Question: 9. If X(1), . . . , X(n) are the order statistics of a sample of size n from a population having a continuous c.d.f.

9. If X(1), . . . , X(n) are the order statistics of a sample of size n from a population having a continuous c.d.f. F(x) and p.d.f. f(x), show that F(x(n)) has mean n/(n + 1) and variance n/[(n + 1)2(n + 2)].

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