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.