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Geoffrey Grimmett and David Stirzaker, (2009) Probability and random processes
4.14 Problems
page 147
61. Choose $P, Q,$ and $R$ uniformly at random within the convex region $C$ illustrated beneath.
By considering the event that four randomly chosen points form a triangle,
show that the mean area of the shaded region is three times the mean area of $\triangle PQR$. |
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