Question: 4.4.1 Consider the Markov chain on f0;1g whose transition probability matrix is (a) Verify that .0;1/ D .=. C/;=. C// is a stationary distribution. (b)

4.4.1 Consider the Markov chain on f0;1g whose transition probability matrix is

0 0 1- 1 0

(a) Verify that .0;1/ D .=. C/;=. C// is a stationary distribution.

(b) Show that the first return distribution to state 0 is given by f .1/
00 D .1????/
and f .n/
00 D .1????????2 for n D 2;3; : : : :

(c) Calculate the mean return time

image text in transcribedand verify that π 0 = 1/m0.

0 0 1- 1 0

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