2. A hard drive in a data center lasts k periods before failing with probability ask, for k = 1,2, . . .. Let X: be the remaining life of the hard drive in service at the end of period 15. Thus, Xt = 0 means that X+1 will be the total operating lifetime of the next hard drive installed. Is {Xi} a Markov chain? Explain your answer. If it is a Markov chain, give the transition probabilities; if it is not, give an example where the Markov property is violated. (4 points.)