Solution Found!
Let W1 < W2 < · · · < Wn be the order statistics of n
Chapter 6, Problem 6E(choose chapter or problem)
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,