lab3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Лабораторная работа №3\n",
    "\n",
    "Геометрическое определение вероятности, задача Бюффона, \n",
    "операторы сравнения в MATLAB, задача о встрече.\n",
    "\n",
    "## 1. Решить и записать в тетрадь решение задачи Бюффона:\n",
    "На плоскость, разграфленную параллельными прямыми линиями, отстоящими друг от друга на расстояние 2а, наудачу бросается игла длиной 2l. Какова вероятность того, что игла пересечет одну из параллельных прямых, если l<=a?\n",
    "Указание: элементарный исход каждого опыта — положение иглы после падения. Опишите его парой чисел (x, u): х - расстояние от центра иглы до ближайшей снизу линии (0 < x < 2a); u - угол между иглой и ближайшей снизу линией (0 < u < pi). Опишите пространство всех элементарных исходов опыта, постройте это множество, определите область благоприятную наступления события A — пересечения линии иглой. Примените геометрическое определение вероятности."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Смоделировать бросание иглы (длиной .5) на плоскость, разграфленную прямыми параллельными линиями (расстояние между линиями 1). \n",
    "Выберите N=10,50,100.Нарисуем область исходов благоприятствующих событию A={игла пересечет одну из параллельных линий} ={(uu,xx)|0 < xx < 0.5*sin(uu) или 1-0.5*sin(uu) < xx < 1 }. Для определения частоты наступления события А на необходимо уметь подсчитывать число попаданий случайной точки (u,x) в область А."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a2c985e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "%matplotlib inline\n",
    "from math import sin\n",
    "import numpy as np\n",
    "from numpy.random import random as rand\n",
    "x1 = []\n",
    "x2 = []\n",
    "u = np.linspace(0,np.pi,num = 100)\n",
    "for phi in u:\n",
    "    x1.append(0.5*sin(phi))\n",
    "    x2.append(1 - 0.5*sin(phi))\n",
    "x1 = [max(q,0) for q in x1 ]\n",
    "x2 = [min(q,1) for q in x2 ]\n",
    "plt.plot(u,x1)\n",
    "plt.plot(u,x2)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Найдите частоту наступления события А в задаче Бюффона для 1000 бросаний иглы.\n",
    "Выполните серию вычислений, найдите A(i) и усредните их. Сообщите оценку вероятности наступления события А в задаче Бюффона."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.63793\n",
      "value of pi: 3.1351402191463014\n"
     ]
    }
   ],
   "source": [
    "a = 0.5\n",
    "N = 100000\n",
    "values = [[a*rand(), np.pi * rand() ] for i in range(N)]\n",
    "A = [(v[0]>=0 and v[0]<=a*sin(v[1])) or (v[0]<1 and v[0]>=1-a*sin(v[1])) for v in values]\n",
    "p = sum(A)/N\n",
    "pi = 2/p\n",
    "print(p)\n",
    "print('value of pi: '+str(pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Решите задачу о встрече \n",
    "Двое договорились о встрече в течение часа, время прихода каждого равномерно распределено в течение этого часа, причем первый ждет второго не более 10 минут и уходит, а второй первого - 20 минут. Оценку вероятности наступления события А={встреча состоялась} показать преподавателю."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1585"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 10000\n",
    "a = 10\n",
    "b = 20\n",
    "answer = 0 \n",
    "for i in range(N):\n",
    "    t1 = 60*rand()\n",
    "    t2 = 60*rand()\n",
    "    answer = answer + (t2>t1 and t2<t1+a) or (t2<t1 and t1<t2 + b)\n",
    "answer/N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}