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**marko612** A high jumper achieves heights X0, X1... which are IID with pdf f and a strictly increasing F. We take X0 to be her first record. Her next record is achieved at "time T", where T=n if Xn>X0 and Xj<=X0, j=1,2...n-1. Show P(T=n) = 1/n(n+1)

I have this following answer:

P(T=n) = P(X0 is the highest among X0 to Xn-1 AND X0 is the highest among X0 to Xn)

Since they are independent,

= P(X0 is the highest among X0 to Xn-1)*P(X0 is the highest among X0 to Xn)

= 1/n * 1/(n+1)

because there is only 1/n chance for X0 to be the highest for the first X0 to Xn-1 (total n trials), and 1/n+1 chance for Xn to be the highest among the X0 to Xn (n+1 trials)

This is my thought, I just want to check if there is any problems if I approach the question in this way, because my TA keeps telling me I have to use conditional probabilities