I was asked to give a simple example to show that $E[XY] = E[X]E[Y]$ is not necessarily true if and when $X$ and $Y$ are not independent. I can't seem to find a simple example without ending with a proof by induction. Thanks.
2026-03-26 11:05:16.1774523116
Expectation and Variance
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Let $X=-1$ with probability $1/2$, and let $X=1$ with probability $1/2$. Let $Y=X$.