Question: 4.1. Consider the Markov chain on (0, 1} whose transition probability matrix is (a) Verify that (Iro, ir,) = ((3/(a + /3), al(a + (3))

4.1. Consider the Markov chain on (0, 1} whose transition probability matrix is

0 1 0

(a) Verify that (Iro, ir,) = ((3/(a + /3), al(a + (3)) is a stationary distribution.

(b) Show that the first return distribution to state 0 is given by f.(') _ (1 -

a) and f . " ' ) = a/3(1 - /3)i-2 f o r n = 2, 3, ... .

(c) Calculate the mean return time mo = Y,'_, nff'' and verify that Trp = 1 /mo.

0 1 0

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