Just answer B 17-42. At U of A, promotion from assistant to associate professor requires the equivalent of five points (years) of acceptable performance. Performance reviews are conducted once a year, and the candidate is given an average rating, a good rating, or an excellent rating. An average rating is the same as probation, and the candidate gains no points toward promotion. A good rating is equivalent to gaining one point, and an excellent rating adds two points. Statistics show that in any year 10% of the candidates are rated average and 70% are rated good, and the rest are rated excellent.

(a) Express the problem as a Markov chain.

(b) Determine the average number of years until a new assistant professor is promoted