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2. At a sales agency, newly hired employees are classified as beginners (B) for one year. Every year the performance of each agent is reviewed. Past records indicate that transitions through the ranks to intermediate (I) and qualified (Q) can be modeled by the following Markov chain, where (F) indicates workers who were fired: B IQ F 1.5 .3 0 2 .1 .5 .3 .1 0 0 1 0 0 0 0 1 P= (a) What is the expected time until a beginner either becomes qualified or is fired? (b) Regarding your answer to part (a), how many of those years are expected to be in beginner rank, and how many are expected to be in intermediate rank? (c) What fraction of beginners eventually become qualified? (d) Given that an employee reaches intermediate status, what is the conditional probability they eventually become qualified? 2. At a sales agency, newly hired employees are classified as beginners (B) for one year. Every year the performance of each agent is reviewed. Past records indicate that transitions through the ranks to intermediate (I) and qualified (Q) can be modeled by the following Markov chain, where (F) indicates workers who were fired: B IQ F 1.5 .3 0 2 .1 .5 .3 .1 0 0 1 0 0 0 0 1 P= (a) What is the expected time until a beginner either becomes qualified or is fired? (b) Regarding your answer to part (a), how many of those years are expected to be in beginner rank, and how many are expected to be in intermediate rank? (c) What fraction of beginners eventually become qualified? (d) Given that an employee reaches intermediate status, what is the conditional probability they eventually become qualified

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