# $\max(X_1, X_2, … X_n)$ mean value [duplicate]

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 $$\textrm{variance(Z)}$$?