Question 1

For a situation with weekly dining at either an Italian or Mexican restaurant,

Accepted Answer

A) the weekly visit is the trial and the restaurant is the state. 
B) the weekly visit is the state and the restaurant is the trial. 
C) the weekly visit is the trend and the restaurant is the transition. 
D) the weekly visit is the transition and the restaurant is the trend. 
A) the weekly visit is the trial and the restaurant is the state. 
B) the weekly visit is the state and the restaurant is the trial. 
C) the weekly visit is the trend and the restaurant is the transition. 
D) the weekly visit is the transition and the restaurant is the trend. A

Question 2

All Markov chains have steady-state probabilities.

Accepted Answer

A) True 
 B)False  False

Question 3

Bark Bits Company is planning an advertising campaign to raise the brand loyalty of its customers to 0.80.
a.The former transition matrix is as follows:
   
What is the new one? 
b.What are the new steady-state probabilities?
c.If each point of market share increases profit by $15,000,what is the most you would pay for the advertising?

Accepted Answer

a. b. π₁ = 0.5,π₂ = 0.5 c. The increase in market share is 0.5 − 0.444 = 0.056. (5.6 points) ($15,000/point)= $84,000 value for the campaign.

Question 4

All entries in a matrix of transition probabilities sum to 1.

Accepted Answer

A) True 
 B)False

Question 5

Steady-state probabilities are independent of initial state.

Accepted Answer

A) True 
 B)False

Question 6

Transition probabilities are conditional probabilities.

Accepted Answer

A) True 
 B)False

Question 7

A state i is a transient state if there exists a state j that is reachable from i,but the state i is not reachable from state j.

Accepted Answer

A) True 
 B)False

Question 8

The fundamental matrix is derived from the matrix of transition probabilities and is relatively easy to compute for Markov processes with a small number of states.

Accepted Answer

A) True 
 B)False

Question 9

In Markov analysis,we are concerned with the probability that the

Accepted Answer

A) state is part of a system. 
B) system is in a particular state at a given time. 
C) time has reached a steady state. 
D) transition will occur. 
A) state is part of a system. 
B) system is in a particular state at a given time. 
C) time has reached a steady state. 
D) transition will occur.

Question 10

All entries in a row of a matrix of transition probabilities sum to 1.

Accepted Answer

A) True 
 B)False

Question 11

A state,i,is an absorbing state if,when i = j,pij = 1.

Accepted Answer

A) True 
 B)False

Question 12

The probability that a system is in state 2 in the fifth period is π5(2).

Accepted Answer

A) True 
 B)False

Question 13

If a Markov chain has at least one absorbing state,steady-state probabilities cannot be calculated.

Accepted Answer

A) True 
 B)False

Question 14

The probability of reaching an absorbing state is given by the

Accepted Answer

A) R matrix. 
B) NR matrix. 
C) Q matrix. 
D) (I − Q)−1 matrix. 
A) R matrix. 
B) NR matrix. 
C) Q matrix. 
D) (I − Q)−1 matrix.

Question 15

If an absorbing state exists,then the probability that a unit will ultimately move into the absorbing state is given by the steady-state probability.

Accepted Answer

A) True 
 B)False

Question 16

State j is an absorbing state if pij = 1.

Accepted Answer

A) True 
 B)False

Question 17

A unique matrix of transition probabilities should be developed for each customer.

Accepted Answer

A) True 
 B)False

Question 18

Absorbing state probabilities are the same as

Accepted Answer

A) steady-state probabilities. 
B) transition probabilities. 
C) fundamental probabilities. 
D) None of these are correct. 
A) steady-state probabilities. 
B) transition probabilities. 
C) fundamental probabilities. 
D) None of these are correct.

Question 19

Markov process models

Accepted Answer

A) study system evolution over repeated trials. 
B) often study successive time periods. 
C) are often used when the state of the system in any particular period cannot be determined with certainty. 
D) All of these are correct. 
A) study system evolution over repeated trials. 
B) often study successive time periods. 
C) are often used when the state of the system in any particular period cannot be determined with certainty. 
D) All of these are correct.

Question 20

The probability that a system is in a particular state after a large number of periods is

Accepted Answer

A) independent of the beginning state of the system. 
B) dependent on the beginning state of the system. 
C) equal to one half. 
D) the same for every ending system. 
A) independent of the beginning state of the system. 
B) dependent on the beginning state of the system. 
C) equal to one half. 
D) the same for every ending system.

For a situation with weekly dining at either an Italian or Mexican restaurant,

All Markov chains have steady-state probabilities.

All entries in a matrix of transition probabilities sum to 1.

Steady-state probabilities are independent of initial state.

Transition probabilities are conditional probabilities.

A state i is a transient state if there exists a state j that is reachable from i,but the state i is not reachable from state j.

The fundamental matrix is derived from the matrix of transition probabilities and is relatively easy to compute for Markov processes with a small number of states.

In Markov analysis,we are concerned with the probability that the

All entries in a row of a matrix of transition probabilities sum to 1.

A state,i,is an absorbing state if,when i = j,p_ij = 1.

The probability that a system is in state 2 in the fifth period is π₅(2).

If a Markov chain has at least one absorbing state,steady-state probabilities cannot be calculated.

The probability of reaching an absorbing state is given by the

If an absorbing state exists,then the probability that a unit will ultimately move into the absorbing state is given by the steady-state probability.

State j is an absorbing state if p_ij = 1.

A unique matrix of transition probabilities should be developed for each customer.

Absorbing state probabilities are the same as

Markov process models

The probability that a system is in a particular state after a large number of periods is

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, finance, and OM

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 16: Markov Processes

For a situation with weekly dining at either an Italian or Mexican restaurant,

All Markov chains have steady-state probabilities.

All entries in a matrix of transition probabilities sum to 1.

Steady-state probabilities are independent of initial state.

Transition probabilities are conditional probabilities.

A state i is a transient state if there exists a state j that is reachable from i,but the state i is not reachable from state j.

The fundamental matrix is derived from the matrix of transition probabilities and is relatively easy to compute for Markov processes with a small number of states.

In Markov analysis,we are concerned with the probability that the

All entries in a row of a matrix of transition probabilities sum to 1.

A state,i,is an absorbing state if,when i = j,pij = 1.

The probability that a system is in state 2 in the fifth period is π5(2).

If a Markov chain has at least one absorbing state,steady-state probabilities cannot be calculated.

The probability of reaching an absorbing state is given by the

If an absorbing state exists,then the probability that a unit will ultimately move into the absorbing state is given by the steady-state probability.

State j is an absorbing state if pij = 1.

A unique matrix of transition probabilities should be developed for each customer.

Absorbing state probabilities are the same as

Markov process models

The probability that a system is in a particular state after a large number of periods is

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, finance, and OM

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

A state,i,is an absorbing state if,when i = j,p_ij = 1.

The probability that a system is in state 2 in the fifth period is π₅(2).

State j is an absorbing state if p_ij = 1.