The random variables X and Y have joint probability distribution specified by the following table: Please provide all answers to the following to three decimal places. (a) Find the expectation of XY. (b) Find the covariance Cov(X, Y) between X and Y. (c) What is the correlation between X and Y? y=1|y-2 y=3 x=1 0.30 0.05 0.00 x=2 0.05 0.20 0.05 x=3 0.00 0.05 0.30 (d) Suppose the random variables X and Y above are connected to random variables U and V by the relations What is the covariance Cov(U, V)? (e) What is the correlation between U and V? X = 5U +3 Y = 6V +4

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