I'm trying to find the mean and variance of $Y = \max(X_1, ..., X_n)$ where $X_i \sim \mathcal{N}(\mu_i, \sigma^2)$.
Note that the $X_i$ are independent, but not identically distributed. That is, they have the same variance $\sigma^2$ but different means $\mu_i$.
The answer to my previous question may help: Distribution of maximum of normally distributed random variables.