how to write the randn' s code with just using rand and CLT

I wrote this code but I didn't get the correct answer from it. i don't know where the problem is. thank for help

           clc
          clear all
          m = input( 'please enter the number of LINES:');
          n = input( 'please enter the number of ROWS:');

          y = zeros(m,n);
          G = zeros(m,n);
          x = rand(m,n);

            y= 0.2*x+32;
            s(1)=y(1);
            s(m*n)=sum(sum(y));
            for i= 3: m*n
                s(i-1)= s(i-2) + y(i-1);
            end
           G = zeros(m,n);

            for i= 1:m*n
                G(i) = s(i)/(i) ;
            end

            disp(G)
            hist(G)

[Walter Roberson]

What is CLT in this context?

[jgg]

I think your problem might be that rand generates numbers uniformly on [0,1]. I'm not at all clear what is going on with your code here, since it seems to be doing something specific, and not generally solving the problem, but you need to use rand to produce a variable with the same mean and variance. If you don't have that, you can't get anywhere in the first place. For instance, y here has mean 32.1 and variance of like approx 0.2/12

I'm assuming you directly want to do this using the CLT, and not just use the inverse of the normal CDF? Because that's way easier.

[alireza kooshafar]

@Walter Roberson

Central Limit Theorem

@jgg

thanks yes you are right about the fault but I have no idea about using Cumulative distribution function here

and I am just going to write randn's code by using rand and the way is not importent

[jgg]

If you don't care about the method, see the answer below.

Answer 1

[jgg]

Since you don't actually want to use the CLT, then inverse sampling is your solution.

 notrandn = @(n,m)(norminv(rand(n,m),0,1));
 out = notrandn(10000,1);  
 out2 = randn(10000,1);
 ecdf(out)
 hold on
 ecdf(out2)