Write a program using MATLAB that performs a simulated experiment of N trials, w
ID: 3546547 • Letter: W
Question
Write a program using MATLAB that performs a simulated experiment of N trials, where each trial simulates flipping a sequence of n fair coins, identified as coin-1 through coin-n. The program must allow the user to enter the number of coins to be used in each trial, and the total number of trials. The program is to keep count of the number of trials that resulted in zero heads, one head, two heads, and so on. The program must compute the percent relative frequency distribution of trials associated with each number of heads obtained in the simulation, as well as the theoretical percent relative frequency distribution, and save these results to an ASCII file. As an application, obtain the simulation and theoretical distributions for an experiment of 100 trials, with 30 coins being used in each trial.
Explanation / Answer
clc; clear all; close all; N = input('trials to be done : '); n = input('coins in the experiment : '); H=zeros(1,n); % number of heads in each trials for i=1:N %calculate number of heads in each trial count=0; m=randi([0 1],1,n); % generate random 0 & 1 in every loop for j=1:n if m(1,j)==0 count=count+1; end end if count>0 H(count)=H(count)+1; end endfor i=1:n P(i)=(H(i)-min(H))/100; end plot(P); % Plot of number of heads in each trial experimently
%theoretically %c(n,k) = n!/(n-k)!k! p(n,k) = c(n,k)/2^n H1=zeros(1,n); for i=1:n H1(i)=factorial(n)/(factorial(n-i)*factorial(i)); P1(i)=H1(i)/2^n; end figure; plot(P1);
clc; clear all; close all; N = input('trials to be done : '); n = input('coins in the experiment : '); H=zeros(1,n); % number of heads in each trials for i=1:N %calculate number of heads in each trial count=0; m=randi([0 1],1,n); % generate random 0 & 1 in every loop for j=1:n if m(1,j)==0 count=count+1; end end if count>0 H(count)=H(count)+1; end end
for i=1:n P(i)=(H(i)-min(H))/100; end plot(P); % Plot of number of heads in each trial experimently
%theoretically %c(n,k) = n!/(n-k)!k! p(n,k) = c(n,k)/2^n H1=zeros(1,n); for i=1:n H1(i)=factorial(n)/(factorial(n-i)*factorial(i)); P1(i)=H1(i)/2^n; end figure; plot(P1);
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