Question 6 and 7. Both these questions including parts with explanations.

(6) Give an example of a discrete random variable X such that IE(X\") = 3""1 for n = 1, 2, . . .. Then nd Var(X), and Var(X2). (7) The joint probability mass function of the random variables X and Y is given as f X34517, y) = C(m +y) for .7; = 0,1,2,3. (a) Find the value of c. (b) Find IP(X > Y). (c) Find IP(X + Y = 3)