Question

Literally in a desperate situation. Appreciate so much if any expert could give me a hand! Many thanks in advance!!!

Will give a thumb up afterwards definitely!

Problem 4. Let Xk be an independent identically distributed sequence o continuous real valued random variables on a probability space (Ý, F, P). Suppose that Xk models your result in match k N. We say that you achieve a personal best in m atch n N if Xn > Xk for all 1-k 〈 n. (a) (6p) Show that the probability that a personal best is achieved in match n E N equals . (b 6p Show that the expected number of personal bests that have been achieved by match n є N equals Ž k=1 k. (c) (8p) Let Y equal the minimum of all n > 1 such that a personal best is achieved in match n, if this minimum exists, and let Y-0 otherwise. Show that E(Y)oo.

Answer 1

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