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(b) Find the stationary distribution of the Markov chain. 

(c) Suppose X0 = 0. What is the expected number of steps until the first time the Markov chain will return to state 0? 


sol1.jpg

Screen Shot 2019-05-17 at 12.33.27 AM.png

1. Consider the Markov chain with state Space {0, 1, 2} and transition matrix 0 1 2
0 0.8 0.2 0
1 0.1 0.8 0.1
2 0 0.2 0.8 P: (a) Suppose X0 = 0. Find the probability that X2 : 0.

sol1.jpg

1( a)
0.8 0. 2 0 .
0 1 1 08 0 1
Lo
to fo. 8 ) + 0 . 02 +0
= 0. 68 + 0102
1 -
1(b) TIP - II
To = 018 To + 0. 1 7,
TO = 0. 2 To + 0.8 TT, + 0. 2 1/2
0.2 T, =0 21 0 + 0.2 1/ 2
21 1, - 2TTo = 2 1 /2
2To = 2 1 12
To = The
1 (0 ) = ) 4

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