21. Let X_(i), i = 1, ..., n, denote the order statistics from a set of n uniform

(0, 1) random variables and note that the density function of X_(i) is given by f(x) =

$$

\frac{(n-1)!}{(i-1)!(n-i)!}x^{i-1}(1-x)^{n-i}

$$, 0 ≤ x ≤ 1

(a) Compute Var(X_(i)), i = 1, ..., n.

(b) Which value of i minimizes and which value maximizes Var(X_(i))?