If $X$ and $Y$ are independent random variables, is the following statement true: $E(XYX)=E(X)E(Y)E(X)$? I am somewhat confused about this expectation of the product. Thanks in advance.
2026-04-01 12:49:13.1775047753
Expectation of product of random variables
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No. If $Y=1$ then $X$ and $Y$ are independent for any $X$. Your equation becomes $EX^{2}=(EX)^{2}$ which is true only whne $X$ is a.s. constant.