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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!

Mike Meng
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    https://math.stackexchange.com/questions/89030/expectation-of-the-maximum-of-gaussian-random-variables seems relevant – Nap D. Lover Apr 04 '19 at 02:16

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