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

## Question:

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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