Suppose an unweighted random number generator outputs a random integer in the range $[0,u]$, and suppose I generate $n$ numbers and store the maximum number generated, $m$. Given only $m$ and $n$, can I find a probability distribution function for $u$?
This seems doable, since the $m=u$ should be true for an infinite number of trials, and it makes intuitive sense to me that as $n-m$ grows, the mode of the pdf increases in magnitude and shifts closer to $m$ and vice versa. However, as far as rigourously explaining why and finding a general solution goes, I'm stumped.
