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# A PhD candidate typically must divide their time in the office between research, teaching, and service (ignoring coursework for now).

A PhD candidate typically must divide their time in the office between research, teaching, and service (ignoring coursework for now). The amount of time that she spends on each is exponentially distributed. If the candidate is conducting research, she will always switch to service or teaching, with equal probability, after an average of 50 minutes. When the candidate is teaching, she does so for an average of 40 minutes, and then switches to research with probability 0.6 or to the service with probability 0.4. When she is involved in service, she does so for an average of 15 minutes. After service, she always switches back to research.

1. Draw the CTMC rate diagram, clearly label your states and transition rates (qij 's)
2. Find the transition rates out of the states (vi's) and transition probabilities (Pij 's).
3. Find the limiting probabilities (make sure to write out the balance equations).

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