A component in a stystem is placed into service, where it operates until its failuer, whereupon it is replaced at the end of the period with a new component having statistically identical properties, and the process repeats. The probability that a component lasts for k periods is alpha_k, for k = 1,2,.... Let X_n be the remaining life of the component in service at the end-of-period n. Then, X_n means that X_n+1 will be the total operating life of the next component. Give the transition probabilities for the Markov chain {X_n}