{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2ac48ee6",
   "metadata": {},
   "source": [
    "# Lesson 13 activity: probability distributions - Solution\n",
    "\n",
    "## Learning objectives\n",
    "\n",
    "This activity will help you to:\n",
    "\n",
    "1. Understand and apply binomial distributions to model discrete events\n",
    "2. Demonstrate the Central Limit Theorem through sampling distributions\n",
    "3. Visualize theoretical and empirical probability distributions\n",
    "4. Connect statistical theory to real-world data analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0819d4c1",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "Import the required libraries and load the weather dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ab75cb13",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "891fc841",
   "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>weather_condition</th>\n",
       "      <th>wind_strength</th>\n",
       "      <th>temperature_c</th>\n",
       "      <th>rainfall_inches</th>\n",
       "      <th>humidity_percent</th>\n",
       "      <th>pressure_hpa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>8.2</td>\n",
       "      <td>0.13</td>\n",
       "      <td>48.8</td>\n",
       "      <td>1016.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Snowy</td>\n",
       "      <td>Gale</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.29</td>\n",
       "      <td>89.6</td>\n",
       "      <td>1009.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Rainy</td>\n",
       "      <td>Strong Wind</td>\n",
       "      <td>7.3</td>\n",
       "      <td>0.01</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1003.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Cloudy</td>\n",
       "      <td>Light Breeze</td>\n",
       "      <td>21.6</td>\n",
       "      <td>0.62</td>\n",
       "      <td>49.3</td>\n",
       "      <td>1006.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Sunny</td>\n",
       "      <td>Calm</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1.09</td>\n",
       "      <td>38.6</td>\n",
       "      <td>1016.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  weather_condition wind_strength  temperature_c  rainfall_inches  \\\n",
       "0             Sunny  Light Breeze            8.2             0.13   \n",
       "1             Snowy          Gale            1.6             0.29   \n",
       "2             Rainy   Strong Wind            7.3             0.01   \n",
       "3            Cloudy  Light Breeze           21.6             0.62   \n",
       "4             Sunny          Calm           12.0             1.09   \n",
       "\n",
       "   humidity_percent  pressure_hpa  \n",
       "0              48.8        1016.5  \n",
       "1              89.6        1009.4  \n",
       "2             100.0        1003.3  \n",
       "3              49.3        1006.9  \n",
       "4              38.6        1016.0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the weather dataset\n",
    "url = 'https://gperdrizet.github.io/FSA_devops/assets/data/unit2/weather.csv'\n",
    "df = pd.read_csv(url)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "080e1009",
   "metadata": {},
   "source": [
    "## Exercise 1: binomial distribution - modeling rainy days\n",
    "\n",
    "**Objective**: Understand and visualize binomial distributions using real weather data.\n",
    "\n",
    "The binomial distribution models the number of successes in a fixed number of independent trials. In weather forecasting, we can use it to model the probability of rainy days over a period of time.\n",
    "\n",
    "**Tasks**:\n",
    "\n",
    "1. **Calculate the probability of rain**:\n",
    "   - Count how many days in the dataset have `rainfall_inches > 0`\n",
    "   - Calculate the proportion of rainy days (this is your probability `p`)\n",
    "   - Print this probability with an interpretation (e.g., \"Based on our data, there's a X% chance of rain on any given day\")\n",
    "\n",
    "2. **Create a theoretical binomial distribution**:\n",
    "   - Assume you're looking at a 30-day period (like a month)\n",
    "   - Using the probability from step 1, calculate the theoretical probability of getting exactly k rainy days for k = 0, 1, 2, ..., 30\n",
    "   - Use `scipy.stats.binom.pmf()`\n",
    "\n",
    "3. **Visualize the distribution**:\n",
    "   - Create a bar plot showing the probability of each possible number of rainy days (0 to 30)\n",
    "   - Add a vertical line showing the expected value (mean = n × p)\n",
    "   - Label the axes appropriately\n",
    "   - Include a title with the probability of rain\n",
    "\n",
    "4. **Interpret** your findings:\n",
    "   - What is the most likely number of rainy days in a 30-day period?\n",
    "   - What is the expected (mean) number of rainy days?\n",
    "   - What's the probability of having 15 or more rainy days in a month?\n",
    "   - How does this distribution help weather forecasters make predictions?\n",
    "   - **Bonus**: Calculate the standard deviation and explain what it tells you about the variability in monthly rainfall patterns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0fa8e75",
   "metadata": {},
   "source": [
    "### Probability of rain calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "996e854d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Based on our data, there's a 19.5% chance of rain on any given day\n"
     ]
    }
   ],
   "source": [
    "rainy_days = len(df[df['weather_condition'] == 'Rainy'])\n",
    "total_days = len(df)\n",
    "p_rain = rainy_days / total_days\n",
    "\n",
    "print(f\"Based on our data, there's a {p_rain*100:.1f}% chance of rain on any given day\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32786f54",
   "metadata": {},
   "source": [
    "### Binomial distribution calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "58ffa8be",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2. Create theoretical binomial distribution\n",
    "n_days = 30\n",
    "k_values = np.arange(0, n_days + 1)\n",
    "probabilities = stats.binom.pmf(k_values, n_days, p_rain)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22f972af",
   "metadata": {},
   "source": [
    "### Binomial distribution plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bc16b9bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
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XF6hUKly7dk1jcGpWVhZycnIqHFRbF77//nsUFRXhu+++02hBOHr06FM5Xl5eHvbu3QtnZ+cyA3G1OTo6Ytq0aZg2bRqys7PRpUsXLFu2DAMHDgRQt3/ppqenl2mp+f333wH8O9tK3aLy+KwrAGVa+GoSm/rfNiUlpcy6q1evwtbWtkzLVm21bdsW33777RPtY+bMmWLLRWV8fHyqfF4W8KiF5cGDB+L3Tp064fPPP8eVK1c0WqrUDxjt1KlTjWNW0/5jRhAEXL9+Xew+BIBVq1Zh8eLFVe7LxcVFbHlq2rQpmjRpgnPnzpWpd+bMmSeKuSKNGzfW6Ao8fPgwmjVrhrZt21a63R9//AEAaNKkSZl1N27cqPL/SXp2mCBRvVRSUoKffvoJcrm8Tn6gDBo0CPPnz0dUVJTG02zVD1McPHjwEx+jIupWA+1Wgujo6Do/1sOHD/Hmm2/i/v37+PDDDyttkcnLy9Po2rOzs4OTk5NGN4aZmZnGL9cnUVpaik8++UQcB6Z+snCTJk3g6ekJAGjZsiUA4Pjx4+IvPaVSiU8//bTM/qobm6OjIzp16oStW7ciLCwMVlZWAB61sv3000/VnilZHd7e3vj888/xxx9/1LgbSa02Y5Dy8/MhkUjKjGv59ttv8ffff2t0Xw8bNgwhISH4+OOPsWHDBgCP7s3NmzejadOm6NmzZ63iBoCvvvoKYWFhYtfu7t27kZGRofFU8dqMQQIePQhz69atuHXrlthKExcXh99//11sjQUe/exITU2FpaWl2PL0pHbu3ImzZ89i1apV4mzV3NxcGBkZabRcCYKADz74AADg5+dXZj9JSUkYO3ZsncRET44JEtUL//3vf3H16lUAQHZ2NmJiYsRpylWN+agODw8PBAYG4tNPP0VOTg58fHxw5swZbN26FcOHD9cYoF3XBgwYALlcjqFDh2LKlCnIy8sTn3BcXpdBdf3111/4+uuvATxqNbp8+bL4JO3Zs2drDIjW9s8//6BZs2Z49dVX4eHhgUaNGuHw4cM4e/YsVq9eLdbz9PTEzp07ERoaim7duqFRo0YYOnRoreJ1cnLC8uXLcfPmTbzwwgvYuXMnkpOT8emnn4pTojt06IAePXogLCwM9+/fh7W1NXbs2CG2Jj6uJrGtXLkSAwcOhLe3NyZOnChO87e0tKzT99MNHjwYBgYGOHz4MCZPnlyrfdRmDNK1a9fg6+uLMWPGoG3btpBKpTh37hy+/vprKBQKzJw5U6zbrFkzzJo1CytXrkRJSQm6deuGffv24eeff8a2bds0ugHVT7qPjo7G+PHjq4zD2toavXr1QlBQELKyshAVFYVWrVppvJeuNmOQAGD+/PnYtWsX+vbti5kzZyIvLw8rV66Em5sbgoKCxHp//fUX2rVrh8DAQI1nYR0/fhzHjx8HANy5cwf5+fliMtO7d2/07t1brLdkyRIMGDAANjY2OHXqFKKjo+Hv769xHZOSkhAQEICAgAC0atUKDx8+xN69e3HixAlMnjwZXbp00Yg/MTER9+/fx7Bhw2p87vSU6Gj2HFG1lDfN39jYWOjUqZOwadMmjSnRglDxNP87d+6Uu9/Hp4uXlJQIixcvFlxdXQVDQ0PB2dlZCAsLKzM9uKIp9ADKTItXTylfuXJlmZge99133wnu7u6CsbGxoFAohOXLlwtbtmwpE2NNpvmrr5dEIhEsLCyEDh06CJMmTRJOnz5d7jaPX7uioiJhzpw5goeHh2Bubi6YmZkJHh4eZZ6+nZeXJ7z++uuClZWVxtRr9bTuXbt2lTlORdP8O3ToIJw7d07w9vYWjI2NBRcXF2HDhg1ltk9NTRV8fX0FIyMjwd7eXpg/f774xOTH91lRbOVN8xcEQTh8+LDw4osvCiYmJoKFhYUwdOhQ4fLlyxp1anI/VeTll18W+vfvX+722k+ML+9a1cadO3eEyZMnC23bthXMzMwEuVwutG7dWpg1a1aZcxEEQVAqlcKHH34ouLi4CHK5XOjQoYPw9ddfl6m3fv16AYAQGxtb6fHV57F9+3YhLCxMsLOzE0xMTITBgwdrPBbjSV28eFEYMGCAYGpqKlhZWQljx44VMjMzNeqo//0DAwM1yit7vMDjP1OuX78uDBgwQLC1tRWMjIyEtm3bChEREUJRUZHG/v744w9h1KhRgkKhEIyNjQVTU1PB09NT2Lx5c5mfW4IgCHPnzhWaN29e7jrSDb6LjYjoGfr555/Rp08fXL16tcysrvpm9OjRuHnzJs6cOVNpvfj4ePTt2xe7du3Cq6+++oyiqz+KioqgUCgwb948jVYo0i3OYiMieoZeeuklDBgwACtWrNB1KE9EEATEx8eL3VBUe9HR0TA0NCzzfC3SLbYgERHRU8UWJKqP2IJEREREpIUtSERERERa2IJEREREpIUJEhEREZEWPiiyllQqFdLT02Fubs4XCxIREdUTgiDgn3/+gZOTk/jk8/IwQaql9PT0Mm9uJyIiovrh1q1baNasWYXrmSDVkvpdQrdu3aqTV12QDuTnA+o3k6enA3X0QlIiItJfubm5cHZ2Fn+PV4QJUi2pu9UsLCyYINVXj71TChYWTJCIiBqQqobHcJA2ERERkRYmSERERERa2MVGDZeBARAY+O8yERHR//C3AjVcRkbAl1/qOgoiqoBSqURJSYmuw6B6xtDQELLHx5jWEhMkIiLSK4IgIDMzEzk5OboOheopKysrODg4PNFzCpkgUcMlCEBBwaNlU1OAD/wk0gvq5MjOzg6mpqZ8GC9VmyAIKCgoQHZ2NgDA0dGx1vtigkQNV0EB0KjRo+W8PE7zJ9IDSqVSTI5sbGx0HQ7VQyYmJgCA7Oxs2NnZ1bq7jbPYiIhIb6jHHJmamuo4EqrP1PfPk4xhY4JERER6h91q9CTq4v5hgkRERESkhQkSERER1VifPn0wa9YsXYfx1DBBIiIiekLjx4+HRCIp8/H399d1aBp0ndSUd52qukZKpRLvv/8+XF1dYWJigpYtW2Lp0qUQBOGpxspZbERERHXA398f0dHRGmVGRkY6ikZ/aV+nqq7R8uXLsWnTJmzduhUdOnTAuXPnEBQUBEtLS8yYMeOpxckWJGq4ZDLg1VcffergqatE1LAZGRnBwcFB49O4cWMAQHx8PORyOX7++Wex/ooVK2BnZ4esrCwAj1p3goODERwcDEtLS9ja2uL999/XaCkpKirCu+++i6ZNm8LMzAxeXl6Ij4/XiOPEiRPo06cPTE1N0bhxY/j5+eHvv//G+PHjcezYMaxbt05svbl58yYA4OLFixg4cCAaNWoEe3t7vPnmm7h79664z/z8fIwbNw6NGjWCo6MjVq9eXWfXSX2NKnLy5EkMGzYMgwcPhkKhwKuvvooBAwbgzJkztY6hOpggUcNlbAzs2vXoY2ys62iIqCr5+RV/CgurX/fhw6rr1jF119abb76JBw8e4Pz583j//ffx+eefw97eXqy3detWGBgY4MyZM1i3bh3WrFmDzz//XFwfHByMhIQE7NixAxcuXMCoUaPg7++Pa9euAQCSk5PRv39/tG/fHgkJCfjll18wdOhQKJVKrFu3Dt7e3pg0aRIyMjKQkZEBZ2dn5OTkoF+/fujcuTPOnTuH2NhYZGVlYfTo0eJx58yZg2PHjmH//v346aefEB8fj6SkJI1zXLRoERQKRZXXIj4+HnZ2dmjTpg2mTp2Ke/fuVVq/Z8+eiIuLw++//w4A+PXXX/HLL79g4MCBVR7rSbCLjRocxbwDNap/M3LwU4qEiGpE/WDX8gwaBBx47P9tO7t/n5SvzccHeLzVRaEAHmstAfDoSfs19MMPP6CRVozz58/H/PnzAQAffPABDh06hMmTJ+PixYsIDAzEyy+/rFHf2dkZa9euhUQiQZs2bfDbb79h7dq1mDRpEtLS0hAdHY20tDQ4OTkBAN59913ExsYiOjoaH374IVasWIGuXbvi448/FvfZoUMHcVkul8PU1BQODg5i2YYNG9C5c2d8+OGHYtmWLVvg7OyM33//HU5OTvjiiy/w9ddfo3///gAeJXLNmjXTiN3W1hYtW7as9Br5+/tjxIgRcHV1RWpqKubPn4+BAwciISGhwgc6zps3D7m5uWjbti1kMhmUSiWWLVuGsWPHVnqsJ8UEiYiIqA707dsXmzZt0iiztrYWl+VyObZt2wZ3d3e4uLhg7dq1ZfbRo0cPjWf4eHt7Y/Xq1VAqlfjtt9+gVCrxwgsvaGxTVFQkPnU8OTkZo0aNqlHcv/76K44ePVomuQOA1NRUPHz4EMXFxfDy8tI4rzZt2mjUVXcPVua1114Tl93c3ODu7o6WLVsiPj5eTL60ffPNN9i2bRtiYmLQoUMHJCcnY9asWXByckJgYGBNTrVGmCBRvVWTlqDyWoFMigtxZe2rAIB2IbvxUM5uNiK9lpdX8Trt1of/vYurXFKt0SX/G4fzpMzMzNCqVatK65w8eRIAcP/+fdy/fx9mNXjFUV5eHmQyGRITE8u0tqiTG/VrNmoiLy8PQ4cOxfLly8usc3R0xPXr12u8z+pq0aIFbG1tcf369QoTpDlz5mDevHlicuXm5oY///wTERERTzVB0vkYpI0bN0KhUMDY2BheXl6VDrq6dOkSRo4cCYVCAYlEgqioqDJ11Ou0P9OnTxfr9OnTp8z6t99++2mcHhER1RUzs4o/2uMIK6urnUSUV+cpSE1NRUhICD777DN4eXkhMDAQKpVKo87p06c1vp86dQqtW7eGTCZD586doVQqkZ2djVatWml81F1m7u7uiIuLqzAGuVwOpVKpUdalSxdcunQJCoWizH7NzMzQsmVLGBoaasT2999/i2OCnsTt27dx7969Sl8qW1BQAKlWUiuTycpcu7qm0wRp586dCA0NRXh4OJKSkuDh4QE/Pz/xLbzaCgoK0KJFC0RGRmr0nz7u7Nmz4uCzjIwMHDp0CADKNDk+PkgtIyMDK1asqNuTIyKiBqWoqAiZmZkaH/VMMKVSiTfeeAN+fn4ICgpCdHQ0Lly4UGY2WFpaGkJDQ5GSkoLt27dj/fr1mDlzJgDghRdewNixYzFu3Djs2bMHN27cwJkzZxAREYED/xt/FRYWhrNnz2LatGm4cOECrl69ik2bNolxKBQKnD59Gjdv3sTdu3ehUqkwffp03L9/HwEBATh79ixSU1Nx8OBBBAUFQalUolGjRpg4cSLmzJmDI0eO4OLFixg/fnyZpGXDhg0VtgIBj1qq5syZg1OnTuHmzZuIi4vDsGHD0KpVK/j5+Yn1+vfvjw0bNojfhw4dimXLluHAgQO4efMm9u7dizVr1uCVV155gn+tqum0i23NmjWYNGkSgoKCAACbN2/GgQMHsGXLFsybN69M/W7duqFbt24AUO56AGjSpInG98jISLRs2RI+Pj4a5dqD1IiIiJ5EbGxsmZaQNm3a4OrVq1i2bBn+/PNP/PDDDwAedV19+umnCAgIwIABA+Dh4QEAGDduHB4+fIju3btDJpNh5syZmDx5sri/6OhofPDBB5g9ezb++usv2NraokePHhgyZAiAR0nUTz/9hPnz56N79+4wMTGBl5cXAgICADwa1B0YGIj27dvj4cOHuHHjBhQKBU6cOIG5c+diwIABKCoqgouLC/z9/cUkaOXKlWJXnLm5OWbPno0HDx5onOvdu3eRmppa4fWRyWS4cOECtm7dipycHDg5OWHAgAFYunSpxrOQUlNTNR4xsH79erz//vuYNm0asrOz4eTkhClTpmDhwoU1/jeqCYnwtB9FWYHi4mKYmppi9+7dGD58uFgeGBiInJwc7N+/v9LtFQoFZs2aVekTQYuLi+Hk5ITQ0FBxFgHwqIvt0qVLEAQBDg4OGDp0KN5///1K3x5dVFSEoqIi8Xtubi6cnZ3x4MEDWFhYVH3CVOdqOwZJvV11xyBxFhvRs1NYWIgbN27A1dUVxg3s8Rt9+vRBp06dyh0+QjVT2X2Um5sLS0vLKn9/66wF6e7du1AqlRrPfwAAe3t7XL16tU6OsW/fPuTk5GD8+PEa5a+//jpcXFzg5OSECxcuYO7cuUhJScGePXsq3FdERAQWL15cJ3ERERGRfnuuZ7F98cUXGDhwoPi8CLXHmyvd3Nzg6OiI/v37IzU1tcJnOISFhSE0NFT8rm5BIiIiouePzhIkW1tbyGQy8RHrallZWXUyNujPP//E4cOHK20VUlM/2+H69esVJkhGRkZ8p85zRiWV4kiLruIyEZEuab8yhHRLZ78V5HI5PD09NaYjqlQqxMXFwdvb+4n3Hx0dDTs7OwweXPX4keTkZACodJohPX+KDOSYMGoRJoxahCIDua7DISIiPaLTLrbQ0FAEBgaia9eu6N69O6KiopCfny/Oahs3bhyaNm2KiIgIAI8GXV++fFlc/uuvv5CcnIxGjRppPJxLpVIhOjoagYGBMDDQPMXU1FTExMRg0KBBsLGxwYULFxASEoLevXvD3d39GZ05ERFVRkfzh+g5URf3j04TpDFjxuDOnTtYuHAhMjMz0alTJ8TGxooDt9PS0jSes5Ceno7OnTuL31etWoVVq1bBx8dHo2ny8OHDSEtLw4QJE8ocUy6X4/Dhw2Iy5uzsjJEjR2LBggVP70SJiKhaDA0NATx67l1tngpNBDy6f4B/76fa0Nk0//quutME6empi2n+iRsevezQM3gbp/kT6YmMjAzk5OTAzs4OpqamGu8mI6qMIAgoKChAdnY2rKysyh06o/fT/In0gWlJUdWViOiZUk/UqeitCkRVsbKyeuIJX0yQiIhIr0gkEjg6OsLOzg4lJSW6DofqGUNDwzIv860NJkhERKSXZDJZnfyiI6oNPvyFiIiISAsTJCIiIiItTJCIiIiItHAMEjVYKokEp5w7istERERqTJCowSoyNMJrr0fqOgwiItJD7GIjIiIi0sIEiYiIiEgLEyRqsEyKC5H40etI/Oh1mBQX6jocIiLSIxyDRA2azcNcXYdARER6iC1IRERERFqYIBERERFpYYJEREREpIUJEhEREZEWJkhEREREWjiLjRoslUSCXx1ai8tERERqTJCowSoyNMKwwLW6DoOIiPQQu9iIiIiItDBBIiIiItLCBIkaLOOSQvyyaQJ+2TQBxiV81QgREf2LY5CowZIIQLPcbHGZiIhIjS1IRERERFqYIBERERFpYYJEREREpIUJEhEREZEWJkhEREREWjiLjRosQQL8btNcXCYiIlJjgkQNVqGhMQa89bGuwyAiIj3ELjYiIiIiLUyQiIiIiLQwQaIGy7ikED99Pg0/fT6NrxohIiINHINEDZZEAF64lyYuExERqbEFiYiIiEgLEyQiIiIiLUyQiIiIiLQwQSIiIiLSovMEaePGjVAoFDA2NoaXlxfOnDlTYd1Lly5h5MiRUCgUkEgkiIqKKlNn0aJFkEgkGp+2bdtq1CksLMT06dNhY2ODRo0aYeTIkcjKyqrrUyMiIqJ6SqcJ0s6dOxEaGorw8HAkJSXBw8MDfn5+yM7OLrd+QUEBWrRogcjISDg4OFS43w4dOiAjI0P8/PLLLxrrQ0JC8P3332PXrl04duwY0tPTMWLEiDo9N9J/ggS4bWGH2xZ2fNUIERFp0Ok0/zVr1mDSpEkICgoCAGzevBkHDhzAli1bMG/evDL1u3Xrhm7dugFAuevVDAwMKkygHjx4gC+++AIxMTHo168fACA6Ohrt2rXDqVOn0KNHjyc9LaonCg2N0WvqFl2HQUREekhnLUjFxcVITEyEr6/vv8FIpfD19UVCQsIT7fvatWtwcnJCixYtMHbsWKSlpYnrEhMTUVJSonHctm3bonnz5k98XCIiIno+6CxBunv3LpRKJezt7TXK7e3tkZmZWev9enl54csvv0RsbCw2bdqEGzdu4KWXXsI///wDAMjMzIRcLoeVlVWNjltUVITc3FyNDxERET2fnrsnaQ8cOFBcdnd3h5eXF1xcXPDNN99g4sSJtd5vREQEFi9eXBchkp4wKinCNzGPumpHvx6JIkMjHUdERET6QmctSLa2tpDJZGVmj2VlZVU6ALumrKys8MILL+D69esAAAcHBxQXFyMnJ6dGxw0LC8ODBw/Ez61bt+osRtINqSDAI/MaPDKvQSrwXSNERPQvnSVIcrkcnp6eiIuLE8tUKhXi4uLg7e1dZ8fJy8tDamoqHB0dAQCenp4wNDTUOG5KSgrS0tIqPa6RkREsLCw0PkRERPR80mkXW2hoKAIDA9G1a1d0794dUVFRyM/PF2e1jRs3Dk2bNkVERASARwO7L1++LC7/9ddfSE5ORqNGjdCqVSsAwLvvvouhQ4fCxcUF6enpCA8Ph0wmQ0BAAADA0tISEydORGhoKKytrWFhYYF33nkH3t7enMFGVVLMO1Cj+jcjBz+lSIiI6GnSaYI0ZswY3LlzBwsXLkRmZiY6deqE2NhYceB2WloapNJ/G7nS09PRuXNn8fuqVauwatUq+Pj4ID4+HgBw+/ZtBAQE4N69e2jSpAl69eqFU6dOoUmTJuJ2a9euhVQqxciRI1FUVAQ/Pz98/PHHz+akiYiISO/pfJB2cHAwgoODy12nTnrUFAoFhCrGiuzYsaPKYxobG2Pjxo3YuHFjteMkIiKihkPnrxohIiIi0jc6b0Ei0qV7JhxsT0REZTFBogbrodwYnjNidB0GERHpIXaxEREREWlhgkRERESkhQkSNVhGJUXYETMPO2LmwaikSNfhEBGRHuEYJGqwpIKAHrcuistERERqbEEiIiIi0sIEiYiIiEgLEyQiIiIiLRyDRDrFl78SEZE+YgsSERERkRa2IFGDVmBopOsQiIhIDzFBogbrodwY7UO/1XUYRESkh9jFRkRERKSFCRIRERGRFnaxUYNlVFqMTXs/BABMfWU+igzkOo6IiIj0BRMkarCkKhX6/XFOXCYiIlJjFxsRERGRFiZIRERERFqYIBERERFpYYJEREREpIUJEhEREZEWJkhEREREWjjNnxqsh3JjKOb+oOswiIhID7EFiYiIiEgLEyQiIiIiLexiowbLqLQYa35YDQAIHTKbrxohIiIRW5CowZKqVBiccgKDU07wVSNERKSBCRIRERGRFiZIRERERFqYIBERERFpYYJEREREpIUJEhEREZEWJkhEREREWvgcJGqwHhoaoV3IbnGZiIhIjQkSNVwSCR7KjXUdBRER6SF2sRERERFpYQsSNVjy0hJ8eHADAGC+XzCKDQx1HBEREekLnbcgbdy4EQqFAsbGxvDy8sKZM2cqrHvp0iWMHDkSCoUCEokEUVFRZepERESgW7duMDc3h52dHYYPH46UlBSNOn369IFEItH4vP3223V9aqTnZColXr0Yh1cvxkGmUuo6HCIi0iM6TZB27tyJ0NBQhIeHIykpCR4eHvDz80N2dna59QsKCtCiRQtERkbCwcGh3DrHjh3D9OnTcerUKRw6dAglJSUYMGAA8vPzNepNmjQJGRkZ4mfFihV1fn5ERERUP+m0i23NmjWYNGkSgoKCAACbN2/GgQMHsGXLFsybN69M/W7duqFbt24AUO56AIiNjdX4/uWXX8LOzg6JiYno3bu3WG5qalphkkVEREQNm85akIqLi5GYmAhfX99/g5FK4evri4SEhDo7zoMHDwAA1tbWGuXbtm2Dra0tOnbsiLCwMBQUFFS6n6KiIuTm5mp8iIiI6Pmksxaku3fvQqlUwt7eXqPc3t4eV69erZNjqFQqzJo1Cy+++CI6duwolr/++utwcXGBk5MTLly4gLlz5yIlJQV79uypcF8RERFYvHhxncRFRERE+u25nsU2ffp0XLx4Eb/88otG+eTJk8VlNzc3ODo6on///khNTUXLli3L3VdYWBhCQ0PF77m5uXB2dn46gRMREZFO6SxBsrW1hUwmQ1ZWlkZ5VlZWnYwNCg4Oxg8//IDjx4+jWbNmldb18vICAFy/fr3CBMnIyAhGRnzaMhERUUOgszFIcrkcnp6eiIuLE8tUKhXi4uLg7e1d6/0KgoDg4GDs3bsXR44cgaura5XbJCcnAwAcHR1rfVyqfx4aGqHLO9vQ5Z1tfNUIERFp0GkXW2hoKAIDA9G1a1d0794dUVFRyM/PF2e1jRs3Dk2bNkVERASARwO7L1++LC7/9ddfSE5ORqNGjdCqVSsAj7rVYmJisH//fpibmyMzMxMAYGlpCRMTE6SmpiImJgaDBg2CjY0NLly4gJCQEPTu3Rvu7u46uAqkMxIJ7pta6joKIiLSQzpNkMaMGYM7d+5g4cKFyMzMRKdOnRAbGysO3E5LS4NU+m8jV3p6Ojp37ix+X7VqFVatWgUfHx/Ex8cDADZt2gTg0cMgHxcdHY3x48dDLpfj8OHDYjLm7OyMkSNHYsGCBU/3ZImIiKje0Pkg7eDgYAQHB5e7Tp30qCkUCgiCUOn+qlrv7OyMY8eO1ShGej7JS0uw4MjnAIAP+r3FV40QEZFI568aIdIVmUqJcecPYNz5A3zVCBERaWCCRERERKSFCRIRERGRFiZIRERERFqYIBERERFpYYJEREREpIUJEhEREZEWnT8HiUhXCg3l6PX2F+IyERGRGhMkarAEiRS3Le11HQYREekhdrERERERaWELEjVYhsoSvHv8/wAAq3q/iRIZXzVCRESPsAWJGiwDpRJTzuzBlDN7YKDkq0aIiOhfTJCIiIiItDBBIiIiItLCBImIiIhICxMkIiIiIi1MkIiIiIi0MEEiIiIi0sLnIFGDVWgox38mbBSXiYiI1JggUYMlSKS41sRF12EQEZEeqlUX29GjR+s6DiIiIiK9UasEyd/fHy1btsQHH3yAW7du1XVMRM+EobIEs37Zhlm/bIOhskTX4RARkR6pVYL0119/ITg4GLt370aLFi3g5+eHb775BsXFxXUdH9FTY6BUYtaJ7Zh1YjtfNUJERBpqlSDZ2toiJCQEycnJOH36NF544QVMmzYNTk5OmDFjBn799de6jpOIiIjomXniaf5dunRBWFgYgoODkZeXhy1btsDT0xMvvfQSLl26VBcxEhERET1TtU6QSkpKsHv3bgwaNAguLi44ePAgNmzYgKysLFy/fh0uLi4YNWpUXcZKRERE9EzUapr/O++8g+3bt0MQBLz55ptYsWIFOnbsKK43MzPDqlWr4OTkVGeBEhERET0rtUqQLl++jPXr12PEiBEwMjIqt46trS0fB0BERET1Uq262MLDwzFq1KgyyVFpaSmOHz8OADAwMICPj8+TR0hERET0jNWqBalv377IyMiAnZ2dRvmDBw/Qt29fKDllmuqBIgNDvDxujbhMRESkVqsESRAESCSSMuX37t2DmZnZEwdF9CyopDJccHxB12EQEZEeqlGCNGLECACARCLB+PHjNbrYlEolLly4gJ49e9ZthERERETPWI0SJEtLSwCPWpDMzc1hYmIirpPL5ejRowcmTZpUtxESPSWGyhIEnfsOABDd9WWUyNjNRkREj9QoQYqOjgYAKBQKvPvuu+xOo3rNQKnE/PhH9/T/dR7MBImIiES1GoMUHh5e13EQERER6Y1qJ0hdunRBXFwcGjdujM6dO5c7SFstKSmpToIjIiIi0oVqJ0jDhg0TB2UPHz78acVD9FxSzDtQo/o3Iwc/pUiIiKg6qp0gPd6txi42IiIiep7V+mW1dWXjxo1QKBQwNjaGl5cXzpw5U2HdS5cuYeTIkVAoFJBIJIiKiqrVPgsLCzF9+nTY2NigUaNGGDlyJLKysurytIiIiKgeq3aC1LhxY1hbW1frU107d+5EaGgowsPDkZSUBA8PD/j5+SE7O7vc+gUFBWjRogUiIyPh4OBQ632GhITg+++/x65du3Ds2DGkp6eLz3giIiIiqnYXW0WtNU9izZo1mDRpEoKCggAAmzdvxoEDB7BlyxbMmzevTP1u3bqhW7duAFDu+urs88GDB/jiiy8QExODfv36AXj0+IJ27drh1KlT6NGjR52fJ+mnIgNDvBbwobhMRESkVu0EKTAwsE4PXFxcjMTERISFhYllUqkUvr6+SEhIeGr7TExMRElJCXx9fcU6bdu2RfPmzZGQkFBhglRUVISioiLxe25ubq1iJP2hkspwqrm7rsMgIiI9VO0utscTgtzc3Eo/1XH37l0olUrY29trlNvb2yMzM7O6YdV4n5mZmZDL5bCysqrRcSMiImBpaSl+nJ2daxUjERER6b9qtyA1btwYGRkZsLOzg5WVVbnPQVK/xFapVNZpkPogLCwMoaGh4vfc3FwmSfWcgbIUAb/GAgC2e/ijVFar56YSEdFzqNq/EY4cOSIOwD569OgTH9jW1hYymazM7LGsrKwKB2DXxT4dHBxQXFyMnJwcjVakqo5rZGSk8XJeqv8MlaVYemgzAGB3R18mSEREJKr2bwQfH59yl2tLLpfD09MTcXFx4oMnVSoV4uLiEBwc/NT26enpCUNDQ8TFxWHkyJEAgJSUFKSlpcHb2/uJz4uIiIjqv1r/yfz333/jiy++wJUrVwAA7du3R1BQUI2m+YeGhiIwMBBdu3ZF9+7dERUVhfz8fHEG2rhx49C0aVNEREQAeDQI+/Lly+LyX3/9heTkZDRq1AitWrWq1j4tLS0xceJEhIaGwtraGhYWFnjnnXfg7e3NGWxEREQEoJYJ0vHjxzF06FBYWlqia9euAICPPvoIS5Yswffff4/evXtXaz9jxozBnTt3sHDhQmRmZqJTp06IjY0VB1mnpaVBKv13HHl6ejo6d+4sfl+1ahVWrVoFHx8fxMfHV2ufALB27VpIpVKMHDkSRUVF8PPzw8cff1ybS0FERETPoVolSNOnT8eYMWOwadMmyGQyAIBSqcS0adMwffp0/Pbbb9XeV3BwcIVdauqkR02hUEAQhCfaJwAYGxtj48aN2LhxY7XjJCIiooajVq8auX79OmbPni0mRwAgk8kQGhqK69ev11lwRERERLpQqwSpS5cu4tijx125cgUeHh5PHBQRERGRLlW7i+3ChQvi8owZMzBz5kxcv35dHNh86tQpbNy4EZGRkXUfJdFTUGxgiKBXw8VlIiIitWonSJ06dYJEItEYA/Tee++Vqff6669jzJgxdRMd0VOklMpwtGU3XYdBRER6qNoJ0o0bN55mHERERER6o9oJkouLy9OMg+iZM1CWYvjleADAvvZ9+CRtIiISPdFvhMuXLyMtLQ3FxcUa5S+//PITBUX0LBgqS7HqxygAwIE2vZggERGRqFa/Ef744w+88sor+O233zTGJalfYPs8vqyWiIiIGo5aTfOfOXMmXF1dkZ2dDVNTU1y6dAnHjx9H165dyzzckYiIiKi+qVULUkJCAo4cOQJbW1tIpVJIpVL06tULERERmDFjBs6fP1/XcRIRERE9M7VqQVIqlTA3NwcA2NraIj09HcCjgdwpKSl1Fx0RERGRDtSqBaljx4749ddf4erqCi8vL6xYsQJyuRyffvopWrRoUdcxEhERET1TtUqQFixYgPz8fADAkiVLMGTIELz00kuwsbHBzp076zRAIiIiometVgmSn5+fuNyqVStcvXoV9+/fR+PGjcWZbET6rtjAENOGzROXiYiI1J74wS+3bt0CADg7Oz9xMETPklIqw49te+k6DCIi0kO1GqRdWlqK999/H5aWllAoFFAoFLC0tMSCBQtQUlJS1zESERERPVO1akF65513sGfPHqxYsQLe3t4AHk39X7RoEe7du4dNmzbVaZBET4NMpYTf7wkAgIMveEMplek4IiIi0he1SpBiYmKwY8cODBw4UCxzd3eHs7MzAgICmCBRvSAvLcHH+yMBAO1CduOhnAkSERE9UqsuNiMjIygUijLlrq6ukMvlTxoTERERkU7VqgUpODgYS5cuRXR0NIyMjAAARUVFWLZsGYKDg+s0QNJ/inkHalT/ZuTgpxQJERFR3ah2gjRixAiN74cPH0azZs3g4eEBAPj1119RXFyM/v37122ERERERM9YtRMkS0tLje8jR47U+M5p/kRERPS8qHaCFB0d/TTjICIiItIbT/SgyDt37ogvp23Tpg2aNGlSJ0ERERER6VKtEqT8/Hy88847+Oqrr6BSqQAAMpkM48aNw/r162FqalqnQRI9DSUyA7w7aJa4TEREpFaraf6hoaE4duwYvv/+e+Tk5CAnJwf79+/HsWPHMHv27LqOkeipKJUZYLebL3a7+aKUCRIRET2mVr8Vvv32W+zevRt9+vQRywYNGgQTExOMHj2aD4okIiKieq1WCVJBQQHs7e3LlNvZ2aGgoOCJgyJ6FmQqJXrfSAIAHHftwleNEBGRqFZdbN7e3ggPD0dhYaFY9vDhQyxevFh8NxuRvpOXliB692JE714MeSlfskxERP+qVQtSVFQU/P39yzwo0tjYGAcPHqzTAImIiIietVolSG5ubrh27Rq2bduGq1evAgACAgIwduxYmJiY1GmARERERM9ajROkkpIStG3bFj/88AMmTZr0NGIiIiIi0qkaj0EyNDTUGHtERERE9Lyp1SDt6dOnY/ny5SgtLa3reIiIiIh0rlZjkM6ePYu4uDj89NNPcHNzg5mZmcb6PXv21ElwRERERLpQqwTJysoKI0eOrOtYiJ6pEpkB3v/P2+IyERGRWo1+K6hUKqxcuRK///47iouL0a9fPyxatIgz16heKpUZ4P+6DNF1GEREpIdqNAZp2bJlmD9/Pho1aoSmTZvio48+wvTp059WbEREREQ6UaME6auvvsLHH3+MgwcPYt++ffj++++xbds2qFSqJwpi48aNUCgUMDY2hpeXF86cOVNp/V27dqFt27YwNjaGm5sbfvzxR431Eomk3M/KlSvFOgqFosz6yMjIJzoPql+kKiV6pF1Aj7QLkKqUug6HiIj0SI0SpLS0NAwaNEj87uvrC4lEgvT09FoHsHPnToSGhiI8PBxJSUnw8PCAn58fsrOzy61/8uRJBAQEYOLEiTh//jyGDx+O4cOH4+LFi2KdjIwMjc+WLVsgkUjKjJtasmSJRr133nmn1udB9Y9RaQl2bJ+PHdvnw4ivGiEiosfUKEEqLS2FsbGxRpmhoSFKSmr/y2XNmjWYNGkSgoKC0L59e2zevBmmpqbYsmVLufXXrVsHf39/zJkzB+3atcPSpUvRpUsXbNiwQazj4OCg8dm/fz/69u2LFi1aaOzL3Nxco572bDwiIiJqmGo0SFsQBIwfPx5GRkZiWWFhId5++22N5KK60/yLi4uRmJiIsLAwsUwqlcLX1xcJCQnlbpOQkIDQ0FCNMj8/P+zbt6/c+llZWThw4AC2bt1aZl1kZCSWLl2K5s2b4/XXX0dISAgMDMq/JEVFRSgqKhK/5+bmVnV6REREVE/VKEEKDAwsU/bGG2/U+uB3796FUqmEvb29Rrm9vb34jjdtmZmZ5dbPzMwst/7WrVthbm6OESNGaJTPmDEDXbp0gbW1NU6ePImwsDBkZGRgzZo15e4nIiICixcvru6pERERUT1WowQpOjr6acXx1GzZsgVjx44t0zX4eCuUu7s75HI5pkyZgoiICI0WMrWwsDCNbXJzc+Hs7Pz0AiciIiKd0enT8WxtbSGTyZCVlaVRnpWVBQcHh3K3cXBwqHb9n3/+GSkpKdi5c2eVsXh5eaG0tBQ3b95EmzZtyqw3MjIqN3EiIiKi50+t3sVWV+RyOTw9PREXFyeWqVQqxMXFwdvbu9xtvL29NeoDwKFDh8qt/8UXX8DT0xMeHh5VxpKcnAypVAo7O7sangURERE9b3T+foXQ0FAEBgaia9eu6N69O6KiopCfn4+goCAAwLhx49C0aVNEREQAAGbOnAkfHx+sXr0agwcPxo4dO3Du3Dl8+umnGvvNzc3Frl27sHr16jLHTEhIwOnTp9G3b1+Ym5sjISEBISEheOONN9C4ceOnf9KkF0plMnzYJ0hcJiIiUtN5gjRmzBjcuXMHCxcuRGZmJjp16oTY2FhxIHZaWhqk0n8bunr27ImYmBgsWLAA8+fPR+vWrbFv3z507NhRY787duyAIAgICAgoc0wjIyPs2LEDixYtQlFREVxdXRESElJmdhw930pkhvjUi+8UJCKisnSeIAFAcHAwgoODy10XHx9fpmzUqFEYNWpUpfucPHkyJk+eXO66Ll264NSpUzWOk4iIiBoGvUiQiHRBqlKiY1YqAOCifUuopOxmIyKiR5ggUYNlVFqC77561K3aLmQ3HsqZIBER0SM6ncVGREREpI+YIBERERFpYYJEREREpIUJEhEREZEWJkhEREREWpggEREREWnhNH9qsEplMkS9GCAuExERqTFBogarRGaIqF5jdR0GERHpIXaxEREREWlhCxI1WBJBhVZ3bwEArts6Q5Dw7wUiInqECRI1WMYlxTi0ZToA9atGjHUcERER6Qv+yUxERESkhQkSERERkRYmSERERERamCARERERaWGCRERERKSFCRIRERGRFk7zpwarVCbDJ91HiMtERERqTJCowSqRGSKi7wRdh0FERHqICRKRnlPMO1Cj+jcjBz+lSIiIGg4mSNRgSQQVmubeAQD8ZdGErxohIiIREyRqsIxLivHL5okA+KoRIiLSxD+ZiYiIiLQwQSIiIiLSwgSJiIiISAsTJCIiIiItTJCIiIiItDBBIiIiItLCaf7UYCmlMnzVebC4TEREpMYEiRqsYgNDLBwwVddhEBGRHmIXGxEREZEWtiBRwyUIsH6YCwC4b2IBSCQ6DoiIiPQFEyRqsExKipC0fiwAvmqEiIg0sYuNiIiISAsTJCIiIiItTJCIiIiItOhFgrRx40YoFAoYGxvDy8sLZ86cqbT+rl270LZtWxgbG8PNzQ0//vijxvrx48dDIpFofPz9/TXq3L9/H2PHjoWFhQWsrKwwceJE5OXl1fm5ERERUf2j8wRp586dCA0NRXh4OJKSkuDh4QE/Pz9kZ2eXW//kyZMICAjAxIkTcf78eQwfPhzDhw/HxYsXNer5+/sjIyND/Gzfvl1j/dixY3Hp0iUcOnQIP/zwA44fP47Jkyc/tfMkIiKi+kPnCdKaNWswadIkBAUFoX379ti8eTNMTU2xZcuWcuuvW7cO/v7+mDNnDtq1a4elS5eiS5cu2LBhg0Y9IyMjODg4iJ/GjRuL665cuYLY2Fh8/vnn8PLyQq9evbB+/Xrs2LED6enpT/V8iYiISP/pNEEqLi5GYmIifH19xTKpVApfX18kJCSUu01CQoJGfQDw8/MrUz8+Ph52dnZo06YNpk6dinv37mnsw8rKCl27dhXLfH19IZVKcfr06XKPW1RUhNzcXI0P1W9KqQy7O/bH7o79+aoRIiLSoNPnIN29exdKpRL29vYa5fb29rh69Wq522RmZpZbPzMzU/zu7++PESNGwNXVFampqZg/fz4GDhyIhIQEyGQyZGZmws7OTmMfBgYGsLa21tjP4yIiIrB48eLanCbpqWIDQ7w7OETXYRARkR56Lh8U+dprr4nLbm5ucHd3R8uWLREfH4/+/fvXap9hYWEIDQ0Vv+fm5sLZ2fmJYyUiIiL9o9MuNltbW8hkMmRlZWmUZ2VlwcHBodxtHBwcalQfAFq0aAFbW1tcv35d3If2IPDS0lLcv3+/wv0YGRnBwsJC40P1nCDApLgQJsWFgCDoOhoiItIjOk2Q5HI5PD09ERcXJ5apVCrExcXB29u73G28vb016gPAoUOHKqwPALdv38a9e/fg6Ogo7iMnJweJiYlinSNHjkClUsHLy+tJTonqEZOSIlxZ+yqurH0VJiVFug6HiIj0iM5nsYWGhuKzzz7D1q1bceXKFUydOhX5+fkICgoCAIwbNw5hYWFi/ZkzZyI2NharV6/G1atXsWjRIpw7dw7BwcEAgLy8PMyZMwenTp3CzZs3ERcXh2HDhqFVq1bw8/MDALRr1w7+/v6YNGkSzpw5gxMnTiA4OBivvfYanJycnv1FICIiIr2i8zFIY8aMwZ07d7Bw4UJkZmaiU6dOiI2NFQdip6WlQSr9N4/r2bMnYmJisGDBAsyfPx+tW7fGvn370LFjRwCATCbDhQsXsHXrVuTk5MDJyQkDBgzA0qVLYWRkJO5n27ZtCA4ORv/+/SGVSjFy5Eh89NFHz/bkiYiISC/pPEECgODgYLEFSFt8fHyZslGjRmHUqFHl1jcxMcHBgwerPKa1tTViYmJqFCcRERE1DDrvYiMiIiLSN0yQiIiIiLQwQSIiIiLSohdjkIh0QSWV4kCbF8VlIiIiNSZI1GAVGcgxfXhY1RWJiKjB4Z/NRERERFqYIBERERFpYYJEDZZJcSFuLh+Cm8uHPHofGxER0f8wQSIiIiLSwgSJiIiISAsTJCIiIiItTJCIiIiItDBBIiIiItLCBImIiIhIC5+kTQ2WSirFkRZdxWUiIiI1JkjUYBUZyDFh1CJdh0FERHqICRKJFPMOVLvuzcjBTzESIiIi3WK/AhEREZEWJkjUYJkUF+LympG4vGYkXzVCREQa2MVGDZppSZGuQyAiIj3EFiQiIiIiLUyQiIiIiLQwQSIiIiLSwgSJiIiISAsTJCIiIiItnMVGDZZKIsEp547iMhERkRoTJGqwigyN8NrrkboOg4iI9BC72IiIiIi0MEEiIiIi0sIEiRosk+JCJH70OhI/ep2vGiEiIg0cg0QNms3DXF2HQEREeogJEtFzTDHvQLXr3owc/BQjISKqX9jFRkRERKSFCRIRERGRFiZIRERERFqYIBERERFp4SBtarBUEgl+dWgtLhMREakxQaIGq8jQCMMC1+o6DCIi0kN60cW2ceNGKBQKGBsbw8vLC2fOnKm0/q5du9C2bVsYGxvDzc0NP/74o7iupKQEc+fOhZubG8zMzODk5IRx48YhPT1dYx8KhQISiUTjExnJ93IRERGRHiRIO3fuRGhoKMLDw5GUlAQPDw/4+fkhOzu73PonT55EQEAAJk6ciPPnz2P48OEYPnw4Ll68CAAoKChAUlIS3n//fSQlJWHPnj1ISUnByy+/XGZfS5YsQUZGhvh55513nuq5EhERUf2g8wRpzZo1mDRpEoKCgtC+fXts3rwZpqam2LJlS7n1161bB39/f8yZMwft2rXD0qVL0aVLF2zYsAEAYGlpiUOHDmH06NFo06YNevTogQ0bNiAxMRFpaWka+zI3N4eDg4P4MTMze+rnS/rDuKQQv2yagF82TYBxCV81QkRE/9JpglRcXIzExET4+vqKZVKpFL6+vkhISCh3m4SEBI36AODn51dhfQB48OABJBIJrKysNMojIyNhY2ODzp07Y+XKlSgtLa39yVC9IxGAZrnZaJabDYmg62iIiEif6HSQ9t27d6FUKmFvb69Rbm9vj6tXr5a7TWZmZrn1MzMzy61fWFiIuXPnIiAgABYWFmL5jBkz0KVLF1hbW+PkyZMICwtDRkYG1qxZU+5+ioqKUFRUJH7PzeU7vIiIiJ5Xz/UstpKSEowePRqCIGDTpk0a60JDQ8Vld3d3yOVyTJkyBRERETAyMiqzr4iICCxevPipx0xERES6p9MuNltbW8hkMmRlZWmUZ2VlwcHBodxtHBwcqlVfnRz9+eefOHTokEbrUXm8vLxQWlqKmzdvlrs+LCwMDx48ED+3bt2q4uyIiIiovtJpgiSXy+Hp6Ym4uDixTKVSIS4uDt7e3uVu4+3trVEfAA4dOqRRX50cXbt2DYcPH4aNjU2VsSQnJ0MqlcLOzq7c9UZGRrCwsND4EBER0fNJ511soaGhCAwMRNeuXdG9e3dERUUhPz8fQUFBAIBx48ahadOmiIiIAADMnDkTPj4+WL16NQYPHowdO3bg3Llz+PTTTwE8So5effVVJCUl4YcffoBSqRTHJ1lbW0MulyMhIQGnT59G3759YW5ujoSEBISEhOCNN95A48aNdXMhiIiISG/oPEEaM2YM7ty5g4ULFyIzMxOdOnVCbGysOBA7LS0NUum/DV09e/ZETEwMFixYgPnz56N169bYt28fOnbsCAD466+/8N133wEAOnXqpHGso0ePok+fPjAyMsKOHTuwaNEiFBUVwdXVFSEhIRrjkuj5J0iA322ai8tERERqOk+QACA4OBjBwcHlrouPjy9TNmrUKIwaNarc+gqFAoJQ+ZztLl264NSpUzWOk54vhYbGGPDWx7oOg4iI9JDOHxRJREREpG+YIBERERFpYYJEDZZxSSF++nwafvp8Gl81QkREGvRiDBKRLkgE4IV7aeIyERGRGluQiIiIiLQwQSIiIiLSwgSJiIiISAsTJCIiIiItTJCIiIiItHAWGzVYggS4bWEnLhMREakxQaIGq9DQGL2mbtF1GEREpIfYxUZERESkhQkSERERkRYmSNRgGZUUYf/WEOzfGgKjkiJdh0NERHqEY5CowZIKAjwyr4nLREREamxBIiIiItLCFiQiKkMx70CN6t+MHPyUIiEi0g22IBERERFpYYJEREREpIUJEhEREZEWjkGiBu2eiYWuQyAiIj3EBOk5w8G11fdQbgzPGTG6DoOIiPQQu9iIiIiItDBBIiIiItLCBIkaLKOSIuyImYcdMfP4qhEiItLAMUjUYEkFAT1uXRSXiYiI1NiCRERERKSFCRIRERGRFiZIRERERFqYIBERERFpYYJEREREpIWz2KhBKzA00nUIRESkh5ggUYP1UG6M9qHf6joMIiLSQ0yQiKhO8X2ARPQ84BgkIiIiIi1sQaIGy6i0GJv2fggAmPrKfBQZyHUcERER6QsmSNRgSVUq9PvjnLhMRESkxi42IiIiIi16kSBt3LgRCoUCxsbG8PLywpkzZyqtv2vXLrRt2xbGxsZwc3PDjz/+qLFeEAQsXLgQjo6OMDExga+vL65du6ZR5/79+xg7diwsLCxgZWWFiRMnIi8vr87PjYiIiOofnXex7dy5E6Ghodi8eTO8vLwQFRUFPz8/pKSkwM7Orkz9kydPIiAgABERERgyZAhiYmIwfPhwJCUloWPHjgCAFStW4KOPPsLWrVvh6uqK999/H35+frh8+TKMjY0BAGPHjkVGRgYOHTqEkpISBAUFYfLkyYiJiXmm509E/6rJDDjOfiOip0nnCdKaNWswadIkBAUFAQA2b96MAwcOYMuWLZg3b16Z+uvWrYO/vz/mzJkDAFi6dCkOHTqEDRs2YPPmzRAEAVFRUViwYAGGDRsGAPjqq69gb2+Pffv24bXXXsOVK1cQGxuLs2fPomvXrgCA9evXY9CgQVi1ahWcnJye0dmXj9OkiYiIdEunXWzFxcVITEyEr6+vWCaVSuHr64uEhIRyt0lISNCoDwB+fn5i/Rs3biAzM1OjjqWlJby8vMQ6CQkJsLKyEpMjAPD19YVUKsXp06fr7PyIiIioftJpC9Ldu3ehVCphb2+vUW5vb4+rV6+Wu01mZma59TMzM8X16rLK6mh33xkYGMDa2lqso62oqAhFRUXi9wcPHgAAcnNzKz3H2lAVFdSo/uMxPKttdXHMJ9m2vO2UxYVQlyqLCqASyp/JVhfx1tdrpM/bPr5dx/CDNTrmxcV+dbItEdU/6p8dgiBUWk/nXWz1RUREBBYvXlym3NnZWQfRaLKMevbb6uKYT7JtRdtZqhc+Hlfnx3ySbRvKMZ9k2/oWLxHpl3/++QeWlpYVrtdpgmRrawuZTIasrCyN8qysLDg4OJS7jYODQ6X11f/NysqCo6OjRp1OnTqJdbKzszX2UVpaivv371d43LCwMISGhorfVSoV7t+/DxsbG0gkkmqc7ZPJzc2Fs7Mzbt26BQsLi6d+vPqI16h6eJ2qxmtUNV6jqvEaVU0X10gQBPzzzz9VjjfWaYIkl8vh6emJuLg4DB8+HMCjxCMuLg7BwcHlbuPt7Y24uDjMmjVLLDt06BC8vb0BAK6urnBwcEBcXJyYEOXm5uL06dOYOnWquI+cnBwkJibC09MTAHDkyBGoVCp4eXmVe1wjIyMYGWm++d3KyqqWZ157FhYW/B+tCrxG1cPrVDVeo6rxGlWN16hqz/oaVdZypKbzLrbQ0FAEBgaia9eu6N69O6KiopCfny/Oahs3bhyaNm2KiIgIAMDMmTPh4+OD1atXY/DgwdixYwfOnTuHTz/9FAAgkUgwa9YsfPDBB2jdurU4zd/JyUlMwtq1awd/f39MmjQJmzdvRklJCYKDg/Haa6/pfAYbERER6Z7OE6QxY8bgzp07WLhwITIzM9GpUyfExsaKg6zT0tIglf472a5nz56IiYnBggULMH/+fLRu3Rr79u0Tn4EEAO+99x7y8/MxefJk5OTkoFevXoiNjRWfgQQA27ZtQ3BwMPr37w+pVIqRI0fio48+enYnTkRERPpLoHqhsLBQCA8PFwoLC3Udit7iNaoeXqeq8RpVjdeoarxGVdPnayQRhCrmuRERERE1MHrxLjYiIiIifcIEiYiIiEgLEyQiIiIiLUyQiIiIiLQwQaonNm7cCIVCAWNjY3h5eeHMmTO6DklvLFq0CBKJROPTtm1bXYelU8ePH8fQoUPh5OQEiUSCffv2aawXBAELFy6Eo6MjTExM4Ovri2vXrukmWB2q6jqNHz++zL3l7++vm2B1ICIiAt26dYO5uTns7OwwfPhwpKSkaNQpLCzE9OnTYWNjg0aNGmHkyJFl3nbwPKvONerTp0+Z++jtt9/WUcS6sWnTJri7u4sPhPT29sZ///tfcb0+3kdMkOqBnTt3IjQ0FOHh4UhKSoKHhwf8/PzKvC6lIevQoQMyMjLEzy+//KLrkHQqPz8fHh4e2LhxY7nrV6xYgY8++gibN2/G6dOnYWZmBj8/PxQWFj7jSHWrqusEAP7+/hr31vbt259hhLp17NgxTJ8+HadOncKhQ4dQUlKCAQMGID8/X6wTEhKC77//Hrt27cKxY8eQnp6OESNG6DDqZ6s61wgAJk2apHEfrVixQkcR60azZs0QGRmJxMREnDt3Dv369cOwYcNw6dIlAHp6H+n4MQNUDd27dxemT58uflcqlYKTk5MQERGhw6j0R3h4uODh4aHrMPQWAGHv3r3id5VKJTg4OAgrV64Uy3JycgQjIyNh+/btOohQP2hfJ0EQhMDAQGHYsGE6iUcfZWdnCwCEY8eOCYLw6L4xNDQUdu3aJda5cuWKAEBISEjQVZg6pX2NBEEQfHx8hJkzZ+ouKD3VuHFj4fPPP9fb+4gtSHquuLgYiYmJ8PX1FcukUil8fX2RkJCgw8j0y7Vr1+Dk5IQWLVpg7NixSEtL03VIeuvGjRvIzMzUuKcsLS3h5eXFe6oc8fHxsLOzQ5s2bTB16lTcu3dP1yHpzIMHDwAA1tbWAIDExESUlJRo3Ett27ZF8+bNG+y9pH2N1LZt2wZbW1t07NgRYWFhKCgo0EV4ekGpVGLHjh3Iz8+Ht7e33t5HOn/VCFXu7t27UCqV4qtX1Ozt7XH16lUdRaVfvLy88OWXX6JNmzbIyMjA4sWL8dJLL+HixYswNzfXdXh6JzMzEwDKvafU6+gRf39/jBgxAq6urkhNTcX8+fMxcOBAJCQkQCaT6Tq8Z0qlUmHWrFl48cUXxVc7ZWZmQi6Xl3lxd0O9l8q7RgDw+uuvw8XFBU5OTrhw4QLmzp2LlJQU7NmzR4fRPnu//fYbvL29UVhYiEaNGmHv3r1o3749kpOT9fI+YoJE9d7AgQPFZXd3d3h5ecHFxQXffPMNJk6cqMPIqL577bXXxGU3Nze4u7ujZcuWiI+PR//+/XUY2bM3ffp0XLx4scGP76tMRddo8uTJ4rKbmxscHR3Rv39/pKamomXLls86TJ1p06YNkpOT8eDBA+zevRuBgYE4duyYrsOqELvY9JytrS1kMlmZ0fxZWVlwcHDQUVT6zcrKCi+88AKuX7+u61D0kvq+4T1Vcy1atICtrW2Du7eCg4Pxww8/4OjRo2jWrJlY7uDggOLiYuTk5GjUb4j3UkXXqDxeXl4A0ODuI7lcjlatWsHT0xMRERHw8PDAunXr9PY+YoKk5+RyOTw9PREXFyeWqVQqxMXFwdvbW4eR6a+8vDykpqbC0dFR16HoJVdXVzg4OGjcU7m5uTh9+jTvqSrcvn0b9+7dazD3liAICA4Oxt69e3HkyBG4urpqrPf09IShoaHGvZSSkoK0tLQGcy9VdY3Kk5ycDAAN5j6qiEqlQlFRkd7eR+xiqwdCQ0MRGBiIrl27onv37oiKikJ+fj6CgoJ0HZpeePfddzF06FC4uLggPT0d4eHhkMlkCAgI0HVoOpOXl6fx1+mNGzeQnJwMa2trNG/eHLNmzcIHH3yA1q1bw9XVFe+//z6cnJwwfPhw3QWtA5VdJ2trayxevBgjR46Eg4MDUlNT8d5776FVq1bw8/PTYdTPzvTp0xETE4P9+/fD3NxcHA9iaWkJExMTWFpaYuLEiQgNDYW1tTUsLCzwzjvvwNvbGz169NBx9M9GVdcoNTUVMTExGDRoEGxsbHDhwgWEhISgd+/ecHd313H0z05YWBgGDhyI5s2b459//kFMTAzi4+Nx8OBB/b2PdDZ/jmpk/fr1QvPmzQW5XC50795dOHXqlK5D0htjxowRHB0dBblcLjRt2lQYM2aMcP36dV2HpVNHjx4VAJT5BAYGCoLwaKr/+++/L9jb2wtGRkZC//79hZSUFN0GrQOVXaeCggJhwIABQpMmTQRDQ0PBxcVFmDRpkpCZmanrsJ+Z8q4NACE6Olqs8/DhQ2HatGlC48aNBVNTU+GVV14RMjIydBf0M1bVNUpLSxN69+4tWFtbC0ZGRkKrVq2EOXPmCA8ePNBt4M/YhAkTBBcXF0EulwtNmjQR+vfvL/z000/ien28jySCIAjPMiEjIiIi0nccg0RERESkhQkSERERkRYmSERERERamCARERERaWGCRERERKSFCRIRERGRFiZIRERERFqYIBHRU3fz5k1IJBLxFQv64OrVq+jRoweMjY3RqVOnp3qsPn36YNasWU/1GERUt5ggETUA48ePh0QiQWRkpEb5vn37IJFIdBSVboWHh8PMzAwpKSka74B6nPq6SSQSGBoawtXVFe+99x4KCwtrdKw9e/Zg6dKldRF2hb788ksxVplMhsaNG8PLywtLlizBgwcPnuqxiZ5HTJCIGghjY2MsX74cf//9t65DqTPFxcW13jY1NRW9evWCi4sLbGxsKqzn7++PjIwM/PHHH1i7di0++eQThIeH1+hY1tbWMDc3r3Ws1WVhYYGMjAzcvn0bJ0+exOTJk/HVV1+hU6dOSE9Pf+rHJ3qeMEEiaiB8fX3h4OCAiIiICussWrSoTHdTVFQUFAqF+H38+PEYPnw4PvzwQ9jb28PKygpLlixBaWkp5syZA2trazRr1gzR0dFl9n/16lX07NkTxsbG6NixI44dO6ax/uLFixg4cCAaNWoEe3t7vPnmm7h79664vk+fPggODsasWbNga2tb4UtjVSoVlixZgmbNmsHIyAidOnVCbGysuF4ikSAxMRFLliyBRCLBokWLKrwmRkZGcHBwgLOzM4YPHw5fX18cOnRIXH/v3j0EBASgadOmMDU1hZubG7Zv366xD+0uNoVCgQ8//BATJkyAubk5mjdvjk8//VRc369fPwQHB2vs486dO5DL5RW2dqnPy8HBAY6OjmjXrh0mTpyIkydPIi8vD++9955YLzY2Fr169YKVlRVsbGwwZMgQpKam1uj4H3/8MVq3bg1jY2PY29vj1VdfrTAuovqICRJRAyGTyfDhhx9i/fr1uH379hPt68iRI0hPT8fx48exZs0ahIeHY8iQIWjcuDFOnz6Nt99+G1OmTClznDlz5mD27Nk4f/48vL29MXToUNy7dw8AkJOTg379+qFz5844d+4cYmNjkZWVhdGjR2vsY+vWrZDL5Thx4gQ2b95cbnzr1q3D6tWrsWrVKly4cAF+fn54+eWXce3aNQBARkYGOnTogNmzZyMjIwPvvvtutc774sWLOHnyJORyuVhWWFgIT09PHDhwABcvXsTkyZPx5ptv4syZM5Xua/Xq1ejatSvOnz+PadOmYerUqUhJSQEAvPXWW4iJiUFRUZFY/+uvv0bTpk3Rr1+/asWqZmdnh7Fjx+K7776DUqkEAOTn5yM0NBTnzp1DXFwcpFIpXnnlFahUqmod/9y5c5gxYwaWLFmClJQUxMbGonfv3jWKi0jv6fRVuUT0TAQGBgrDhg0TBEEQevToIUyYMEEQBEHYu3ev8PiPgfDwcMHDw0Nj27Vr1wouLi4a+3JxcRGUSqVY1qZNG+Gll14Sv5eWlgpmZmbC9u3bBUEQhBs3bggAhMjISLFOSUmJ0KxZM2H58uWCIAjC0qVLhQEDBmgc+9atWwIAISUlRRAEQfDx8RE6d+5c5fk6OTkJy5Yt0yjr1q2bMG3aNPG7h4eHEB4eXul+AgMDBZlMJpiZmQlGRkYCAEEqlQq7d++udLvBgwcLs2fPFr/7+PgIM2fOFL+7uLgIb7zxhvhdpVIJdnZ2wqZNmwRBePRm88aNGws7d+4U67i7uwuLFi2q8JjR0dGCpaVlues2bdokABCysrLKXX/nzh0BgPDbb79V6/jffvutYGFhIeTm5lYYD1F9xxYkogZm+fLl2Lp1K65cuVLrfXTo0AFS6b8/Puzt7eHm5iZ+l8lksLGxQXZ2tsZ23t7e4rKBgQG6du0qxvHrr7/i6NGjaNSokfhp27YtAGh0/3h6elYaW25uLtLT0/Hiiy9qlL/44ou1Oue+ffsiOTkZp0+fRmBgIIKCgjBy5EhxvVKpxNKlS+Hm5gZra2s0atQIBw8eRFpaWqX7dXd3F5fVXWPq62VsbIw333wTW7ZsAQAkJSXh4sWLGD9+fI3jBwBBEMTjAMC1a9cQEBCAFi1awMLCQuxCVcdc1fH/85//wMXFBS1atMCbb76Jbdu2oaCgoFaxEekrJkhEDUzv3r3h5+eHsLCwMuukUqn4y1StpKSkTD1DQ0ON7+pZXtpl6i6b6sjLy8PQoUORnJys8bl27ZpG942ZmVm191kXzMzM0KpVK3h4eGDLli04ffo0vvjiC3H9ypUrsW7dOsydOxdHjx5FcnIy/Pz8qhxAXtX1euutt3Do0CHcvn0b0dHR6NevH1xcXGp1DleuXIGFhYU4GH3o0KG4f/8+PvvsM5w+fRqnT58GoDnovbLjm5ubIykpCdu3b4ejoyMWLlwIDw8P5OTk1Co+In3EBImoAYqMjMT333+PhIQEjfImTZogMzNTI0mqy2cXnTp1SlwuLS1FYmIi2rVrBwDo0qULLl26BIVCgVatWml8apIUWVhYwMnJCSdOnNAoP3HiBNq3b/9E8UulUsyfPx8LFizAw4cPxf0OGzYMb7zxBjw8PNCiRQv8/vvvT3QcAHBzc0PXrl3x2WefISYmBhMmTKjVfrKzsxETE4Phw4dDKpXi3r17SElJwYIFC9C/f3+0a9eu3JmNVR3fwMAAvr6+WLFiBS5cuICbN2/iyJEjtYqRSB8xQSJqgNzc3DB27Fh89NFHGuV9+vTBnTt3sGLFCqSmpmLjxo3473//W2fH3bhxI/bu3YurV69i+vTp+Pvvv8VfvNOnT8f9+/cREBCAs2fPIjU1FQcPHkRQUJA4uLi65syZg+XLl2Pnzp1ISUnBvHnzkJycjJkzZz7xOYwaNQoymQwbN24EALRu3RqHDh3CyZMnceXKFUyZMgVZWVlPfBzgUStOZGQkBEHAK6+8UmV9QRCQmZmJjIwMXLlyBVu2bEHPnj1haWkpPgOrcePGsLGxwaefforr16/jyJEjCA0NrdHxf/jhB3z00UdITk7Gn3/+ia+++goqlQpt2rSpk/Mm0gdMkIgaqCVLlpTpAmvXrh0+/vhjbNy4ER4eHjhz5ky1Z3hVR2RkJCIjI+Hh4YFffvkF3333HWxtbQFAbPVRKpUYMGAA3NzcMGvWLFhZWWmMd6qOGTNmIDQ0FLNnz4abmxtiY2Px3XffoXXr1k98DgYGBggODsaKFSuQn5+PBQsWoEuXLvDz80OfPn3g4OCA4cOHP/FxACAgIAAGBgYICAiAsbFxlfVzc3Ph6OiIpk2bwtvbG5988gkCAwNx/vx5ODo6AnjUCrZjxw4kJiaiY8eOCAkJwcqVK2t0fCsrK+zZswf9+vVDu3btsHnzZmzfvh0dOnSok/Mm0gcSQXvAARER6YWbN2+iZcuWOHv2LLp06dLgjk+kS0yQiIj0TElJCe7du4d3330XN27cKDOe6nk/PpE+YBcbEZGeOXHiBBwdHXH27NkKH4b5PB+fSB+wBYmIiIhIC1uQiIiIiLQwQSIiIiLSwgSJiIiISAsTJCIiIiItTJCIiIiItDBBIiIiItLCBImIiIhICxMkIiIiIi1MkIiIiIi0/H+8tu+GTf7fKgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3. Visualize the distribution\n",
    "expected_value = n_days * p_rain\n",
    "\n",
    "plt.bar(k_values, probabilities)\n",
    "plt.axvline(expected_value, color='red', linestyle='--', label=f'Expected: {expected_value:.1f}')\n",
    "plt.xlabel('Number of Rainy Days')\n",
    "plt.ylabel('Probability')\n",
    "plt.title(f'Binomial Distribution (n=30, p={p_rain:.3f})')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdb005d0",
   "metadata": {},
   "source": [
    "### Interpretation\n",
    "\n",
    "**Most likely number of rainy days**: The mode of the distribution (tallest bar) shows the most probable outcome - 6 rainy days.\n",
    "\n",
    "**Expected number of rainy days**: The expected value (mean) is `n × p = 5.85`.\n",
    "\n",
    "**Probability of 15+ rainy days**: We can calculate this using the cumulative distribution function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ecbe5a9",
   "metadata": {},
   "source": [
    "### Probability of >= 15 rainy days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5bc3a33e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of 15+ rainy days: 0.0002 (0.02%)\n"
     ]
    }
   ],
   "source": [
    "prob_15_or_more = 1 - stats.binom.cdf(14, n_days, p_rain)\n",
    "\n",
    "print(f\"Probability of 15+ rainy days: {prob_15_or_more:.4f} ({prob_15_or_more*100:.2f}%)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "981ac816",
   "metadata": {},
   "source": [
    "### Extra: Binomial cumulative distribution function (CDF) visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4763a550",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# CDF plot of the binomial distribution\n",
    "cumulative_probs = stats.binom.cdf(k_values, n_days, p_rain)\n",
    "\n",
    "plt.step(k_values, cumulative_probs, where='post')\n",
    "plt.xlabel('Number of Rainy Days')\n",
    "plt.ylabel('Cumulative Probability')\n",
    "plt.title(f'CDF of Binomial Distribution (n=30, p={p_rain:.3f})')\n",
    "plt.grid(alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c569dd29",
   "metadata": {},
   "source": [
    "**How this helps forecasters**: The binomial distribution allows forecasters to quantify uncertainty in predictions. Instead of just saying \"it might rain,\" they can provide probabilities for different scenarios (e.g., \"there's a 5% chance of more than 15 rainy days this month\")."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "172761bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard deviation: 2.17\n"
     ]
    }
   ],
   "source": [
    "std_dev = np.sqrt(n_days * p_rain * (1 - p_rain))\n",
    "print(f\"Standard deviation: {std_dev:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14e2cba3",
   "metadata": {},
   "source": [
    "**Standard deviation interpretation**: The standard deviation indicates the typical variability in the number of rainy days per month. A higher standard deviation means more unpredictable monthly rainfall patterns."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cec1874",
   "metadata": {},
   "source": [
    "## Exercise 2: central limit theorem - sampling distribution of rainfall\n",
    "\n",
    "**Objective**: Demonstrate the Central Limit Theorem by creating and analyzing a sampling distribution.\n",
    "\n",
    "The Central Limit Theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's original distribution. This is fundamental to statistical inference.\n",
    "\n",
    "**Tasks**:\n",
    "\n",
    "1. **Examine the population distribution**:\n",
    "   - Create a histogram of all `rainfall_inches` values in the dataset\n",
    "   - Calculate and print the population mean and standard deviation\n",
    "   - Note the shape of this distribution (is it normal, skewed, etc.?)\n",
    "\n",
    "2. **Create a sampling distribution**:\n",
    "   - Take 1000 random samples from the rainfall data, each of size n=30\n",
    "   - For each sample, calculate the mean rainfall\n",
    "   - Store all 1000 sample means in a list or array\n",
    "   - Hint: Use `df['rainfall_inches'].sample(n=30, replace=True)` for each sample\n",
    "\n",
    "3. **Visualize the sampling distribution**:\n",
    "   - Create a histogram of the 1000 sample means\n",
    "   - Overlay a normal distribution curve using the theoretical mean (μ) and standard error (σ/√n)\n",
    "   - Add a vertical line at the population mean\n",
    "   - You can use `scipy.stats.norm.pdf()` to create the normal curve\n",
    "   - Label axes and add a descriptive title\n",
    "\n",
    "4. **Compare distributions**:\n",
    "   - Create two side-by-side histograms:\n",
    "     - Left: Original rainfall distribution (from step 1)\n",
    "     - Right: Sampling distribution of means (from step 3)\n",
    "   - Make sure both use the same y-axis scale for comparison\n",
    "   - Include the mean and standard deviation in each subplot title\n",
    "\n",
    "5. **Interpret** your findings:\n",
    "   - How does the shape of the sampling distribution compare to the original distribution?\n",
    "   - Is the sampling distribution approximately normal? (This demonstrates the CLT!)\n",
    "   - Calculate the standard error: population σ divided by √30. How does this compare to the standard deviation of your sample means?\n",
    "   - What does the CLT tell us about why we can use normal-based methods (like confidence intervals) even when our data isn't normally distributed?\n",
    "   - **Bonus**: Repeat the experiment with different sample sizes (n=5, n=10, n=50). How does sample size affect the spread and normality of the sampling distribution?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c879505c",
   "metadata": {},
   "source": [
    "### Population distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da2ffd4c",
   "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": [
      "Population mean: 0.3037\n",
      "Population std: 0.3115\n"
     ]
    }
   ],
   "source": [
    "population_mean = df['rainfall_inches'].mean()\n",
    "population_std = df['rainfall_inches'].std()\n",
    "\n",
    "plt.hist(df['rainfall_inches'], bins=50)\n",
    "plt.xlabel('Rainfall (inches)')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Population Distribution of Rainfall')\n",
    "plt.show()\n",
    "\n",
    "print(f\"Population mean: {population_mean:.4f}\")\n",
    "print(f\"Population std: {population_std:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "305f895b",
   "metadata": {},
   "source": [
    "The population distribution is highly right-skewed with many zero values (no rain) and a long tail of higher rainfall amounts."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2b5ce7c",
   "metadata": {},
   "source": [
    "### Sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b1cacd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 1000\n",
    "sample_size = 30\n",
    "sample_means = []\n",
    "\n",
    "for _ in range(n_samples):\n",
    "    sample = df['rainfall_inches'].sample(n=sample_size, replace=True)\n",
    "    sample_means.append(sample.mean())\n",
    "\n",
    "sample_means = np.array(sample_means)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af68a64a",
   "metadata": {},
   "source": [
    "### Sampling distribution plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6dd93618",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "standard_error = population_std / np.sqrt(sample_size)\n",
    "\n",
    "# Normal curve\n",
    "x = np.linspace(sample_means.min(), sample_means.max(), 100)\n",
    "\n",
    "plt.title('Sampling Distribution of Sample Means (n=30)')\n",
    "plt.hist(sample_means, bins=30, density=True)\n",
    "plt.plot(x, stats.norm.pdf(x, population_mean, standard_error), label='Normal curve')\n",
    "plt.axvline(population_mean, color='black', label=f'Population mean: {population_mean:.3f}')\n",
    "plt.xlabel('Sample Mean Rainfall (inches)')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebf6dae2",
   "metadata": {},
   "source": [
    "### Sampling distribution versus population comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c0fa2f75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 4. Compare distributions\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(12, 4))\n",
    "\n",
    "ax1.set_title(f'Population Distribution\\nMean={population_mean:.3f}, SD={population_std:.3f}')\n",
    "ax1.hist(df['rainfall_inches'], bins=30)\n",
    "ax1.set_xlabel('Rainfall (inches)')\n",
    "ax1.set_ylabel('Frequency')\n",
    "\n",
    "ax2.set_title(f'Sampling Distribution\\nMean={sample_means.mean():.3f}, SD={sample_means.std():.3f}')\n",
    "ax2.hist(sample_means, bins=30)\n",
    "ax2.set_xlabel('Sample Mean Rainfall (inches)')\n",
    "ax2.set_ylabel('Frequency')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e75e4b17",
   "metadata": {},
   "source": [
    "### Interpretation\n",
    "\n",
    "**Shape comparison**: The original rainfall distribution is highly right-skewed, but the sampling distribution of means is approximately normal and symmetric. This is the Central Limit Theorem in action!\n",
    "\n",
    "**Normality**: Yes, the sampling distribution is approximately normal despite the original data being non-normal.\n",
    "\n",
    "**Standard error comparison**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5798baf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical standard error: 0.0569\n",
      "Empirical standard error: 0.0540\n",
      "Difference: 0.0028\n"
     ]
    }
   ],
   "source": [
    "theoretical_se = population_std / np.sqrt(sample_size)\n",
    "empirical_se = sample_means.std()\n",
    "\n",
    "print(f\"Theoretical standard error: {theoretical_se:.4f}\")\n",
    "print(f\"Empirical standard error: {empirical_se:.4f}\")\n",
    "print(f\"Difference: {abs(theoretical_se - empirical_se):.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80bc2af7",
   "metadata": {},
   "source": [
    "The theoretical and empirical standard errors match closely, confirming the CLT prediction.\n",
    "\n",
    "**Why CLT matters**: The CLT explains why we can use normal-based statistical methods (like confidence intervals and hypothesis tests) even when our data isn't normally distributed. As long as our sample size is large enough, the sampling distribution of the mean will be approximately normal, allowing us to make valid inferences."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4ecf183",
   "metadata": {},
   "source": [
    "### Bonus: Effect of Sample Size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3d4a818c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bonus: Different sample sizes\n",
    "sample_sizes = [5, 10, 30, 50]\n",
    "fig, axes = plt.subplots(1, 4, figsize=(16, 4))\n",
    "\n",
    "for idx, n in enumerate(sample_sizes):\n",
    "\n",
    "    sample_means_n = []\n",
    "\n",
    "    for _ in range(1000):\n",
    "        sample = df['rainfall_inches'].sample(n=n, replace=True)\n",
    "        sample_means_n.append(sample.mean())\n",
    "    \n",
    "    sample_means_n = np.array(sample_means_n)\n",
    "    \n",
    "    axes[idx].hist(sample_means_n, bins=30)\n",
    "    axes[idx].set_xlabel('Sample Mean')\n",
    "    axes[idx].set_ylabel('Frequency')\n",
    "    axes[idx].set_title(f'n={n}\\nSD={sample_means_n.std():.4f}')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44e072a2",
   "metadata": {},
   "source": [
    "**Observation**: As sample size increases, the sampling distribution becomes more normal and has less spread (smaller standard error). Larger samples provide more precise estimates of the population mean."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}