Question: 3.2.1 Consider the Markov chain whose transition probability matrix is given by Suppose that the initial distribution is pi D 14 for i D 0;1;2;

3.2.1 Consider the Markov chain whose transition probability matrix is given by

0 1 2 3 00.4 0.3 0.2 0.1 1 0.1 0.4 0.3

Suppose that the initial distribution is pi D 14 for i D 0;1;2; 3. Show that PrfXn D kg D 1 4 ; k D 0;1;2; 3, for all n. Can you deduce a general result from this example?

0 1 2 3 00.4 0.3 0.2 0.1 1 0.1 0.4 0.3 0.2 P = 2 0.3 0.2 0.1 0.4 3 0.2 0.1 0.4 0.3

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