Question 1

In a matrix of transition probabilities (where i equals the row number and j equals the column number),

Accepted Answer

A) each number represents the conditional probability of being in state j in the next period given that it is currently in the state of i. 
B) each number represents the probability that if something is in state i,it will go to state j in the next period. 
C) the number in row 3,column 3 represents the probability that something will remain in state 3 from one period to the next. 
D) the probabilities are usually determined empirically. 
E) All of the above 
A) each number represents the conditional probability of being in state j in the next period given that it is currently in the state of i. 
B) each number represents the probability that if something is in state i,it will go to state j in the next period. 
C) the number in row 3,column 3 represents the probability that something will remain in state 3 from one period to the next. 
D) the probabilities are usually determined empirically. 
E) All of the above E

Question 2

Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (CS1U1B11S1U1B0),Frenzy (CS1U1B12S1U1B0),and Tremor (CS1U1B13S1U1B0).A transition matrix,indicating the probability that a resident in one city will travel to another,is given below.Cuthbert's job is to schedule the required number of seats,one to each person making the trip (transition),on a daily basis.
C F T
Transition matix:     π(0)= [100,100,100] S1U1B1 S1U1B0
-Using the data given in Table 14-4,how many people can we expect to find in each city tomorrow evening?

Accepted Answer

A) Chaos = 90,Frenzy = 110,Tremor = 100 
B) Chaos = 110,Frenzy = 100,Tremor = 90 
C) Chaos = 80,Frenzy = 90,Tremor = 130 
D) Chaos = 100,Frenzy = 130,Tremor = 70 
E) None of the above 
A) Chaos = 90,Frenzy = 110,Tremor = 100 
B) Chaos = 110,Frenzy = 100,Tremor = 90 
C) Chaos = 80,Frenzy = 90,Tremor = 130 
D) Chaos = 100,Frenzy = 130,Tremor = 70 
E) None of the above B

Question 3

"Events" are used to identify all possible conditions of a process or a system.

Accepted Answer

A) True 
 B)False  False

Question 4

Describe the concept of "mutually exclusive" in the context of Markov analysis.

Accepted Answer

Mutually exclusive m

Question 5

Markov analysis might be effectively used for

Accepted Answer

A) market share analysis. 
B) university enrollment predictions. 
C) machine breakdowns. 
D) bad debt prediction. 
E) All of the above 
A) market share analysis. 
B) university enrollment predictions. 
C) machine breakdowns. 
D) bad debt prediction. 
E) All of the above

Question 6

Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (CS1U1B11S1U1B0),Frenzy (CS1U1B12S1U1B0),and Tremor (CS1U1B13S1U1B0).A transition matrix,indicating the probability that a resident in one city will travel to another,is given below.Cuthbert's job is to schedule the required number of seats,one to each person making the trip (transition),on a daily basis.
C F T
Transition matix:     π(0)= [100,100,100] S1U1B1 S1U1B0
-Using the data given in Table 14-4,how many seats should Cuthbert schedule for travel from Chaos to Tremor for tomorrow?

Accepted Answer

A) 80 
B) 70 
C) 20 
D) 60 
E) None of the above 
A) 80 
B) 70 
C) 20 
D) 60 
E) None of the above

Question 7

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

Accepted Answer

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

Question 8

The vector of state probabilities gives the probability of being in particular states at a particular point in time.

Accepted Answer

A) True 
 B)False

Question 9

To find the equilibrium state in Markov analysis,

Accepted Answer

A) it is necessary to know both the vector of state probabilities and the matrix of transition probabilities. 
B) it is necessary only to know the matrix of transition probabilities. 
C) it is necessary only to know the vector of state probabilities for the initial period. 
D) one should develop a table of state probabilities over time and then determine the equilibrium conditions empirically. 
E) None of the above 
A) it is necessary to know both the vector of state probabilities and the matrix of transition probabilities. 
B) it is necessary only to know the matrix of transition probabilities. 
C) it is necessary only to know the vector of state probabilities for the initial period. 
D) one should develop a table of state probabilities over time and then determine the equilibrium conditions empirically. 
E) None of the above

Question 10

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 
E) None of the above 
A) 0.16 
B) 0.64 
C) 0.66 
D) 0.80 
E) None of the above

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium.This state contains three cities: Chaos (CS1U1B11S1U1B0),Frenzy (CS1U1B12S1U1B0),and Tremor (CS1U1B13S1U1B0).A transition matrix,indicating the probability that a resident in one city will travel to another,is given below.Cuthbert's job is to schedule the required number of seats,one to each person making the trip (transition),on a daily basis.
C F T
Transition matix:     π(0)= [100,100,100] S1U1B1 S1U1B0
-Using the data given in Table 14-4,what is the equilibrium travel population of Chaos (rounded to the nearest whole person)?

Accepted Answer

A) 79 
B) 95 
C) 126 
D) 100 
E) None of the above 
A) 79 
B) 95 
C) 126 
D) 100 
E) None of the above

Question 13

Collectively exhaustive means that a system can be in only one state at any point in time.

Accepted Answer

A) True 
 B)False

Question 14

In Markov analysis,we also assume that the sates are

Accepted Answer

A) collectively exhaustive. 
B) mutually exclusive. 
C) independent. 
D) A and B 
E) A,B,and C 
A) collectively exhaustive. 
B) mutually exclusive. 
C) independent. 
D) A and B 
E) A,B,and C

Question 15

An equilibrium condition exists if the state probabilities for a future period are the same as the state probabilities for a previous period.

Accepted Answer

A) True 
 B)False

Question 16

A state probability when equilibrium has been reached is called

Accepted Answer

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

Question 17

Table 14-3
The following data consists of a matrix of transition probabilities (P)of three office locations (A,B,C)within a large company and how employees shift from one location to the other from year to year.The company CEO would like to understand the movement of employees over time and the long-run proportion of employees in each location.Assume that there is always a total of 3000 employees.
A B C
P =     π(0)= [1000,1000,1000] S1U1B1 S1U1B0S1U1B1 S1U1B0
-Using the data given in Table 14-3,how many employees do we expect in location A two years from now?

Accepted Answer

A) 1000 
B) 1400 
C) 1420 
D) 1500 
E) 820 
A) 1000 
B) 1400 
C) 1420 
D) 1500 
E) 820

Question 18

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) All of the above 
E) None of the above 
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) All of the above 
E) None of the above

Question 19

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 
E) None of the above 
A) 0.650 
B) 0.390 
C) 0.510 
D) 0.490 
E) None of the above

Question 20

A firm currently has a 20% market share for its product,lint pickers.It has identified 2 plans to improve its market share.The transition matrices for both plans are listed below.Plan 1 costs $1 million and Plan 2 costs $1.5 million.The company's goal is to determine what its demand will be in the long-term.
Plan 1: 20% Share 40% Share 60% Share
20 Share 0.25 0.40 0.35
40 Share 0.20 0.35 0.45
60 Share 0.10 0.50 0.40
Plan 2: 20% Share 40% Share 60% Share
20 Share 0.30 0.30 0.40
40 Share 0.10 0.50 0.40
60 Share 0.20 0.30 0.50
A single percentage point of market share translates into an annual demand of 1,000 units per year.Also,each percentage point of market share means $100,000 of profit for the firm.Choose the plan that maximizes the firm's net income.

Accepted Answer

Plan 1 has the highest net income.Averag

In a matrix of transition probabilities (where i equals the row number and j equals the column number),

"Events" are used to identify all possible conditions of a process or a system.

Describe the concept of "mutually exclusive" in the context of Markov analysis.

Markov analysis might be effectively used for

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

The vector of state probabilities gives the probability of being in particular states at a particular point in time.

To find the equilibrium state 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?

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

Collectively exhaustive means that a system can be in only one state at any point in time.

In Markov analysis,we also assume that the sates are

An equilibrium condition exists if the state probabilities for a future period are the same as the state probabilities for a previous period.

A state probability when equilibrium has been reached is called

In a matrix of transition probabilities,

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Exam 14: Markov Analysis

In a matrix of transition probabilities (where i equals the row number and j equals the column number),

"Events" are used to identify all possible conditions of a process or a system.

Describe the concept of "mutually exclusive" in the context of Markov analysis.

Markov analysis might be effectively used for

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

The vector of state probabilities gives the probability of being in particular states at a particular point in time.

To find the equilibrium state 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?

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

Collectively exhaustive means that a system can be in only one state at any point in time.

In Markov analysis,we also assume that the sates are

An equilibrium condition exists if the state probabilities for a future period are the same as the state probabilities for a previous period.

A state probability when equilibrium has been reached is called

In a matrix of transition probabilities,

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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