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Nov 15, 2019 at 11:13 comment added James Propp Perhaps I should have been clearer about “Are there...?” and “etc.” in my OP. I want to know whether formulas for more general expected values of this kind (e.g., the expected value of $X_1^2 X_2$) are already in the literature. I’ll modify the OP accordingly.
Nov 15, 2019 at 8:13 history answered Fedor Petrov CC BY-SA 4.0