Question 1

If in an absorbing state, the probability of being in an absorbing state in the future is

Accepted Answer

A) 25%. 
B) 50%. 
C) 75%. 
D) 100%. 
A) 25%. 
B) 50%. 
C) 75%. 
D) 100%.

Question 2

For any absorbing state, the probability that a state will remain unchanged in the future is one.

Accepted Answer

A) True 
 B)False

Question 3

Once a Markov process is in equilibrium, it stays in equilibrium.

Accepted Answer

A) True 
 B)False

Question 4

In a tree diagram, the numbers associated with the arcs moving from one state to the next would be represented in the matrix of transition probabilities.

Accepted Answer

A) True 
 B)False

Question 5

In a(n)________ state, you cannot go to another state in the future.

Accepted Answer

A) transition 
B) equilibrium 
C) locked 
D) absorbing 
A) transition 
B) equilibrium 
C) locked 
D) absorbing

Question 6

There is a 60% chance that a customer without a smart phone will buy one this year.There is a 95% chance that a customer with a smart phone will continue with a smart phone going into the next year.If 30% of target market currently own smart phones, what proportion of the target market is expected to own a smart phone next year?

Accepted Answer

The answer of There is a 60% chance that a...

Question 7

What are the dimensions of an identity matrix that contains as many 1's as 0's?

Accepted Answer

A) 1x1 
B) 1x2 
C) 2x2 
D) 3x3 
A) 1x1 
B) 1x2 
C) 2x2 
D) 3x3

Question 8

In the matrix of transition probabilities, Pij is the conditional probability of being in state i in the future, given the current state j.

Accepted Answer

A) True 
 B)False

Question 9

Occasionally, a state is entered that will not allow going to any other state in the future.This is called

Accepted Answer

A) stability dependency. 
B) market saturation. 
C) incidental mobility. 
D) an absorbing state. 
A) stability dependency. 
B) market saturation. 
C) incidental mobility. 
D) an absorbing state.

Question 10

Where P is the matrix of transition probabilities, π(4)=

Accepted Answer

A) π(3)P P P. 
B) π(3)P P. 
C) π(2)P P P. 
D) π(1)P P P. 
A) π(3)P P P. 
B) π(3)P P. 
C) π(2)P P P. 
D) π(1)P P P.

Question 11

The probabilities in any column of the matrix of transition probabilities will always sum to one.

Accepted Answer

A) True 
 B)False

Question 12

The probability that we will be in a future state, given a current or existing state, is called

Accepted Answer

A) state probability. 
B) prior probability. 
C) steady state probability. 
D) transition probability. 
A) state probability. 
B) prior probability. 
C) steady state probability. 
D) transition probability.

Question 13

Table 14-1
The following data consists of a matrix of transition probabilities (P)of three competing companies, and the initial market share π(0).Assume that each state represents a company (Company 1, Company 2, Company 3, respectively)and the transition probabilities represent changes from one month to the next.
P =   π(0)= (0.3, 0.6, 0.1)
-Using the data in Table 14-1, determine Company 1's estimated market share in the next period.

Accepted Answer

A) 0.10 
B) 0.20 
C) 0.42 
D) 0.47 
A) 0.10 
B) 0.20 
C) 0.42 
D) 0.47

Question 14

One of the problems with using the Markov model to study population shifts is that we must assume that the reasons for moving from one state to another remain the same over time.

Accepted Answer

A) True 
 B)False

Question 15

The weather is becoming important to you since you would like to go on a picnic today.If it was sunny yesterday, there is a 65% chance it will be sunny today.If it was raining yesterday, there is a 30% chance it will be sunny today.If the probability that it was raining yesterday is 0.4, what is the probability that it will be sunny today?

Accepted Answer

A) 0.650 
B) 0.390 
C) 0.510 
D) 0.490 
A) 0.650 
B) 0.390 
C) 0.510 
D) 0.490

Question 16

Markov analysis is a technique that deals with the probabilities of future occurrences by

Accepted Answer

A) using the simplex solution method. 
B) analyzing currently known probabilities. 
C) statistical sampling. 
D) the minimal spanning tree. 
A) using the simplex solution method. 
B) analyzing currently known probabilities. 
C) statistical sampling. 
D) the minimal spanning tree.

Question 17

In a matrix of transition probabilities

Accepted Answer

A) the probabilities for any column will sum to 1. 
B) the probabilities for any row will sum to 1. 
C) the probabilities for any column are mutually exclusive and collectively exhaustive. 
D) the probabilities of all columns will sum to 1. 
A) the probabilities for any column will sum to 1. 
B) the probabilities for any row will sum to 1. 
C) the probabilities for any column are mutually exclusive and collectively exhaustive. 
D) the probabilities of all columns will sum to 1.

Question 18

In the long run, in Markov analysis

Accepted Answer

A) all state probabilities will eventually become zeros or ones. 
B) generally, the vector of state probabilities, when multiplied by the matrix of transition probabilities, will yield the same vector of state probabilities. 
C) the matrix of transition probabilities will change to an equilibrium state. 
D) the matrices will become inverted. 
A) all state probabilities will eventually become zeros or ones. 
B) generally, the vector of state probabilities, when multiplied by the matrix of transition probabilities, will yield the same vector of state probabilities. 
C) the matrix of transition probabilities will change to an equilibrium state. 
D) the matrices will become inverted.

Question 19

The copy machine in an office is very unreliable.If it was working yesterday, there is an 80% chance it will work today.If it was not working yesterday, there is a 10% chance it will work today.If it is working today, what is the probability that it will be working 2 days from now?

Accepted Answer

A) 0.16 
B) 0.64 
C) 0.66 
D) 0.80 
A) 0.16 
B) 0.64 
C) 0.66 
D) 0.80

Question 20

Table 14-6
The following data consists of a matrix of transition probabilities (P)of four majors in the College of Business, and the initial proportion of students in each major π(0).Assume that each state represents a major and the transition probabilities represent changes from one major to the next after taking the introductory class in each discipline.
P =
   
π(0)= (.4, .3, .2, .1)
-Using the data in Table 14-6, which major will end up with the greatest proportion of students?

Accepted Answer

A) Major 1 
B) Major 2 
C) Major 3 
D) Major 4 
A) Major 1 
B) Major 2 
C) Major 3 
D) Major 4

If in an absorbing state, the probability of being in an absorbing state in the future is

For any absorbing state, the probability that a state will remain unchanged in the future is one.

Once a Markov process is in equilibrium, it stays in equilibrium.

In a tree diagram, the numbers associated with the arcs moving from one state to the next would be represented in the matrix of transition probabilities.

In a(n)________ state, you cannot go to another state in the future.

What are the dimensions of an identity matrix that contains as many 1's as 0's?

In the matrix of transition probabilities, P_ij is the conditional probability of being in state i in the future, given the current state j.

Occasionally, a state is entered that will not allow going to any other state in the future.This is called

Where P is the matrix of transition probabilities, π(4)=

The probabilities in any column of the matrix of transition probabilities will always sum to one.

The probability that we will be in a future state, given a current or existing state, is called

One of the problems with using the Markov model to study population shifts is that we must assume that the reasons for moving from one state to another remain the same over time.

Markov analysis is a technique that deals with the probabilities of future occurrences by

In a matrix of transition probabilities

In the long run, in Markov analysis

The copy machine in an office is very unreliable.If it was working yesterday, there is an 80% chance it will work today.If it was not working yesterday, there is a 10% chance it will work today.If it is working today, what is the probability that it will be working 2 days from now?

Introduction to Quantitative Analysis

Probability Concepts and Applications

Decision Analysis

Regression Models

Forecasting

Inventory Control Models

Linear Programming Models: Graphical and Computer Methods

Linear Programming Applications

Transportation, Assignment, and Network Models

Integer Programming, Goal Programming, and Nonlinear Programming

Project Management

Waiting Lines and Queuing Theory Models

Simulation Modeling

Statistical Quality Control

Analytic Hierarchy Process

Dynamic Programming

Decision Theory and the Normal Distribution

Game Theory

Mathematical Tools: Determinants and Matrices

Calculus-Based Optimization

Linear Programming: The Simplex Method

Transportation, Assignment, and Network Algorithms

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Exam 14: Markov Analysis

If in an absorbing state, the probability of being in an absorbing state in the future is

For any absorbing state, the probability that a state will remain unchanged in the future is one.

Once a Markov process is in equilibrium, it stays in equilibrium.

In a tree diagram, the numbers associated with the arcs moving from one state to the next would be represented in the matrix of transition probabilities.

In a(n)________ state, you cannot go to another state in the future.

What are the dimensions of an identity matrix that contains as many 1's as 0's?

In the matrix of transition probabilities, Pij is the conditional probability of being in state i in the future, given the current state j.

Occasionally, a state is entered that will not allow going to any other state in the future.This is called

Where P is the matrix of transition probabilities, π(4)=

The probabilities in any column of the matrix of transition probabilities will always sum to one.

The probability that we will be in a future state, given a current or existing state, is called

One of the problems with using the Markov model to study population shifts is that we must assume that the reasons for moving from one state to another remain the same over time.

Markov analysis is a technique that deals with the probabilities of future occurrences by

In a matrix of transition probabilities

In the long run, in Markov analysis

The copy machine in an office is very unreliable.If it was working yesterday, there is an 80% chance it will work today.If it was not working yesterday, there is a 10% chance it will work today.If it is working today, what is the probability that it will be working 2 days from now?

Introduction to Quantitative Analysis

Probability Concepts and Applications

Decision Analysis

Regression Models

Forecasting

Inventory Control Models

Linear Programming Models: Graphical and Computer Methods

Linear Programming Applications

Transportation, Assignment, and Network Models

Integer Programming, Goal Programming, and Nonlinear Programming

Project Management

Waiting Lines and Queuing Theory Models

Simulation Modeling

Statistical Quality Control

Analytic Hierarchy Process

Dynamic Programming

Decision Theory and the Normal Distribution

Game Theory

Mathematical Tools: Determinants and Matrices

Calculus-Based Optimization

Linear Programming: The Simplex Method

Transportation, Assignment, and Network Algorithms

Filters

In the matrix of transition probabilities, P_ij is the conditional probability of being in state i in the future, given the current state j.