Question

Write a well-documented MATLAB script that verifies the Central Limit Theorem based

on uniform distribution. Write a MATLAB script that would allow you to specify n and k where n is the sample size and k is the number of times that you repeat this experiment (to obtain the distribution that you will compare with the normal distribution). Use n = 10; 000 and k = 1; 000. The

result of the script should be the histogram for the probability density function.

Answer 1

clc;
n=10000;
k=1000;
mu=1;
sigma2=1/12; % pupulation mean and variance of uniform(0,2)
for i=1:k
    x(:,i)=unifrnd(0,2,n,1);
end
y=mean(x);
z=100*(y-mu)/(1/12)^(1/2);
hist(z)

$a258sEwAAAABJRU5ErkJggg==$

From above histogram we can observe that distribution is symmetric about zero which is same as standard normal distribution, hence central limit theorem is proved