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for questions involving inequalities, upper and lower bounds.

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Randomly scaled random variables

Consider two possibly correlated scalar random variables $N$ and $X$. It is known that $1\leq N \leq N_{\max}$. Given that $\mathbb{E}[NX]\leq 0$, does it always hold that $\mathbb{E}[X] \leq 0$? Whi …
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