Question: 2.19 Let X(n) be the largest value in a sample of size n from the pdf fX. (a) Show that limn!1 P(n1X(n) x)

2.19 Let X(n) be the largest value in a sample of size n from the pdf fX.

(a) Show that limn!1 P(n1X(n)  x) ¼ exp (a=px) if fX(x) ¼ a/[p(a2+x2)] (Cauchy).

(b) Show that limn!1 P(n2X(n)  x) ¼ exp (

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