How to multiple set of normally distributed data?

I developed the following code to find the multiplication of 2 sets of random variables:

rng(0, 'twister');
b2=1.00;    % average
a2=0.50; % standard deviation
x2=a2.*randn(10000000,1)+b2;

rng(0, 'twister');
b1=0.23;  %average
a1=0.12;  %standard deviation
x1=a1.*randn(10000000,1)+b1;

x3=x2.*x1;
m1=mean(x3)
s1=std(x3)
c1=s1/m1;

Now I want to modify code by using "for" loop(target: to find x3=x2.*x1 for arrays of a1,a2,b1, b2)

rng(0, 'twister');
b2=[1.00];
a2=[0.50];
b1=[0.23];
a1=[0.12];

for i=1:length(b2)
x2=a2(i).*randn(10000000,1)+b2(i);
x1=a1(i).*randn(10000000,1)+b1(i);
x3(:,i)=x2.*x1;
m1(i)=mean(x3(:,i))
s1(i)=std(x3(:,i))
c1(i)=s1(i)/m1(i);
end

However, the resluts of "for" loop is not coincede with the results of previous method.

How can I solve this problem?

Answer 1

[dpb]

You rest the RNG before each of the two sets in first code segment but only at the beginning of the loop in the second so the two x1 sequences aren't the same.

No idea what the purpose of this might be for, but either

rng(0, 'twister');
b2=1.00;    % average
a2=0.50; % standard deviation
x2=a2.*randn(10000000,1)+b2;

%rng(0, 'twister');
b1=0.23;  %average
a1=0.12;  %standard deviation
x1=a1.*randn(10000000,1)+b1;

x3=x2.*x1;
m1=mean(x3)
s1=std(x3)
c1=s1/m1;

without changing the second code segment or

b2=[1.00];
a2=[0.50];
b1=[0.23];
a1=[0.12];

for i=1:length(b2)
  rng(0, 'twister');
  x2=a2(i).*randn(10000000,1)+b2(i);
  rng(0, 'twister');
  x1=a1(i).*randn(10000000,1)+b1(i);
  x3(:,i)=x2.*x1;
  m1(i)=mean(x3(:,i))
  s1(i)=std(x3(:,i))
  c1(i)=s1(i)/m1(i);
end

leaving the first unchanged will produce the same overall sequence of randn()

It makes no sense to me to do either in isolation here; I suppose there might be some situation this mimics that it would be a reason for one or the other cases this simulates.

[Kuhinur Shukurjonov]

Great. Thank you I got what I wanted. The code works well.