Have you come across order statistics? You will need to modify it slightly due to having correlation, but the central idea of order statistics should still apply to your situation.
Just came across this site, and I've enjoyed reading through some of the responses. I am hoping someone could help me with my problem.
I have been provided two normally correlated, dependent variables with a mean of zero and a standard deviation of 1 (N~(0,1)). I am trying to find the expectation, and the variance, of the maximum of the two random variables at hand. I know that the maximum is simply the joint cumulative distribution, and so in the independent case this is quite simple. However, I am unsure about how to go about this in the correlated case.
Given there is no "probability" section, it seemed appropriate to perhaps post my question here. Thanks ahead of time!