Suppose $S$ is a set of $n$ points in a plane. A point is called maximal (or Pareto-optimal) if no other point in $S$ is both above and to the right of that point.
If each point in $S$ is chosen independently and uniformly at random from the unit square $[0,1]\times [1,0]$. What is the exact expected number of Pareto-optimal points in $S$?