Let $(X_n; n \geq 1)$ be a collection of independent positive identically distributed random variables, with density $f(x)$. They are inspected in order from $n = 1$. An observer conjectures that $X_1$ will be greater than all the subsequent $X_n, n \geq 2$. Show that this conjecture will be proved wrong with probability 1.

@Simple i'd probably compute the probability for any finite collection and deduce the result

@loch i will try that