Question 1

All Markov chain transition matrices have the same number of rows as columns.

Accepted Answer

A) True 
 B)False  True

Question 2

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  True

Question 3

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. B

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

The fundamental matrix is used to calculate the probability of the process moving into each absorbing state.

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

A transition probability describes

Accepted Answer

A) the probability of a success in repeated, independent trials. 
B) the probability a system in a particular state now will be in a specific state next period. 
C) the probability of reaching an absorbing state. 
D) None of the alternatives is correct. 
A) the probability of a success in repeated, independent trials. 
B) the probability a system in a particular state now will be in a specific state next period. 
C) the probability of reaching an absorbing state. 
D) None of the alternatives is correct.

Question 8

A state i is an absorbing state if pii = 0.

Accepted Answer

A) True 
 B)False

Question 9

All Markov chains have steady-state probabilities.

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

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 12

Steady state probabilities are independent of initial state.

Accepted Answer

A) True 
 B)False

Question 13

At steady state

Accepted Answer

A)  $\pi $1(n+1) >  $\pi $1(n) 
B)  $\pi $1 =  $\pi $2 
C)  $\pi $1 +  $\pi $2 > 1 
D)  $\pi $1(n+1) =  $\pi $1 
A)  $\pi $1(n+1) >  $\pi $1(n) 
B)  $\pi $1 =  $\pi $2 
C)  $\pi $1 +  $\pi $2 > 1 
D)  $\pi $1(n+1) =  $\pi $1

Question 14

Markov processes use historical probabilities.

Accepted Answer

A) True 
 B)False

Question 15

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.

Question 16

Analysis of a Markov process

Accepted Answer

A) describes future behavior of the system. 
B) optimizes the system. 
C) leads to higher order decision making. 
D) All of the alternatives are true. 
A) describes future behavior of the system. 
B) optimizes the system. 
C) leads to higher order decision making. 
D) All of the alternatives are true.

Question 17

Absorbing state probabilities are the same as

Accepted Answer

A) steady state probabilities. 
B) transition probabilities. 
C) fundamental probabilities. 
D) None of the alternatives is true. 
A) steady state probabilities. 
B) transition probabilities. 
C) fundamental probabilities. 
D) None of the alternatives is true.

Question 18

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.

Question 19

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 20

A Markov chain cannot consist of all absorbing states.

Accepted Answer

A) True 
 B)False

Exam 16: Markov Processes

All Markov chain transition matrices have the same number of rows as columns.

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.

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

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

The fundamental matrix is used to calculate the probability of the process moving into each absorbing state.

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

A transition probability describes

A state i is an absorbing state if pii = 0.

All Markov chains have steady-state probabilities.

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

The probability of reaching an absorbing state is given by the

Steady state probabilities are independent of initial state.

At steady state

Markov processes use historical probabilities.

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

Analysis of a Markov process

Absorbing state probabilities are the same as

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

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.

A Markov chain cannot consist of all absorbing states.

Introduction

Introduction to Linear Programming

LP Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications

Advanced Linear Programming Applications

Distribution and Network Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

LP: 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 p_ii = 0.