A PhD candidate in IOE 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.

- In the long run, what is the probability that the student is not doing research?
- The student is her office 50% of the time when doing research, 30 percent of the time while teaching and 20 percent of the time during service work, what proportion of the time is she in the office?

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