Question: My answer is below. Please verify my answer. Thank you! 1. Consider the Markov chain with state Space {0, 1, 2} and transition matrix 0

My answer is below. Please verify my answer. Thank you!

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. 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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