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Suppose $X_1, X_2 ...X_n$ are non-correlated and Gaussian random variables, all with mean value $\mu=0$ and variance=$\sigma$.

Is there an expression for the distribution of $Z=\max(X_1, X_2, ... X_n)$? If not, can we find its expected value $\textrm{mean(Z)}$ and $\textrm{variance(Z)}$?

Thanks a lot!

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marked as duplicate by heropup, Lee David Chung Lin, mrtaurho, Daryl, Cesareo Apr 5 at 9:32

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