Hey:) Consider 3 points in 3D space that create a triangle with edges denoted with X,Y and Z. Let's say the points' locations are distributed according to an unknown distribution (maybe the pdf doesn't matter). My question is how am I able to find the E[XY] because as far as I know X and Y are obviously dependent. Is any case where the dependence between X and Y is almost negligible so as to approximate E[XY] as E[X]E[Y]? Running simulations I found that when the XYZ angle takes small values the approximation holds.
2026-04-03 17:55:32.1775238932
Mean of the product of two edges of a random triangle
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