Question: 3.3.7 A component in a system is placed into service, where it operates until its failure, whereupon it is replaced at the end of the

3.3.7 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 k, for k D 1;2; : : : . Let Xn be the remaining life of the component in service at the end-of-period n. Then, Xn D 0 means that XnC1 will be the total operating life of the next component.

Give the transition probabilities for the Markov chain fXng.

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