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
2
$\begingroup$
probability
statistics
normal-distribution
-
0No, you do not use the correlation matrix but the cholesky-factor. This generalizes then immediately to arbitrarily many variables. – 2012-05-30
-
0Sorry but I fail to see the reason which prevents you from accepting this answer. – 2012-07-28
1 Answers
5
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.