1.13. Consider the Markov chain with transition matrix: 1 0 0 0.1 0.9 2 0 0...

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1.13. Consider the Markov chain with transition matrix: 1 0 0 0.1 0.9 2 0 0 0.6 0.4 3 0.8 0.2 0 0 4 0.4 0.6 0 0 (a) Compute p2. (b) Find the stationary distributions of p and all of the stationary distributions ofp2. (c) Find the limit of p2n(x, x) as n → oo.

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Answer 1

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Solution : @ civen PE Co o 0.1 0.97 L03 0.2 0 0 Now we will find p? : Р: РxP 1000! 0.97 To O 10 o 0.6 0.4 0 0 0.8 0.2 0. 0 0.

(2 b. for stationary distribution of D, we request to find row vector x? Such that xx P = x So, we have to solve [a bed] - [

abcd7 г., т. о. цн 0. 56 | с. 64 o- Ф о | o o е o с. 2 o <a о o oss p. 6 o4ot c-4 ст. This gives а О.Саха + O • 6ч хь b = 0:5

... La 7x gente sempre a sisse ] S-1579 8-15% 244 12 cohere ocasa This gives all the stationary - distributions of p² (c.) qu

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