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Say I have the expression for $\mathrm{Cov}(X^2,Y)>0$, where both $X$ and $Y$ are known non-negative random variables. What if anything can we say about $\mathrm{Cov}(X,Y)$ without having to derive it from scratch? I think we can say that $\mathrm{Cov}(X,Y)>0$, but can we say anything more, given the expression for $\mathrm{Cov}(X^2,Y)$?

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