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Covariance Theorem: For independent X and Y,E[X.Y]=E[X].E[Y]. Theorem: For independent X and Y,Cov(X,Y)=0. Proof:Cov(X,Y)=E[(X-E[X])(Y-E[Y])] =E[X-EX☒]E[Y-E[Y] =0.Covariance Theorem: For independent X and Y , E[X ·Y ] = E[X]·E[Y ]. Theorem: For independent X and Y , Cov(X,Y ) = 0. Proof: Cov(X,Y ) = E[(X E[X])(Y E[Y ])] = E[X E[X]]E[Y E[Y ]] = 0