(a) Find the stationary distributions of the cat chain and of the mouse chain.

(b) Note that there are 4 possible (cat, mouse) states: both in Room 1, cat in Room 1 and mouse in Room 2, cat in Room 2 and mouse in Room 1, and both in Room 2. Number these cases 1, 2, 3, 4 respectively, and let be the number of the current (cat, mouse) state at time n. Is a Markov chain?

Solution: Consult iTunes course for full detailed solutions.
(a.) For the cat Markov chain, the stationary distribution is (1/2, 1/2) by symmetry.
For the mouse Markov chain: solving sQ = s and normalizing yields (2/3, 1/3).
(b.) Yes, it is a Markov chain. Given the current (cat, mouse) state, the past history
of where the cat and mouse were previously are irrelevant for computing the
probabilities of what the next state will be

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