## Posts Tagged ‘Absorbing States’

## Problem 1186

Identify the absorbing states in the transition matrix.

P =

**Solution:-**

Absorbing States and Transition Matrices

A state in a Markov chain is absorbing if and only if the row of the transition matrix corresponding to the state has a 1 on the main diagonal and 0’s elsewhere.

The row that corresponds 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.