Let $X=\max\{X_1, X_2, \cdots, X_N\}$, where each $X_i \sim N(0,1)$ and are independent. What is the approximate value of $X$ for large $N$.
The term "approximate" isn't defined very clearly. I'm assuming it means the mean, but I can't really figure out a nice way to calculate that, since the PDF of the $N$th order statistic uses CDF of the normal.
Any thoughts would be appreciated.
Thanks in advance!