Question

need help with matLab

Question 1 (20 Points) Write a well-documented MATLAB script hmwk7Q1.m that simulates tossing 100 coins into a unit square. As shown in the scatter plot. Location of Simulated Coins In Unit Square 1 o0 Ooo 05 04 03 02 oo 0.1 2 03 4 05 07 1 xpostion Hmwk7Q1.fig Consider organizing your MATLAB script into the following sections. % housekeeping (performs clearing of figures, workspace, and command lines) % Initialize the Number of Coins To Simulate (Solution Requires 100, you could play around with more) Locate the Coins (Using Uniformly Generated Random Variables draw x.y locations %Scatter Plot (Label & Hold) %Inscribe A Quarter Circle x + y = 1Onto Scatter Plot Form a Vector of Distance of Each Coin to The Origin r +y % Using Logical Indexing Count the Number of Coins Inside The Quarter Circle Form The Ratio of The Number of Coins Inside The Quarter Circle To The Total Number of Coins Associate Pi With 4 * The Ratio of The Number of Coins Inside The Quarter Circle To The Total Number of Coins Grading: 5 Points for hmwkr7q1. fig. 15 Points for hmwkr7q1.m submitted to Canvas.

Answer 1

MATLAB CODE:

% Perform housekeeping
clear;
clc;
clf;

% Number of coins
n = 100;

% Generate random variables x, y
x = rand(1, n);
y = rand(1, n);

% Scatter plot
plot(x, y, 'o');
title('Location of Simulated Coins in Unit Square');
xlabel('x position');
ylabel('y position');
hold on;

% Inscribe a quarter circle x^2 + y^2 = 1
theta = linspace(0, pi/2);
% Draw circle using x = r*cos(theta) and y = r*sin(theta)
xx = cos(theta);% Here r = 1
yy = sin(theta);% Here r = 1
plot(xx, yy);
hold off;

% Vector of distance of each coin to the origin
r = sqrt(x.^2 + y.^2);

% Count number of coins inside the quarter circle
insideCount = length(find(r < 1));

% Ratio of the number of coins inside the quarter circle to the total
% number of coins
ratio = insideCount/n;

% Associate Pi with 4 * The Ratio of the Number of Coins inside the quarter
% circle to the total number of coins
result = pi*4*ratio;

SAMPLE PLOT:

Location of Simulated Coins in Unit Square 0000 y position 0.2 0.6 0.8 0.4 x position

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