Solution Found!
Let W1 < W2 < < Wn be the order statistics of n independent observations from a U(0, 1)
Chapter 6, Problem 6.3-6(choose chapter or problem)
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:
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 3
The PDF of a uniformly distributed variable over (0,1) is given as,
Also,
(a)
For , PDF of is,
For , PDF of is,