Suppose that a random variable X with a probability function mass given by:  () = (0.5) 2 ^  ;  = 0, 1, 2,  (a) Show that f (x) is a probability mass function. (b) Calculate  (3    7),  (3 <  7),  (3 < <7). (c) Calculate the distribution function for  = 0, 1, 2,  (all integers), as well as x = 3, 5. (d) Calculate the conditional probability  (X> k + j | X> k) for  = 0, 1, 2,  (e) Calculate the generating function of the moments M (t) of X. Hint: you have to work with geometric series