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Suppose X,Y are discrete random variables, each taking only two distinct values. Prove that if E(XY)=E(X)E(Y)...

Suppose X,Y are discrete random variables, each taking only two distinct values.

Prove that if E(XY)=E(X)E(Y) then X,Y are independent (Be aware that you have to prove E(XY) =E(X)E(Y) -> X,Y independent and NOT the converse)

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