Question 1: Random Variables [20 marks] Two discrete random variables X and Y have the following support sets: \\ = {0,1} and ) = {-1,0, 1}. The joint probability mass function (pmf) describing the two random variables is given by the following table: Px. Y ( x, y ) -10 1 HO a) Determine whether X and Y are independent random variables. [6 marks] b) Compute the probability that X and Y are nonnegative, i.e., Pr(X 2 0, Y 2 0). [5 marks] c) Give the expectation of X + Y, i.e., E(X + Y). Is your result in a) relevant to this computation? [5 marks] d) Obtain the support and pmf of a new random variable Z defined as Z = Y2. /4 marks]