Suppose that X and Y are discrete random vari- ables, each taking values 0, 1 and 2. Suppose that their joint probability mass function is given by the following table. 2 1 8. 8. 2 (a) Determine the value of a. (b) Find the (marginal) probability mass func- tions for each of X and Y. Are X and Y independent? (c) Find the mean and variance for each of X and Y. (d) Find the (cumulative) distribution func- tions for each of X and Y. 1/08 1/8