Order Statistics of the Uniform Distribution: Min, Max, and Range

Let $X_1, X_2, \ldots, X_n$ be iid $\text{Uniform}(0, 1)$ random variables. Denote the minimum by $X_{(1)}$ and the maximum by $X_{(n)}$.

(a) Derive the PDF of $X_{(1)}$ and the PDF of $X_{(n)}$.

(b) Compute $E[X_{(1)}]$ and $E[X_{(n)}]$.

(c) The range is $W = X_{(n)} - X_{(1)}$. Compute $E[W]$ for $n = 5$.