Expected Value of Max and Min

The Problem

Let $X_1,X_2,\dots ,X_n$ be i.i.d. $\text{Uniform}(0,1)$ random variables. Define $M_n=\max (X_1,\dots ,X_n)$ and $m_n=\min (X_1,\dots ,X_n)$.

1. Compute $\mathbb{E}[M_n]$ and $\mathbb{E}[m_n]$.
2. Compute $\text{Var}(M_n)$ and $\text{Var}(m_n)$.
3. Compute $\mathbb{E}[M_n-m_n]$ (the expected range).
4. Generalize: for i.i.d. $\text{Uniform}(0,1)$, find the expected $k$-th order statistic $X_{(k)}$.