## expected maximum value

This problem wasn't encountered during a statistics or probability course, but from some original research I am doing.

Specifically, there are independent random variables $X_{1},X_{2}, ..., X_{n}$, with $E[X_{i}] = Y$ for all $1 \le i \le n$.

Then I'm trying to find $M = E[max_{i=1}^{n}(X_{i})]$

As n increases, M should get larger. My gut tells me it should be something like $Y \log{n}$ but I don't know how to even set the problem up. I haven't taken probability and statistics yet, so my knowledge is gleaned from google searches and intuition.