## Posts Tagged ‘transition matrix’

## Problem 1185

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

**Solution:-**

A state is an absorbing state of a Markov chain if P_{ii}=1. Thus, check the entries P_{11, }P_{22, }and P_{33 }to see if any of them are equal to 1.

P_{11} = 0.0

P_{22} = 1.0

P_{33} = 1.0

Since P_{22 }and P_{33} 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 P_{ii}=1. Thus, check the entries P_{11, }P_{22, }and P_{33 }to see if any of them are equal to 1.

P_{11} = 1.1

P_{22} = 0.0

P_{33} = 0.0

Since P_{11} 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.