Let $X, Y,$ and $Z$ be random variables. Assume $X$ is independent of both $Y$ and $Z$. I know that $E[X|Z]=E[X]$. But is it true that $E[XY|Z]=E[X]*E[Y|Z]$?
Sorry for not using formatting.
Let $X, Y,$ and $Z$ be random variables. Assume $X$ is independent of both $Y$ and $Z$. I know that $E[X|Z]=E[X]$. But is it true that $E[XY|Z]=E[X]*E[Y|Z]$?
Sorry for not using formatting.
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