PDF and CDF using central limit theorem

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Eslearner 2019-12-11

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https://ww2.mathworks.cn/matlabcentral/answers/496192-pdf-and-cdf-using-central-limit-theorem

评论： Dheeraj Singh 2019-12-20

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I am struggling to plot the PDF and CDF graphs of

where

using central limt theorem where n = 1; 2; 3; 4; 5; 10; 20; 40

I am taking Xi to be a uniform continuous random variable for values between (0,3).

Here is what i have done so far -

clc
clear all
close all
%different sizes of input X
N = [1 2 3 4 5 10 20 40];
%interval (1,6) for random variables
a=0;
b=3;
%to store sum of differnet sizes of input
for i=1:length(N)
%generates uniform random numbers in the interval
X = a + (b-a).*rand(N(i),1);
S=zeros(1,length(X));
S=cumsum(X);
cd=cdf('Uniform',S,0,3);
plot(cd);
hold on;
end
legend('n=1','n=2','n=3','n=4','n=5','n=10','n=20','n=40');
title('CDF PLOT')
figure;
for i=1:length(N)
%generates uniform random numbers in the interval
X = a + (b-a).*rand(N(i),1);
S=zeros(1,length(X));
S=cumsum(X);
cd=pdf('Uniform',S,0,3);
plot(cd);
hold on;
end
legend('n=1','n=2','n=3','n=4','n=5','n=10','n=20','n=40');