Question: A rat runs through the maze shown in Figure 11.7. At each step it leaves the room it is in by choosing at random one

A rat runs through the maze shown in Figure 11.7. At each step it leaves the room it is in by choosing at random one of the doors out of the room.
(a) Give the transition matrix P for this Markov chain.
(b) Show that it is an ergodic chain but not a regular chain.
(c) Find the fixed vector.
(d) Find the expected number of steps before reaching Room 5 for the first time, starting in Room 1.

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