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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 $S$?

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    +1 for an interesting and slightly unusual probability question. I am familiar with Pareto-optimality in economics but haven't previously encountered the concept in a pure maths context. Is the question prompted by any practical problem or relevant literature, or did it just occur to you?2012-10-04
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    This question is from the headbanging session of an undergraduate algorithms in the computer science department.2012-10-04
  • 0
    Nice question, which received a nice answer.2012-11-29

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