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[Maximum mark: 11]
A university shuttle travels around campus and serves four stops every 5 minutes.
The diagram below represents the probability that the bus travels to each stop from it's current position:
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- [3]
Write the transition matrix P for this Markov chain.
The shuttle is at the main library at noon.
- [2]
Find the probability (rounded to two decimal places) the shuttle is at the Residence Halls at 12:10 PM.
Let the column vector p be the long run proportion of time spent at each stop.
- [5]
Find p.
The university sets a policy that no stop should handle more than 35% of shuttle arrivals in the long run.
- [1]
Using your answer from (c), state whether the current routing meets this goal.
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