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If $X,Y \sim U(0,1)$, what is ${\Bbb E} (XY)$?

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If $X,Y \sim U(0,1)$, what is ${\Bbb E} (XY)$? That is, what is the expected value of the product of two uniformly distributed independent random variables? It is probably not $\frac14$? What is the exact value? How to derive the same?


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