Let W1 < W2 < · · · < Wn be the order statistics of n

Chapter 6, Problem 6E

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QUESTION:

Problem 6E

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.

Questions & Answers

QUESTION:

Problem 6E

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.

ANSWER:

Step 1 of 4

The PDF of a uniformly distributed variable over (0,1) is given as,

                   

Also,

                     

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