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Four points are chosen uniformly and independently from the unit rectangle $(0,1)\times(0,1)$. What is the probability distribution of the area of their convex hull?

See also The PDF of the area of a random triangle in a square. An answer to this question has applications to What is the probability of having a pentagon in 6 points.

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    $\begingroup$ For what it's worth, the area of convex hull of four points is half of the sum of the areas of the four triangles generated by them. I don't know if it helps though. $\endgroup$ – JiK Oct 24 '16 at 11:15
  • $\begingroup$ @JiK Thanks. That is a very astute observation. $\endgroup$ – Otherwise Oct 24 '16 at 17:03
  • $\begingroup$ Perhaps slightly relevant: probability of forming a convex quadrilateral. $\endgroup$ – Lee David Chung Lin Feb 16 at 16:51

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