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.

 

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