I have two correlated normal variables:
X1 ~ N(mu1,var1)
X2 ~ N(mu2, var2)
corr(X1,X2) = rho.
mu1 = mean for the random variable 1
mu2 = mean for the random variable 2
var1 = variance for the random variable 1
var2 = variance for the random variable 2
If one creates Z scores (standard normal Z scores) from X1 and X2, so that:
Z1 = (X1-mu1)/sqrt(var1)
Z2 = (X2-mu2)/sqrt(var2)
sqrt = square root
Does it make sense that corr(Z1,Z2) is equal to corr(X1,X2)?
Perhaps I am doing something wrong, but this is exactly what I got here with simple simulations.
Grateful for any tips.