Consider the following joint pdf of variables X and Y. In your calculations below, correct all decimals to two places. Y -2 2 3 f(x) X 0.27 0.08 0.16 0.0 0.51 6 0 0.04 0.10 0.35 0.49 fly) 0.27 0.12 0.26 0.35 1 You are given E(X) = 4.47 and E(Y) =1.03 a. What are the probabilities that (i) Y=0, (ii) Y=2 given that X=6, and (iii) Y = 2 and X= 6. (1.5 points) b. Complete the following table, correcting to two decimal places. (2 points) fly [ X=3) fly | X=6) 27/51 =0.53 WNONK 16/51 =0.31 35/49=0.72 Then obtain the two conditional means and verify the law of iterated expectations. (3 points) c. The conditional distributions in b. should show a positive relationship between the conditional means E(Y |x) and x. Based on the two values of X in the distribution, determine AE(Y | X)/Ax. (1.5 points) d. It can be shown that ox 2= 2.25 and oy ? = 4.21. Given this information and your calculation in c., dermine Oxy, the covariance between X and Y. (2 points)