Let \(X_1,\cdots, X_n\) be random variables which are i.i.d. \(\text{unifom}(0,1)\). Let \(X_{(1)},\cdots, X_{(n)}\) be the associated order statistics.

1. Find the distribution of \(X_{(n/2)}\) when \(n\) is even.
2. Find \(\mathbf{E} [ X_{(n)} – X_{(1)} ]\).
3. Find the distribution of \(R=X_{(n)} – X_{(1)}\).