_{Don't copy the answers from others! Those are not clear and incorrect, and I won't accept it. Thank you}

ASSIGNMENT 3 Problem 2. Let (Xx), be an independent identically distributed sequence of continuous real-valued random variables on a probability space (2, F, P). Suppose that Xx models your result in match k ( N. We say that you achieve a personal best in match n ( N if X, > Xx for all 1 1 such that a personal best is achieved in match n, if this minimum exists, and let Y = 0 otherwise. Show that E(Y) = co. Hint: you can use the result of exercises from the problem sets without proof, and there is something in problem set 3 that might help here