Problem 1183

Identify the absorbing states in the transition matrix.

P = $\begin{bmatrix} 0.5&0.2 &0.1 &0.2 \\ 0& 0 &1 &0 \\ 0& 0 & 1 &0 \\ 0& 0 &0 &1 \end{bmatrix}$

Solution:-

Absorbing States and Transition Matrices

A state in a Markov chain to A does not have a 1 on the main diagonal, so therefore, A is not an absorbing state.

The row that corresponds to B does not have a 1 on the main diagonal, so therefore, B is not an absorbing state.

The row that corresponds to C has a 1 on the main diagonal, so therefore, C is an absorbing state.

The row that corresponds to D has a 1 on the main diagonal, so therefore, D is an absorbing state.