2. (8 points) Depending on the input a computer program takes variable number of cycles to come up with the answer. Let X be the random variable which takes on the values k = 1, 2, 3, . .. , co for the number of cycles required to come up with the answer where co is the possibility that the program never arrives at an answer. (a) The probability mass function (p.m.f) for completing in k cycles is 2k Px ( k) = 3 k+1 ) k = 1, 2, 3, ... . What is the probability that the computer program never completes? (b) Use part (a) to find probability P(X 2 3). Write your answer in a simplest fraction. (c) Given that the program has not found the answer after 2 cycles, what is the probability that it will never find the