Let W1 < W2 < · · · < Wn be the order statistics of n independent observations from a U(0, 1) distribution.
(a) Find the pdf of W1 and that of Wn.
(b) Use the results of (a) to verify that E(W1) = 1/(n + 1) and E(Wn) = n/(n + 1).
(c) Show that the pdf of Wr is beta.