How do I construct two correlated random variables with correlation $\rho$ given two i.i.d normal r.v.? Do I just multiply the correlation matrix by a vector generated with two i.i.d normal variables?
Constructing correlated random variables
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probability
statistics
normal-distribution
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0Sorry but I fail to see the reason which prevents you from accepting this answer. – 2012-07-28
1 Answers
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If $X$ and $Y$ are independent random variables with the same variance, then
$Z = \rho X + \sqrt{1-\rho^2} Y$
is a random variable such that ${\rm Corr}(X,Z)=\rho$.
Additionally, if $X$ and $Y$ are standard normal, then $Z$ is also standard normal.