Let $X_1, X_2, \ldots$ be independent and identically distributed continuous random variables. Let $N$ be the smallest value of $n$ for which $X_n > X_1$. Show that $P(N > k) = 1/k$ (for $k = 1, 2, \ldots$) and hence that $P(N = k) = 1/[k(k-1)]$. What is $E(N)$?
I have no idea where to start, any hint/sketch of the solution would be much appreciated. Thank you!
Does E(N) exist, since using the definition gives the harmonic series which diverges