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 and the transition probability matrix for this Markov chain. Also draw the associated transition graph.