2. The computers in the Writing Center of a college are inspected at the end of each semester. If a computer needs minor repairs, it will be fixed. If the computer has crashed, it will be replaced with a new one. For k ≥ 0, let pk > 0 be the probability that a new computer needs to be replaced after k semesters. For a computer in use at the end of the nth semester, let Xn be the number of additional semesters it will remain functional.

Show that {Xn : n = 0, 1, . . .} is a Markov chain and find its transition probabilities