Posts Tagged ‘transition matrix’

Problem 1185

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

\begin{bmatrix}  0.0 & 0.00 &1.00 \\  0.0&1.0  & 0.0\\  0.0& 0.0 & 1.0  \end{bmatrix}

 

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.

\begin{bmatrix}  1.0 & 0.00 &0.00 \\  1.0&0.0  & 0.0\\  0.3& 0.7 & 0.0  \end{bmatrix}

 

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 = \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.

 

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

 

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

\begin{bmatrix}  0.0 & 0.0 &1.0 \\  0.0 & 1.0 & 0.0\\  0.0& 0.0 & 1.0  \end{bmatrix}

 

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} 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.

\begin{bmatrix}  1.0 & 0.0 &0.0 \\  1.0 & 0.0 & 0.0\\  0.3& 0.7 & 0.0  \end{bmatrix}

 

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} = 1.0

p_{22} = 0.0

p_{33} = 0.0

Since p_{11} equal 1, state 1 is the absorbing state.