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Let {Xn |n ≥ 0} be a homogeneous Markov chain with state space S = {0, 1, 2, 3, 4} and transition probability matrix 

\(P=\begin{array}{r} \\ 0\\ 1\\ 2\\ 3\\ 4\end{array}\left(\begin{array}{ccccc}0&1&2&3&4\\ 1/4&0&0&3/4&0\\ 0&1&0&0&0\\ 1/3&2/3&0&0&0\\ 3/4&0&0&1/4&0\\ 1/8&1/8&1/2&1/8&1/8\end{array}\right)\)

Let α denote the probability that starting with state 4 the chain will eventually get absorbed in closed class {0, 3}. Then the value of α is 

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  1. \(\frac{6}{21}\)
  2. \(\frac{11}{21}\)
  3. \(\frac{8}{21}\)
  4. \(\frac{10}{21}\)

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Option 4 : \(\frac{10}{21}\)
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The Correct answer is (4).

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Q1.Let {Xn |n ≥ 0} be a homogeneous Markov chain with state space S = {0, 1, 2, 3, 4} and transition probability matrix  \(P=\begin{array}{r} \\ 0\\ 1\\ 2\\ 3\\ 4\end{array}\left(\begin{array}{ccccc}0&1&2&3&4\\ 1/4&0&0&3/4&0\\ 0&1&0&0&0\\ 1/3&2/3&0&0&0\\ 3/4&0&0&1/4&0\\ 1/8&1/8&1/2&1/8&1/8\end{array}\right)\) Let α denote the probability that starting with state 4 the chain will eventually get absorbed in closed class {0, 3}. Then the value of α is 
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