# Thread: On the correlation between two normal variables and the corr between their Z scores

1. ## On the correlation between two normal variables and the corr between their Z scores

Hey, guys,

I have two correlated normal variables:

X1 ~ N(mu1,var1)
X2 ~ N(mu2, var2)

with correlation

corr(X1,X2) = rho.

where:

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)

where

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.

Alonso