## Problem 1185

Find the absorbing state(s) for the transition matrix shown.

Solution:-

A state is an absorbing state of a Markov chain if Pii=1. Thus, check the entries P11,  P22, and P33 to see if any of them are equal to 1.

P11 = 0.0

P22 = 1.0

P33 = 1.0

Since P22 and P33 equals 1, state 2 and 3 are absorbing state.

## Problem 1184

Find the absorbing state(s) for the transition matrix shown.

Solution:-

A state is an absorbing state of a Markov chain if Pii=1. Thus, check the entries P11,  P22, and P33 to see if any of them are equal to 1.

P11 = 1.1

P22 = 0.0

P33 = 0.0

Since P11 equals 1, state 1 is the absorbing state.

## Problem 1183

Identify the absorbing states in the transition matrix.

P =

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.

## Find the absorbing state(s) for the transition matrix shown.

Find the absorbing state(s) for the transition matrix shown.

Solution

A state is an absorbing state of  a Markov chain if = 1. Thus, check the entries , , and to see if any of them are equal to 1.

= 0.0

= 1.0

= 1.0

Since and equal 1, state 2 and 3 are absorbing state.

## Find the absorbing state(s) for the transition matrix shown

Find the absorbing state(s) for the transition matrix shown.

Solution

A state is an absorbing state of  a Markov chain if = 1. Thus, check the entries , , and to see if any of them are equal to 1.

= 1.0

= 0.0

= 0.0

Since equal 1, state 1 is the absorbing state.