10 0 Problem 4: Consider a Markov chain {X„} on states {0,1,2} with a transition matrix P= 0 1 0 a b with a +b+c =1. 1. Compute the power P" for all n > 2; 2. Does the chain have a limiting...

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2; 2. Does the chain have a limiting distribution? If yes - compute this distribution; 3. Does the chain have a stationary distribution? Compute this distribution if it exists. "/>
Extracted text: 10 0 Problem 4: Consider a Markov chain {X„} on states {0,1,2} with a transition matrix P= 0 1 0 a b with a +b+c =1. 1. Compute the power P" for all n > 2; 2. Does the chain have a limiting distribution? If yes - compute this distribution; 3. Does the chain have a stationary distribution? Compute this distribution if it exists.