Suppose $X_i \sim \exp(\theta), i = 1, \ldots, n$, iid. So the pdf is given by $f(x) = \exp(-x/\theta)/\theta, x>0$. Now I need to find the distribution of maximum of $X_i$ i.e. $X(n)=T$ (say).
So from cdf I got the pdf of $T$ as
$f(t)=n (1 - \exp(-t/\theta)^(n-1) \exp(-t/\theta)/\theta ,t>0$
But now I can not find the ${\cal E}(T)$ and $Var(T)$, I used by parts two time but I can not execute it properly. Will you please help me out
