Let X(1), X(2), ..., X(n) be the order statistics of a set of n independent uniform (0, 1) random variables. Find the conditional distribution of X(n) given that X(1) = s(1), X(2) = s(2), ..., X(n-1)=s(n-1).

Let X(1), X(2), ..., X(n) be the order statistics of a set of n independent uniform (0, 1) random variables. Find the conditional distribution of X(n) given that X(1) = s(1), X(2) = s(2), ..., X(n-1)=s(n-1).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 42CR

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Let X(1), X(2), ..., X(n) be the order statistics of a set of n independent uniform (0, 1) random variables.
Find the conditional distribution of X(n) given that X(1) = s(1), X(2) = s(2), ..., X(n-1)=s(n-1).

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