Consider two independent random variables (r.v.'s) X and Y. The support sets of these r.v.'s are " = {-1, 0, 1} and ) = {-1, 1}, respectively. The probability mass function (pmf) of X is px(-1) = 1. px(0) = ; and px(1) = 2. whereas the pmf of Y is py(-1) = ; and py (1) = 1. Consider the r.v. Z defined by the sum of X and Y, i.e., Z = X + Y. a) Give the support set of r.v. Z and its pmf. [10 marks) b) Give the joint pmf pz.v(z, y), using the Bayes theorem. (10 marks]