9. Suppose the random variables Y, X, and are related through the model Y = 9.3 + 1.5X + , where has zero

9. Suppose the random variables Y, X, and ϵ are related through the model Y = 9.3 + 1.5X + ε, where ε has zero mean and variance σ2

ε = 16, σ2X

= 9, and X, ε are independent. Find the covariance of Y and X and that of Y and ε. (Hint. Write Cov(X,Y) = Cov(X, 9.3 + 1.5X + ε) and use part (4) of Proposition 4.4-5. Use a similar process for Cov(ε,Y).)