A mouse runs through the maze shown below. At each step it leaves the room it is in by choosing at random one of the doo
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A mouse runs through the maze shown below. At each step it leaves the room it is in by choosing at random one of the doo
A mouse runs through the maze shown below. At each step it leaves the room it is in by choosing at random one of the doors out of the room. 1 5 3 4 a) Give the transition matrix P for this Markov chain. (6 p.) b) Find the stationary probabilities of each stage. (10 p.) c) Now suppose that a piece of cheese is placed on a deadly trap in Room 5. The mouse starts in Room I. Find the expected number of steps before reaching Room 5 for the first time, starting in Room 1. (4 p.) d) Find the expected time to return to Room 1. (10 p.)
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