\fSuppose X and Y are two independent random variables with the following probability distributions: X = x -1 0 1 Y = y 1 0 1 P(X = 2) 0.30 0.40 0.30 and P(Y = y) 0.40 0.20 0.40 The random variables S and T are defined as: S = X2 + Y2 and T = X+Y. (a) Construct the table of the joint probability distribution of S and T. (8 marks)