Let W1 < W2 < ··· < Wn be the order statistics of n independent observations from a U(0, 1) distribution.
(a) Show that E(Wr2) = r(r + 1)/(n + 1)(n + 2), using a technique similar to that used in determining that E(Wr) = r/(n + 1).
(b) Find the variance of Wr.