a correlation puzzle between 2 geometric random variables - Quant版

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Quant版 - a correlation puzzle between 2 geometric random variables

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D**u
发帖数: 204

Randomly (also uniformly) choose 3 points A,B,C on a 2-dimensional sphere.
Let x be the spherical area of the spherical triangle ABC;
and y be the volume of the (Euclidean) 四面体 formed by A,B,C and O
(the center of the sphere).
If we treat x and y as 2 random varibles,
then what is the correlation between x and y?

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