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Let X i , . . . , X n be an independent and identically distributed sequence of Exponential(1) random variables, where n 3. Find
Let Xi, . . . , Xn be an independent and identically distributed sequence of Exponential(1) random variables, where n 3. Find the conditional probability density function for the maximum M = X(n) given that the second smallest X(2) = 1. Use this to verify that, in the case that n = 4,
E(M X(2) = 1) = 2e2 2e.
Hint: Start by using the "PDF method" to find the density for X(2) and the joint density for (M, X(2)).
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