Question 1

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 2

Calculate the steady state probabilities for this transition matrix.

Accepted Answer

The answer of Calculate the steady state probabilities for this...

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

The medical prognosis for a patient with a certain disease is to recover, to die, to exhibit symptom 1, or to exhibit symptom 2. The matrix of transition probabilities is   ​ 
a.What are the absorbing states?
b.What is the probability that a patient with symptom 2 will recover?

Accepted Answer

a.States 1 and 2 (recover and

Question 5

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 6

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 7

Henry, a persistent salesman, calls North's Hardware Store once a week hoping to speak with the store's buying agent, Shirley. If Shirley does not accept Henry's call this week, the probability she will do the same next week is .35. On the other hand, if she accepts Henry's call this week, the probability she will not do so next week is .20.
a.Construct the transition matrix for this problem.
b.How many times per year can Henry expect to talk to Shirley?
c.What is the probability Shirley will accept Henry's next two calls if she does not accept his call this week?
d.What is the probability of Shirley accepting exactly one of Henry's next two calls if she accepts his call this week?

Accepted Answer

The answer of Henry, a persistent salesman, calls North's Hardware...

Question 8

Steady state probabilities are independent of initial state.

Accepted Answer

A) True 
 B)False

Question 9

​What assumptions are necessary for a Markov process to have stationary transition probabilities?

Accepted Answer

For a Markov process to have stationary

Question 10

Appointments in a medical office are scheduled every 15 minutes. Throughout the day, appointments will be running on time or late, depending on the previous appointment only, according to the following matrix of transition probabilities:   ​ 
a.The day begins with the first appointment on time. What are the state probabilities for periods 1, 2, 3 and 4?
b.What are the steady state probabilities?

Accepted Answer

a.π(0) = (1, 0)π(1) = (.75, .2

Question 11

For Markov processes having the memoryless property, the prior states of the system must be considered in order to predict the future behavior of the system.

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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 14

On any particular day an individual can take one of two routes to work. Route A has a 25% chance of being congested, whereas route B has a 40% chance of being congested.
The probability of the individual taking a particular route depends on his previous day's experience. If one day he takes route A and it is not congested, he will take route A again the next day with probability .8. If it is congested, he will take route B the next day with probability .7.
On the other hand, if on a day he takes route B and it is not congested, he will take route B again the next day with probability .9. Similarly if route B is congested, he will take route A the next day with probability .6.
a.Construct the transition matrix for this problem. (HINT: There are 4 states corresponding to the route taken and the congestion. The transition probabilities are products of the independent probabilities of congestion and next day choice.)
b.What is the long-run proportion of time that route A is taken?

Accepted Answer

​ @#IMG-DLM& ​
b. .3

Question 15

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 16

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 17

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 18

State j is an absorbing state if pij = 1.

Accepted Answer

A) True 
 B)False

Question 19

A television ratings company surveys 100 viewers on March 1 and April 1 to find what was being watched at 6:00 p.m. -- the local NBC affiliate's local news, the CBS affiliate's local news, or "Other" which includes all other channels and not watching TV. The results show
​
​   ​ 
a.What are the numbers in each choice for April 1?
b.What is the transition matrix?
c.What ratings percentages do you predict for May 1?

Accepted Answer

​
a.​
NBC

Question 20

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

Accepted Answer

A) True 
 B)False

A transition probability describes

Calculate the steady state probabilities for this transition matrix.

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

The medical prognosis for a patient with a certain disease is to recover, to die, to exhibit symptom 1, or to exhibit symptom 2. The matrix of transition probabilities is a.What are the absorbing states? b.What is the probability that a patient with symptom 2 will recover?

Absorbing state probabilities are the same as

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

Steady state probabilities are independent of initial state.

What assumptions are necessary for a Markov process to have stationary transition probabilities?

For Markov processes having the memoryless property, the prior states of the system must be considered in order to predict the future behavior of the system.

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

The probability of reaching an absorbing state is given by the

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

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

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.

State j is an absorbing state if p_ij = 1.

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

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

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

A transition probability describes

Calculate the steady state probabilities for this transition matrix.

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

The medical prognosis for a patient with a certain disease is to recover, to die, to exhibit symptom 1, or to exhibit symptom 2. The matrix of transition probabilities is ​ a.What are the absorbing states? b.What is the probability that a patient with symptom 2 will recover?

Absorbing state probabilities are the same as

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

Steady state probabilities are independent of initial state.

​What assumptions are necessary for a Markov process to have stationary transition probabilities?

For Markov processes having the memoryless property, the prior states of the system must be considered in order to predict the future behavior of the system.

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

The probability of reaching an absorbing state is given by the

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

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

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.

State j is an absorbing state if pij = 1.

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

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

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

The medical prognosis for a patient with a certain disease is to recover, to die, to exhibit symptom 1, or to exhibit symptom 2. The matrix of transition probabilities is a.What are the absorbing states? b.What is the probability that a patient with symptom 2 will recover?

What assumptions are necessary for a Markov process to have stationary transition probabilities?

State j is an absorbing state if p_ij = 1.