Expected value for product of three dependent random vars

[hllee]

This was posted on a closed thread a while back without a real answer:

While the two-variable case is easy enough: E[X⋅Y]=Cov[X,Y]+E[X]⋅E[Y]
Does anybody know how to express the product of THREE dependent RVs? In other words, given three RV called X, Y, and Z, I want to derive:

E[X⋅Y⋅Z]=... ?

 

[Greg Bernhardt]

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