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Let X and Y have joint probability function as given in the table below. f ( x, y) -1 0 1 2 fz (y) -1 0.06 0.05 0.08 0.01 0.20 0 y 0.07 0.04 0.09 0.10 0.30 1 0.04 0.02 0.06 0.04 0.16 2 0.05 0.09 0.15 0.05 0.34 f1(x) 0.22 0.20 0.38 0.20 1 a) (2 mark) Are X and Y independent? Justify. b) (6 marks) Solve for the correlation coefficient of X and Y. Interpret the value. c) (3 marks) Find Cov(3X-2Y, 2X-Y+10). d) (1 marks) Find and tabulate the conditional probability function of X given Y=2. e) (3 marks) Find and tabulate the probability function of T=X+3Y