From 45e38d949420b32ca53e9fe4c0b452b7c780bcc0 Mon Sep 17 00:00:00 2001
From: ngumalbright <bngumnumfor@gmail.com>
Date: Sun, 18 Feb 2024 20:38:10 +0000
Subject: [PATCH] Adding lab3 exercise 2 to my repository

---
 Lab03/Lab03-2.ipynb | 105 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 105 insertions(+)
 create mode 100644 Lab03/Lab03-2.ipynb

diff --git a/Lab03/Lab03-2.ipynb b/Lab03/Lab03-2.ipynb
new file mode 100644
index 0000000..19c2575
--- /dev/null
+++ b/Lab03/Lab03-2.ipynb
@@ -0,0 +1,105 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "0986bdf6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "For convergence criterion 0.01:\n",
+      "Average number of draws: 37.2\n",
+      "Standard deviation of draws: 75.69500203668227\n",
+      "\n",
+      "For convergence criterion 0.001:\n",
+      "Average number of draws: 839.4\n",
+      "Standard deviation of draws: 1430.1452296105379\n",
+      "\n",
+      "For convergence criterion 0.0001:\n",
+      "Average number of draws: 286679.5\n",
+      "Standard deviation of draws: 751160.3040932001\n",
+      "\n",
+      "For convergence criterion 1e-05:\n",
+      "Average number of draws: 1135232\n",
+      "Standard deviation of draws: 3526521.0381986317\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "import random\n",
+    "import statistics\n",
+    "\n",
+    "def estimate_pi(convergence_criterion):\n",
+    "    n = 0\n",
+    "    d = 0\n",
+    "    ratios = []\n",
+    "\n",
+    "    while True:\n",
+    "        x = random.random()\n",
+    "        y = random.random()\n",
+    "\n",
+    "        if x**2 + y**2 <= 1.0:\n",
+    "            n += 1\n",
+    "        d += 1\n",
+    "        ratio = 4 * n / d\n",
+    "        ratios.append(ratio)\n",
+    "\n",
+    "        if abs(ratio - 3.141592653589793) / 3.141592653589793 <= convergence_criterion:\n",
+    "            break\n",
+    "\n",
+    "    return d, ratios\n",
+    "\n",
+    "convergence_criteria = [0.01, 0.001, 0.0001, 0.00001]\n",
+    "num_runs = 10\n",
+    "\n",
+    "for criterion in convergence_criteria:\n",
+    "    draws_list = []\n",
+    "\n",
+    "    for _ in range(num_runs):\n",
+    "        num_draws, _ = estimate_pi(criterion)\n",
+    "        draws_list.append(num_draws)\n",
+    "\n",
+    "    avg_draws = statistics.mean(draws_list)\n",
+    "    std_dev_draws = statistics.stdev(draws_list)\n",
+    "\n",
+    "    print(f\"For convergence criterion {criterion}:\")\n",
+    "    print(f\"Average number of draws: {avg_draws}\")\n",
+    "    print(f\"Standard deviation of draws: {std_dev_draws}\")\n",
+    "    print()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d5e87d54",
+   "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": "3.11.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}