3. (5 Points) Let two random variables X and Y are jointly distributed with finite means and variances. Show that, for any 4 constants a, b, c, d, e, f; Cov(aX+by+e, cX+dY+f) = acx Var(X) + bd × Var(Y) + (ad + bc) × Cov(X, Y) [Hint: Recall Cov(X,Y)= E(XY) – E(X)E(Y) for any two random variables X and Y. Try to write down the Covariance term in Expectation of product of certain quantities, then expand the term inside expectation and use linearity of expectation]

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