![Let (X.) be a Marko chain with the state space (1.2,3) and transition proba- bility matrix 0 4 6 P 25 75 0 4 0 6 Let the initial distribution be q(0) [1(0), q2(0), s(0) [0.4, 0.2, 0.4] (a) Find ELX. (b) Calculate PlX,-2, X,-2, X,-11X,-1]. (c) To what matrix will the n-step transition probability matrix converge when n is very large? Your solution should be accurate to two decimal places.](http://img.homeworklib.com/questions/2ce52ac0-f150-11eb-8caa-ebc7a593a658.png?x-oss-process=image/resize,w_560)
Homework Answers
b)
P(X1 = 2 , X2 = 2 , X3 = 1 |X0 = 1) = P12*P22*P21
= 0.4 * 0.75*0.25
= 0.075
c)
P^n when n tend to infinity =
0.2439
0.39024 0.36585
0.2439
0.39024 0.36585
0.2439
0.39024 0.36585
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