Suppose I have a set of $n$ real numbers, $\{x_1, x_2, \dots, x_n\}$.
I choose a uniformly random subset of size $m \le n$.
What is the expected maximum of the subset in terms of $n$, $m$ and $x_i$?
Suppose I have a set of $n$ real numbers, $\{x_1, x_2, \dots, x_n\}$.
I choose a uniformly random subset of size $m \le n$.
What is the expected maximum of the subset in terms of $n$, $m$ and $x_i$?