Hi,
Sorry I took so long to see this. I'm interested in E(max(X_1,X_2,X_3)) where the X_i have arbitrary means mu_i and arbitrary variances sigma^2_i. But they are all independent, so the covariances are all zero. Do your calculations work for that case?
I've tried to find other material on...
Hello,
I'm also interested in this problem. Did you manage to get a general expression for E(max(X_1,X_2,X_3)), with arbitrary mean and covariance?
There is a paper by Charles E. Clark in Operations Research, 1961 that gets an exact analytic solution for two arbitrary normal random variables...