Let $X$ be a random variable and we want to choose $Y$ such that the following inequality is satisfied $$\mathbb{E}[XY]\leq 1.$$ We know that for example $Y=1/X$ is a choice. Among all acceptable random variables $Y$, what can we say about the one with the greatest expected value $\mathbb{E}[Y]$?
2026-03-28 13:32:24.1774704744
Find the random variable with the greatest expected value
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