Posts Tagged ‘Absorbing States’

Problem 1186

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 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.