Generating a random variable that has a predefined covariance with other random variable

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Solomon Gofere
Solomon Gofere 2014-11-1
评论： John D'Errico 2014-11-1
I wanted to generate a normal random variable which has a predefined co-variance with another random number. But I can't figure out how to proceed.Here is the specific problem,
I have e~N(0,1) and I want to generate X such that cov(x,e)=1 and E(X)=0. How can I generate this random number with sample size 500?
Thanks!

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Roger Stafford
Roger Stafford 2014-11-1
You haven't stated what you want the variance of X to be. If it is to be 1, the trivial solution would be to set X = e. For general var(X) = v (which must be greater than or equal to 1,) use this formula for generating X:
X = e(1:500) + sqrt(v-1)*randn(1,500);
where presumably 'e' and randn are statistically independent.

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Matt J
Matt J 2014-11-1
编辑：Matt J 2014-11-1
How about just setting X=e ?
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the cyclist
the cyclist 2014-11-1
编辑：the cyclist 2014-11-1
If you have the Statistics Toolbox, you can use the mvnrnd command.
If you don't, you can use Cholesky decomposition to do this. This page seems to have a pretty good explanation, and there is even some MATLAB code there.

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