Question: 3.7. A component in a system is placed into service, where it operates until its failure, whereupon it is replaced at the end of the

3.7. A component in a system is placed into service, where it operates until its failure, 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 ak, for k = 1, 2, .... Let X,, be the remaining life of the component in service at the end of period n. Then X,, = 0 means that X,, will be the total operating life of the next component. Give the transition probabilities for the Markov chain

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