I have an exam in the morning and there is still one question I cannot do.
$X_1, \ldots, X_n$ are iid random variables each having distribution with density $f_{X_i}(x;\theta)= 1/\theta$, for $x \in [0,\theta]$ where $\theta>0$ compute the CDF of the random variable $\max(X_1,\ldots X_n)$ and prove that $n(\theta-\max(X_1,\ldots,X_n)) \to W$ in distribution and state the CDF of $W$.
How can I do this? I have worked out that the CDF of $\max(X_1,\ldots,X_n)$ is $ (x/\theta)^n$ but that is all :(
Thanks.