Suppose x and y are discrete random variable, I can write them in summation. And it seems like they are equal. Any ideas?

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It's $E[y|x<y]* P(x<y)$ on the second expression but otherwise fine yes. We can prove it using the law of total expectation without independence of $x,y$.

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  • $\begingroup$ He also states the variables are discrete, so one of the signs should be $\leq$ or $\geq$. $\endgroup$ – Raskolnikov Apr 27 '19 at 10:33

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