Using the Law of Iterated Expectations for Random Variables $X$ and $Y$, we know that $E[Y] = E[E[Y|X]]$. Therefore, we also know that $E[XY] = E[E[XY|Y]] = E[YE[X]]$. Is it also valid to say $E[XY^2] = E[E[XY^2|Y]] = E[Y^2E[X|Y]]$?
2026-04-26 08:39:35.1777192775
Law of Iterated Expectations for $E[XY^2]$
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