82. Let X1, X2,... be independent continuous random variables with a common distribution function F and density

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82. Let X1, X2,... be independent continuous random variables with a common distribution function F and density f = F

, and for k  1 let Nk = min{n  k: Xn = kth largest of X1,..., Xn}

(a) Show that P{Nk = n} = k−1 n(n−1), n  k.

(b) Argue that fXNk

(x) = f (x)(F¯

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