While I have seen papers and posts about mean and variance of n i.i.d normal random variables, I am looking for the first order statistics of $n$ (specifically $11$) normal, non-identical (different mean and variances) but independent random variables. Specifically :
- What distribution would that follow? Can it be approximated to known distributions?
- What would be the mean and variance?
I am currently using Monte-carlo simulation for finding this, but would like a more direct value to save computational time.