Kindly, receive the attached code..eventually, all the code are running.i appreciate for you patient.

SURNAME 1

Student's name
Professor's name
Course
University's affiliate

SURNAME 2

Introduction
The central limit theorem is a basic theorem in statistics which states that that the sample mean
of an adequately large sample (n ≥ 30) from a continuous probably distribution with mean µX
and variance σ2X will follow a normal distribution (Gaussian distribution).The CLT analysis
places no requirement on the form of the parent distribution .In other it doesn’t matter the
distribution of the population from which the sampling is done.

Method
N random variable were created each having L samples .This variable were created in such a
way that they were all independent and identical. In Matlab for loop was utilized to accomplish
to create the variables
Sum sn of all the variable in sample were created.
The mean and the standard deviation of the parent distribution was also determined
The vector Zn

Central Limit Theorem
10-Random variable

clc% clears the command window
NumberOfSample1=100; %specify the sample size 100
NumberOfSample2=1000; %%specify the sample size 1000
NumberOfSample3=10000; %%specify the sample size 10000
NumberOfSample4=1000000;%specify the sample size 1000000
NumberOfRandomVarible1=10; %specify the number of variable N=10
SizeParameter=4;

SURNAME 3

PopulationSize=10000000; %specify the population size
Population=random('Rayleigh',SizeParameter,PopulationSize,1); %population
%ofthe reylegh distribution with a parameter size 2
X1=zeros(NumberOfSample1,NumberOfRandomVarible1);%forms a matrix of
%NumberOfSample1*NumberOfRandomVarible1 matrix with all elements being
%Zeros
%The following for loop create NumberOfRandomVarible1 random variables each with NumberOfSample samples
for i=1:NumberOfRandomVarible1
X1(:,i)=Population(randperm(PopulationSize,NumberOfSample1));
end
X2=zeros(NumberOfSample2,NumberOfRandomVarible1);
for i=1:NumberOfRandomVarible1
X2(:,i)=Population(randperm(PopulationSize,NumberOfSample2));
end
X3=zeros(NumberOfSample3,NumberOfRandomVarible1);
for i=1:NumberOfRandomVarible1
X3(:,i)=Population(randperm(PopulationSize,NumberOfSample3));
end
X4=zeros(NumberOfSample4,NumberOfRandomVarible1);
for i=1:NumberOfRandomVarible1
X4(:,i)=Population(randperm(PopulationSize,NumberOfSample4));
end
% The following four lines compute the sum sn of all the samples
SumPerSample1=sum(X1);
SumPerSample2=sum(X2);
SumPerSample3=sum(X3);
SumPerSample4=sum(X4);
Mu=mean(Population);% Determine the mean for the population from which
%we sampled our data sample
Variance=var(Population);% Determine the variance for the population from which
%we sampled our data sample
Sigma=sqrt(Variance);
Zn1=((SumPerSample1-NumberOfSample1*Mu)./(Sigma*(sqrt(NumberOfSample1))))';

Zn2=((SumPerSample2-NumberOfSample1*Mu)./(Sigma*(sqrt(NumberOfSample2))))';
Zn3=((SumPerSample3-NumberOfSample1*Mu)./(Sigma*(sqrt(NumberOfSample3))))';
Zn4=((SumPerSample4-NumberOfSample1*Mu)./(Sigma*(sqrt(NumberOfSample4))))';
figure
subplot(2,2,1),hist(Zn1,30),title('Distribution of the mean-L=10')
subplot(2,2,2),hist(Zn2,30),title('Distribution of the mean-L=1000')
subplot(2,2,3),hist(Zn3,30),title('Distribution of the mean-L=10000')
subplot(2,2,4),hist(Zn4,30),title('Distribution of the mean-L=1000000')

SURNAME 4

Central Limit Theorem
50-Random variable

clc% clears the command window
NumberOfSample1=100; %specify the sample size 100
NumberOfSample2=1000; %%specify the sample size 1000
NumberOfSample3=10000; %%specify the sample size 10000
NumberOfSample4=1000000;%specify the sample size 1000000
NumberOfRandomVarible1=50; %specify the number of variable N=10
SizeParameter=4;
PopulationSize=10000000; %specify the population size
Population=random('Rayleigh',SizeParameter,PopulationSize,1); %population
%ofthe reylegh distribution with a parameter size 2
X1=zeros(NumberOfSample1,NumberOfRandomVarible1);%forms a matrix of
%NumberOfSample1*NumberOfRandomVarible1 matrix with all elements being
%Zeros
%The following for loop create NumberOfRandomVarible1 random variables each with NumberOfSample samples
for i=1:NumberOfRandomVarible1

SURNAME 5

X1(:,i)=Population(randperm(PopulationSize,NumberOfSample1));
end
X2=zeros(NumberOfSample2,NumberOfRandomVarible1);
for i=1:NumberOfRandomVarible1
X2(:,i)=Population(randperm(PopulationSize,NumberOfSample2));
end
X3=zeros(NumberOfSample3,NumberOfRandomVarible1);
for i=1:NumberOfRandomVarible1
X3(:,i)=Population(randperm(PopulationSize,NumberOfSample3));
end
X4=zeros(NumberOfSample4,NumberOfRandomVarible1);
for i=1:NumberOfRandomVarible1
X4(:,i)=Population(randperm(PopulationSize,NumberOfSample4));
end
% The following four lines compute the sum sn of all the samples
SumPerSample1=sum(X1);
SumPerSample2=sum(X2);
SumPerSample3=sum(X3);
SumPerSample4=sum(X4);
Mu=mean(Population);% Determine the mean for the population from which
%we sampled our data sample
Variance=var(Population);% Determine the variance for the population from which
%we sampled our data sample
Sigma=sqrt(Variance);
Zn1=((SumPerSample1-NumberOfSample1*Mu)./(Sigma*(sqrt(NumberOfSample1))))';
Zn2=((SumPerSample2-NumberOfSample1*Mu)./(Sigma*(sqrt(NumberOfSample2))))';
Zn3=((SumPerSample3-NumberOfSample1*Mu)./(Sigma*(sqrt(NumberOfSample3))))';

Zn4=((SumPerSample4-NumberOfSample1*Mu)./(Sigma*(sqrt(NumberOfSample4))))';
figure
subplot(2,2,1),hist(Zn1,30),title('Distribution of the mean-L=10')
subplot(2,2,2),hist(Zn2,30),title('Distribution of the mean-L=1000')
subplot(2,2,3),hist(Zn3,30),title('Distribution of the mean-L=10000')
subplot(2,2,4),hist(Zn4,30),title('Distribution of the mean-L=1000000')

SURNAME 6

Central Limit Theorem
100-Random variable

clc% clears the command window
NumberOfSample1=100; %specify the sample size 100
Num...