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Probability and Statistics: Let X and Y be independent random variables, and E(A) be the expectation of any random variable A. Simplify this expression: E(2XY - 2XE(Y) - 2YE(X) + 2E(X)E(Y)) I think it's supposed to be 0, by the way, but I just don't know how this turns out to be 0.

Mathematics
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*please note the correction: E(2XY... instead of E(4XY...
Do you know about Covariance? Somehow feel this plays a part.
yes, but how..?

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Well, what formula do you know about covariance that involve the expected value and independent random variables?
Thank you, I just figured out the solution (through looking deeper into covariance). This question is actually part of a larger proof that I'm trying to do, which is the variance of the sum of two independent random variables. I attached the proof, please review it if you wish, for correctness.
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