Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Markov Chains
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
1
\(\frac{6}{21}\)
2
\(\frac{11}{21}\)
3
\(\frac{8}{21}\)
4
\(\frac{10}{21}\)