What is the distribution of highest order statistics when the random variables follow exponential distribution with mean ??

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