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.

Week 4: 9/129/18 Statistics Chapter 5: Probability Sections: 14 Probability ● Probability of an event is the sum of the probabilities of the sample points in the sample space for the event ● If an event is impossible, the probability of the event is 0 and if an event is a certainty, the probability of the event is 1 ● Unusual event is an event that has a low probability of occurring ● The classical method of computing probabilities requires equally likely outcomes ● Two events are disjo