Explanation Consider the given matrix to be P , P = 0 1 .8 .2 According to the definition of a transition matrix, P is the constant square matrix of order n such that the entries in the i -th row and j -th column indicate the probability of the system moving from the i -th state and j -th state onto the next observation and the sum of the entries of each row in the probabilities matrix must be 1 . Now, the given matrix is a constant square matrix of order 2 . Then, the sum of each row of the given matrix is, R 1 = 0 + 1 = 1 And, R 2 = .8 + .2 = 1.0 According to the definition of a regular Markov chain, the matrix P is regular if some power of P has only positive entries and the Markov chain is a regular Markov chain if its transition matrix is regular. Now, the entries in the given matrix are not positive because one entry is 0 . Now, multiply the matrices with each other. P 2 = P ⋅ P = 0 1

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Chapter 9.2, Problem 15E

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Whether the given matrix 01.8.2 is the transition matrix of a regular Markov Chain.

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