# Question

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.

(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.

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