Question: =+2.19. Let Xn be the largest value in a sample of size n from the population fx. a Show that limn!1 Pn1Xn 4x expa=px

=+2.19. Let XðnÞ be the largest value in a sample of size n from the population fx.

ðaÞ Show that limn!1 Pðn1XðnÞ 4xÞ ¼ expða=pxÞ if fX ðxÞ ¼ a=½pða2 þ x2Þ

(Cauchy).

ðbÞ Show that limn!1 Pðn2XðnÞ 4xÞ ¼ expða ffiffiffiffiffiffiffiffiffiffi 2=px p Þ if fX ðxÞ ¼

ða= ffiffiffiffiffi 2p p Þx3=2 expða2=2xÞ for x50.

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