Question 1

Every Markov process has at least one absorbing state.

Accepted Answer

A) True 
 B)False

Question 2

The Department of Motor Vehicles (DMV) has 4 stations for driver's license renewal:- fee payment
- eyesight test
- driving record check
- picture taking.
An applicant may start at any station and go from any station to any other station.Generally, an applicant will go to the unvisited station with the shortest line.If we model the stations as "states," can we use a Markov chain to model the DMV renewal process?

Accepted Answer

(No, since the next state dep

Question 3

All Markov processes eventually converge to a steady-state.

Accepted Answer

A) True 
 B)False

Question 4

A stage in a Markov process always corresponds to a fixed time period.

Accepted Answer

A) True 
 B)False

Question 5

Regarding a transition matrix which possesses an absorbing state:

Accepted Answer

A) All row values will not sum to 1. 
B) There will be a complementary absorbing state. 
C) At least two columns will be identical. 
D) That state's row will consist of a "1" and "0's". 
A) All row values will not sum to 1. 
B) There will be a complementary absorbing state. 
C) At least two columns will be identical. 
D) That state's row will consist of a "1" and "0's".

Question 6

What is the fundamental matrix for a Markov process with absorbing states?

Accepted Answer

A) A matrix composed of the identity submatrix, a zero submatrix, a submatrix of the transition probabilities between the non-absorbing states and the absorbing states, and a submatrix of transition probabilities between the non-absorbing states. 
B) A matrix representing the average number of times the process visits the non-absorbing states. 
C) The inverse of the identity matrix minus the matrix of the transition probabilities between the non-absorbing states and the absorbing states. 
D) The matrix product of the limiting transition matrix and the matrix of transition probabilities between the non-absorbing states. 
A) A matrix composed of the identity submatrix, a zero submatrix, a submatrix of the transition probabilities between the non-absorbing states and the absorbing states, and a submatrix of transition probabilities between the non-absorbing states. 
B) A matrix representing the average number of times the process visits the non-absorbing states. 
C) The inverse of the identity matrix minus the matrix of the transition probabilities between the non-absorbing states and the absorbing states. 
D) The matrix product of the limiting transition matrix and the matrix of transition probabilities between the non-absorbing states.

Question 7

In a Markov process, what determines the duration of a stage?

Accepted Answer

(A stage is a period

Question 8

Every week a charter plane brings a group of high-stakes gamblers into Las Begas.Half the group stays and begins gambling at Hot Slots near the Strip, and the other half is housed and begins gambling at Better Bandits, some distance away.(Both hotel/casinos are owned by the same corporation.)Once an hour, dedicated shuttle buses will transport to the other
casino any of the group members who wish to try their luck at the other casino.The transition probabilities are as follows:
$\begin{array}{c}\text { Next Hour }\\begin{array}{lcc} 
&\text { Hot Slots }&\text { Better Bandits }\
\text{This Hot Slots} & .8&.2 & \
\text{Hour Better Bandits} & .3 &  .7
\end{array}\end{array}$

A.After three hours, what proportion of these gamblers are in the Hot Slots Casino?
B.What is the long run average percentage of these gamblers who
will be at Hot Slots Casino?

Accepted Answer

a.(58.75%

Question 9

Steady-state probabilities are independent of the initial state if:

Accepted Answer

A) the number of initial states is finite. 
B) there are no absorbing states. 
C) the number of states and stages are equal. 
D) the process generates a fixed number of transient states. 
A) the number of initial states is finite. 
B) there are no absorbing states. 
C) the number of states and stages are equal. 
D) the process generates a fixed number of transient states.

Every Markov process has at least one absorbing state.

All Markov processes eventually converge to a steady-state.

A stage in a Markov process always corresponds to a fixed time period.

Regarding a transition matrix which possesses an absorbing state:

What is the fundamental matrix for a Markov process with absorbing states?

In a Markov process, what determines the duration of a stage?

Steady-state probabilities are independent of the initial state if:

Introduction to Management Science Models

Introduction to Management Science Models

Applications of Linear and Integer Programming Models

Network Models

Project Scheduling Models

Decision Models

Forecasting

Inventory Models

Queuing Models

Simulation Models

Quality Management Models

Nonlinear Models:dynamic, Goal, and Nonlinear Programming

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Exam 12: Markov Process Models

Every Markov process has at least one absorbing state.

All Markov processes eventually converge to a steady-state.

A stage in a Markov process always corresponds to a fixed time period.

Regarding a transition matrix which possesses an absorbing state:

What is the fundamental matrix for a Markov process with absorbing states?

In a Markov process, what determines the duration of a stage?

Steady-state probabilities are independent of the initial state if:

Introduction to Management Science Models

Introduction to Management Science Models

Applications of Linear and Integer Programming Models

Network Models

Project Scheduling Models

Decision Models

Forecasting

Inventory Models

Queuing Models

Simulation Models

Quality Management Models

Nonlinear Models:dynamic, Goal, and Nonlinear Programming

Filters