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From: DSPtree on 5 May 2010 14:37
Given 2 independent uniform random variables X,Y = U [0,1], consider the random variables Z = g (X,Y) for g (x,y) = sqrt (-2ln(x) ). cos(2piy)..This is the condition.So I need to go for matlab program as the analytic method is tough

1 - 10,000 uniformly distributed random samples for X and Y
2 - For each sample of X and Y, compute Z= g(X,Y)
3 - Draw a histogram over the resulting samples in Z
4 - Estimate the moments mZ for n = 1,2....6.
From: John D'Errico on 5 May 2010 19:01
DSPtree <paulscot45(a)yahoo.com> wrote in message <2024364947.79076.1273099076053.JavaMail.root(a)gallium.mathforum.org>...
> Given 2 independent uniform random variables X,Y = U [0,1], consider the random variables Z = g (X,Y) for g (x,y) = sqrt (-2ln(x) ). cos(2piy)..This is the condition.So I need to go for matlab program as the analytic method is tough
>
> 1 - 10,000 uniformly distributed random samples for X and Y
> 2 - For each sample of X and Y, compute Z= g(X,Y)
> 3 - Draw a histogram over the resulting samples in Z
> 4 - Estimate the moments mZ for n = 1,2....6.

Surely you have tried something? If not, why not?

John
From: Walter Roberson on 5 May 2010 19:16
DSPtree wrote:
> Given 2 independent uniform random variables X,Y = U [0,1], consider the random variables Z = g (X,Y) for g (x,y) = sqrt (-2ln(x) ). cos(2piy)..This is the condition.So I need to go for matlab program as the analytic method is tough
>
> 1 - 10,000 uniformly distributed random samples for X and Y
> 2 - For each sample of X and Y, compute Z= g(X,Y)
> 3 - Draw a histogram over the resulting samples in Z
> 4 - Estimate the moments mZ for n = 1,2....6.

Okay, go ahead, we give you permission to write such a program. If you
should happen to come up with a _specific_ Matlab question, then if you
indicate what you are having trouble with, we may be able to assist you.
From: DSPtree on 6 May 2010 01:54
clear all;
n=10000;
x=randn(1,n);
y=randn(1,n);
subplot(221);bar(x);subplot(222);bar(y);
z=sqrt(-2*log(x))*cos(2*pi*y');
t=hist(z,100);
subplot(212);plot(t);


This is what i have done till now. But I am not sure whether i could take z like that and plot it.
From: DSPtree on 6 May 2010 01:59
the plot shows a normal distribution i guess. shall i have to take some arbitary mean and sigma . this output looks little weird.
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