.70597631-0.j        ],\n",
       "       [-0.57735027+0.j        , -0.26474112+0.4380559j ,\n",
       "        -0.26474112-0.4380559j ],\n",
       "       [-0.57735027+0.j        , -0.4412352 -0.21196253j,\n",
       "        -0.4412352 +0.21196253j]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "9dd130d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We only care about the first vector because it's eigenvalue corresponds to one which is the one that we care about\n",
    "# since the stationary state is a an eijenvector with a scale of 1\n",
    "#Using l1 normalization we obtain the stationary distrubtion as the sum of the state is equal to one since we are dealing with\n",
    "# aprobablity distrubtion\n",
    "# here we are dealing with complxex valued numbers so we take the abs of each engry and abs of the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "dda0378d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.29022743093214814, 0.3548862845339259, 0.3548862845339259]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stationary_state = eigenvectors[0]\n",
    "stationary_state = [ abs(prob/sum(abs(stationary_state))) for prob in stationary_state]\n",
    "stationary_state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be2f2afb",
   "metadata": {},
   "source": [
    "## Entropy measure of surprise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "4bcc585f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.08412707, 0.09126368, 0.09881368, 0.10678077, 0.11516642,\n",
       "       0.12396971, 0.1331871 , 0.1428123 , 0.1528361 , 0.16324622,\n",
       "       0.17402722, 0.18516041, 0.19662373, 0.20839179, 0.22043582,\n",
       "       0.23272368, 0.24521999, 0.25788616, 0.27068057, 0.2835587 ,\n",
       "       0.29647342, 0.30937514, 0.32221216, 0.33493098, 0.34747662,\n",
       "       0.35979301, 0.3718234 , 0.3835108 , 0.39479837, 0.40562991,\n",
       "       0.41595032, 0.42570605, 0.43484557, 0.44331983, 0.45108266,\n",
       "       0.45809123, 0.46430643, 0.46969322, 0.47422096, 0.47786374,\n",
       "       0.48060057, 0.48241562, 0.48329834, 0.48324361, 0.48225175,\n",
       "       0.48032852, 0.47748508, 0.47373787, 0.46910848, 0.46362338,\n",
       "       0.45731373, 0.45021507, 0.44236697, 0.43381266, 0.42459866,\n",
       "       0.41477435, 0.40439152, 0.39350391, 0.38216679, 0.37043644,\n",
       "       0.35836974, 0.34602369, 0.33345498, 0.32071956, 0.30787226,\n",
       "       0.2949664 , 0.28205344, 0.26918269, 0.25640101, 0.24375257,\n",
       "       0.23127865, 0.21901747, 0.20700405, 0.19527012, 0.18384407,\n",
       "       0.1727509 , 0.16201227, 0.15164648, 0.14166862, 0.13209058,\n",
       "       0.12292123, 0.11416654, 0.10582971, 0.09791141, 0.09040987,\n",
       "       0.08332115, 0.0766393 , 0.07035657, 0.06446362, 0.0589497 ,\n",
       "       0.05380286, 0.04901015, 0.04455778, 0.04043132, 0.03661585,\n",
       "       0.03309614, 0.02985673, 0.02688216, 0.02415699, 0.02166599])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdf_fit "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "3aa1aa26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.18723589798518028"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ent = entropy(pdf_fit , 2)\n",
    "ent"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f6ffa1b",
   "metadata": {},
   "source": [
    "## Covariance and Colleration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "8ce8f5d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#We say that a colleartaion exist using the abs(r) >= law 2/sqrt(sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "7ddc5937",
   "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>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>classs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)   \n",
       "0                  5.1               3.5                1.4               0.2  \\\n",
       "1                  4.9               3.0                1.4               0.2   \n",
       "2                  4.7               3.2                1.3               0.2   \n",
       "3                  4.6               3.1                1.5               0.2   \n",
       "4                  5.0               3.6                1.4               0.2   \n",
       "..                 ...               ...                ...               ...   \n",
       "145                6.7               3.0                5.2               2.3   \n",
       "146                6.3               2.5                5.0               1.9   \n",
       "147                6.5               3.0                5.2               2.0   \n",
       "148                6.2               3.4                5.4               2.3   \n",
       "149                5.9               3.0                5.1               1.8   \n",
       "\n",
       "     classs  \n",
       "0         0  \n",
       "1         0  \n",
       "2         0  \n",
       "3         0  \n",
       "4         0  \n",
       "..      ...  \n",
       "145       2  \n",
       "146       2  \n",
       "147       2  \n",
       "148       2  \n",
       "149       2  \n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "4b11aeda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1f9ef0817c0>"
      ]
     },
     "execution_count": 49,
     "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": [
    "plt.figure()\n",
    "plt.scatter(dataset['sepal length (cm)'] , dataset['sepal width (cm)'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "fee17f9a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No linear colleration -0.11756978413300198\n"
     ]
    }
   ],
   "source": [
    "covariance = np.cov(np.array(dataset['sepal length (cm)']), np.array(dataset['sepal width (cm)']))[0][1]\n",
    "correlation = dataset['sepal length (cm)'].corr(dataset['sepal width (cm)'])\n",
    "\n",
    "if abs(correlation) >= 2/math.sqrt(len(dataset)):\n",
    "    print(\"There is a linear colleration \" ,correlation )\n",
    "else:\n",
    "    print(\"No linear colleration\" , correlation)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39211cb0",
   "metadata": {},
   "source": [
    "## Cross entropy and KL divergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "4486326d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.08412707, 0.09126368, 0.09881368, 0.10678077, 0.11516642,\n",
       "       0.12396971, 0.1331871 , 0.1428123 , 0.1528361 , 0.16324622,\n",
       "       0.17402722, 0.18516041, 0.19662373, 0.20839179, 0.22043582,\n",
       "       0.23272368, 0.24521999, 0.25788616, 0.27068057, 0.2835587 ,\n",
       "       0.29647342, 0.30937514, 0.32221216, 0.33493098, 0.34747662,\n",
       "       0.35979301, 0.3718234 , 0.3835108 , 0.39479837, 0.40562991,\n",
       "       0.41595032, 0.42570605, 0.43484557, 0.44331983, 0.45108266,\n",
       "       0.45809123, 0.46430643, 0.46969322, 0.47422096, 0.47786374,\n",
       "       0.48060057, 0.48241562, 0.48329834, 0.48324361, 0.48225175,\n",
       "       0.48032852, 0.47748508, 0.47373787, 0.46910848, 0.46362338,\n",
       "       0.45731373, 0.45021507, 0.44236697, 0.43381266, 0.42459866,\n",
       "       0.41477435, 0.40439152, 0.39350391, 0.38216679, 0.37043644,\n",
       "       0.35836974, 0.34602369, 0.33345498, 0.32071956, 0.30787226,\n",
       "       0.2949664 , 0.28205344, 0.26918269, 0.25640101, 0.24375257,\n",
       "       0.23127865, 0.21901747, 0.20700405, 0.19527012, 0.18384407,\n",
       "       0.1727509 , 0.16201227, 0.15164648, 0.14166862, 0.13209058,\n",
       "       0.12292123, 0.11416654, 0.10582971, 0.09791141, 0.09040987,\n",
       "       0.08332115, 0.0766393 , 0.07035657, 0.06446362, 0.0589497 ,\n",
       "       0.05380286, 0.04901015, 0.04455778, 0.04043132, 0.03661585,\n",
       "       0.03309614, 0.02985673, 0.02688216, 0.02415699, 0.02166599])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu, std = norm.fit(dataset['sepal length (cm)'])\n",
    "x = np.linspace(dataset['sepal length (cm)'].min(), dataset['sepal length (cm)'].max(), 100)\n",
    "P = norm.pdf(x , mu , std)\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "0f26c976",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.04749059, 0.05431507, 0.06192707, 0.07038632, 0.07975235,\n",
       "       0.0900837 , 0.10143702, 0.11386604, 0.12742056, 0.14214522,\n",
       "       0.15807841, 0.17525093, 0.19368484, 0.21339215, 0.23437363,\n",
       "       0.25661767, 0.28009921, 0.30477877, 0.33060168, 0.35749741,\n",
       "       0.38537919, 0.41414376, 0.44367146, 0.47382652, 0.5044577 ,\n",
       "       0.53539911, 0.56647148, 0.59748355, 0.6282339 , 0.65851291,\n",
       "       0.68810502, 0.7167912 , 0.74435157, 0.77056816, 0.79522774,\n",
       "       0.81812467, 0.83906377, 0.85786303, 0.8743563 , 0.88839568,\n",
       "       0.89985378, 0.90862558, 0.91463008, 0.91781153, 0.91814029,\n",
       "       0.9156133 , 0.9102541 , 0.90211251, 0.89126381, 0.87780762,\n",
       "       0.86186635, 0.84358338, 0.82312087, 0.80065739, 0.77638535,\n",
       "       0.75050822, 0.72323774, 0.69479105, 0.66538783, 0.63524756,\n",
       "       0.6045868 , 0.57361676, 0.54254092, 0.51155305, 0.48083533,\n",
       "       0.45055682, 0.42087223, 0.39192095, 0.36382639, 0.33669559,\n",
       "       0.3106191 , 0.28567116, 0.26191004, 0.23937864, 0.21810527,\n",
       "       0.19810454, 0.17937843, 0.16191739, 0.14570159, 0.13070211,\n",
       "       0.11688221, 0.10419856, 0.09260247, 0.08204099, 0.07245806,\n",
       "       0.0637955 , 0.05599393, 0.04899359, 0.04273514, 0.03716024,\n",
       "       0.03221213, 0.02783606, 0.0239797 , 0.02059336, 0.01763023,\n",
       "       0.01504653, 0.01280154, 0.01085765, 0.0091803 , 0.00773794])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu, std = norm.fit(dataset['sepal width (cm)'])\n",
    "x = np.linspace(dataset['sepal width (cm)'].min(), dataset['sepal width (cm)'].max(), 100)\n",
    "Q = norm.pdf(x , mu , std)\n",
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "3feb1724",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.7661178932573"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy = -np.sum(P * np.log(Q))\n",
    "cross_entropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "bebe6c9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-10.469307025860195"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kl_divergence = np.sum(P * np.log(P / Q))\n",
    "kl_divergence"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "371c0908",
   "metadata": {},
   "source": [
    "## KL divergence function visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "828bf073",
   "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 norm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define parameters of the two Gaussian distributions\n",
    "mu1 = 0\n",
    "sigma1 = 1\n",
    "mu2 = 2\n",
    "sigma2 = 1\n",
    "\n",
    "# Define the range of the samples\n",
    "xmin = -5\n",
    "xmax = 5\n",
    "n_samples = 500\n",
    "x = np.linspace(xmin, xmax, n_samples)\n",
    "\n",
    "# Calculate the probability densities of the two distributions at each sample point\n",
    "p1 = norm.pdf(x, mu1, sigma1)\n",
    "p2 = norm.pdf(x, mu2, sigma2)\n",
    "\n",
    "# Calculate the KL divergence between the two distributions at each sample point\n",
    "kl_div = p1 * np.log(p1 / p2)\n",
    "\n",
    "# Plot the KL divergence as a function of x\n",
    "fig = plt.figure()\n",
    "plt.plot(x, kl_div, 'b-', label='KL divergence')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('KL divergence')\n",
    "plt.title('KL Divergence between Two Gaussian Distributions')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "156f1dd9",
   "metadata": {},
   "source": [
    "## P-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "19829923",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Thesehold is 0.05 to reject the null hypothisis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "b471bc41",
   "metadata": {},
   "outputs": [],
   "source": [
    "# P-value of  the hypothesis that the probatlity of getting a sepal length between 0.8 and 0.09 is special\n",
    "# Therebefore we are trying to reject the null hypthosis that that range is not special"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "196d22a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.555818622618241e-10"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a, b = 0.8, 0.9\n",
    "# Fit a normal distribution to the data\n",
    "mu, std = norm.fit(dataset['sepal length (cm)'])\n",
    "x = np.linspace(dataset['sepal length (cm)'].min(), dataset['sepal length (cm)'].max(), len(dataset))\n",
    "\n",
    "# Calculate the PDF using the fitted parameters\n",
    "pdf_fit = norm.pdf(x, mu, std)\n",
    "\n",
    "mu, std = norm.fit(dataset['sepal length (cm)'])\n",
    "random_prob = norm.cdf(b, mu, std) - norm.cdf(a, mu, std)\n",
    "random_prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "dd29a134",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f9ef022b20>]"
      ]
     },
     "execution_count": 59,
     "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": [
    "plt.figure()\n",
    "plt.plot(x, pdf_fit, label='Fitted normal distribution')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "8adf06e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.953554233466662e-10"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob_a_or_rarer = 1 - stats.norm.sf(a, mu, std)\n",
    "prob_b_or_rarer = 1 - stats.norm.sf(b, mu, std)\n",
    "prob_a_or_rarer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "1c3d4aeb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0509372261324756e-09"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob_b_or_rarer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "d0ee8e82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.101874511740966e-09"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value = random_prob + prob_a_or_rarer + prob_b_or_rarer\n",
    "p_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "2c9a5ae5",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.848363028320532e-120"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_stat, p_val = ttest_1samp(dataset['sepal length (cm)'], 0.8)\n",
    "p_val"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "128d93b2",
   "metadata": {},
   "source": [
    "## Naive Bayees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "89e02fde",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "# Load the Iris dataset\n",
    "iris = load_iris()\n",
    "\n",
    "# Extract the features and target classes\n",
    "X = iris.data[: , 0].reshape(-1, 1)\n",
    "y = iris.target\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "7d76101a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of the Gaussian Naive Bayes classifier on the Iris dataset: 86.67%\n"
     ]
    }
   ],
   "source": [
    "# Split the data into training and testing sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
    "\n",
    "# Create a Gaussian Naive Bayes classifier and train it on the training data\n",
    "model = GaussianNB()\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "# Use the model to predict the classes of the test data\n",
    "y_pred = model.predict(X_test)\n",
    "\n",
    "# Compute the accuracy of the model on the test data\n",
    "accuracy = accuracy_score(y_test, y_pred)\n",
    "\n",
    "print(\"Accuracy of the Gaussian Naive Bayes classifier on the Iris dataset: {:.2f}%\".format(accuracy * 100))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c73cdb0",
   "metadata": {},
   "source": [
    "## Gradient descent "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "91c55a20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "import sympy as sp\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "def function(x):\n",
    "    return x**4+2*x**3+3*x**2+2*x+1\n",
    "\n",
    "x = sp.Symbol('x')\n",
    "y = function(x)\n",
    "y_prime = sp.diff(y , x)\n",
    "y_prime = sp.lambdify(x, y_prime)\n",
    "y_prime(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "0ea5630c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1$"
      ],
      "text/plain": [
       "x**4 + 2*x**3 + 3*x**2 + 2*x + 1"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "75002c04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 9$"
      ],
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.subs(x, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "96012e3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  message: Optimization terminated successfully.\n",
      "  success: True\n",
      "   status: 0\n",
      "      fun: 0.5625\n",
      "        x: [-5.000e-01]\n",
      "      nit: 18\n",
      "      jac: [ 1.482e-08]\n",
      " hess_inv: [[ 3.333e-01]]\n",
      "     nfev: 19\n",
      "     njev: 19\n"
     ]
    }
   ],
   "source": [
    "x0 = 20\n",
    "res = minimize(function, x0, jac=y_prime)\n",
    "\n",
    "print(res)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "aa630d05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.48156385e-08])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_prime(res[\"x\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "d1f543ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-18"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "import sympy as sp\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "def function(x):\n",
    "    return -(x**4+2*x**3+3*x**2+2*x+1)\n",
    "\n",
    "x = sp.Symbol('x')\n",
    "y = function(x)\n",
    "y_prime = sp.diff(y , x)\n",
    "y_prime = sp.lambdify(x, y_prime)\n",
    "y_prime(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "94b613e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "#To maximize we simply negate our function meaning it will try to find the minimum values in the negation of our function\n",
    "#Since the negation will reflect the function on the y-axis , minimum becomes maximum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "c6092e56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.44598759e+10])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 500\n",
    "maxi = minimize(function , x0 , jac = y_prime)\n",
    "y_prime(maxi[\"x\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "e0b16283",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_prime = sp.diff(y , x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "668bc7e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 4 x^{3} - 6 x^{2} - 6 x - 2$"
      ],
      "text/plain": [
       "-4*x**3 - 6*x**2 - 6*x - 2"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_prime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5a226190",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}