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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..?

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.