17. In a computerized classroom of a college, 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 remains functional.

Assuming that {Xn : n = 0, 1, . . .} is aMarkov chain with transition probabilitymatrix

show that {Xn : n = 0, 1, . . .} is irreducible, recurrent, and aperiodic. Find the longrun probability that a computer selected randomly at the end of a semester will last at least k additional semesters.

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P = P1 P2 P3 100 0 1 0 001