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Geoffrey Grimmett and David Stirzaker, (2009) Probability and random processes
4.14 Problems
page 14760. Choose P, Q, and R independently at random in the square S(a) of side a.
Show that 𝔼[PQR] = 11a2/144.
Deduce that four points picked at random in a parallelogram form a convex quadrilateral with probability (5/6)2. |
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