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Problem 5.1 (10 points) The PSTAT Department at UCSB has developed a Markov model to simulate graduation rates in their programs. Students might drop out, repeat a year, or move on to the next year until they graduate. Students have a 3% chance of repeating their current year. First-years and sophomores have a 6% chance of dropping out. For juniors and seniors, the drop-out rate is 4%. Provide the state space S, the transition probability matrix for this Markov chain, and draw the associated transition graph