Let $X_1,...,X_n$ be i.i.d. and $X_{(1)}<...<X_{(n)}$ be the order statistics.
Assume $X_i\sim Unif(0,1)$. For any fixed k, find the asymptotic distribution of $nX_{(K)}$ as $n\rightarrow \infty$.
I know that density of $X_{(k)}$ is $f_{X_{(k)}}(x)=\frac{n!}{(k-1)!(n-k)!}x^{k-1}(1-x)^{n-k}$. I'm not sure how to use this information.
