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Math Help - On the correlation between two normal variables and the corr between their Z scores

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    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
    Last edited by Alonso; October 17th 2011 at 08:16 AM.
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