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Post Closed as "Not suitable for this site" by user44191, Nate Eldredge, David White, ARG, Chris Godsil
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If the seta sequence $X_n$ of random variables XnRVs converges in probability to X$X$, does the real series E sequence $\mathbb{E}(XnX_n)$ also converge to E $\mathbb{E}(X)$?

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If the set of random variables Xn converges in probability to X, does the real series E (Xn) also converge to E (X)?

I couldn't find the answer in literature so any idea would be helpful.