Question 1

Describe the concept of "collectively exhaustive" in the context of Markov analysis.

Accepted Answer

Collectively exhaust

Question 2

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 70% chance it will be sunny today. If it was raining yesterday, there is a 30% chance it will be sunny today. What is the probability it will be rainy today, if it was sunny yesterday?

Accepted Answer

A)  0.1 
B)  0.2 
C)  0.7 
D)  0.8 
E)  0.3 
A)  0.1 
B)  0.2 
C)  0.7 
D)  0.8 
E)  0.3

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

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. 
E)  None of the above 
A)  π(3) P P P. 
B)  π(3) P P. 
C)  π(2) P P P. 
D)  π(1) P P P. 
E)  None of the above

Question 5

Table 15-3
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 matrix:     π(0) = [100, 100, 100]
-Using the data given in Table 15-3, 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

Question 6

Markov analysis assumes that while a member of one state may move to a different state over time, the overall makeup of the system will remain the same.

Accepted Answer

A) True 
 B)False

Question 7

What do we do when solving for equilibrium conditions?

Accepted Answer

A)  conduct a statistical t-test 
B)  drop one equation 
C)  partition the matrix of transition probabilities 
D)  subtract matrix B from the identity matrix 
E)  multiply the fundamental matrix by the A matrix 
A)  conduct a statistical t-test 
B)  drop one equation 
C)  partition the matrix of transition probabilities 
D)  subtract matrix B from the identity matrix 
E)  multiply the fundamental matrix by the A matrix

Question 8

Table 15-3
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 matrix:     π(0) = [100, 100, 100]
-Using the data given in Table 15-3, find the equilibrium travel population for Frenzy (rounded to the nearest whole person).

Accepted Answer

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

Question 9

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 not working today, what is the probability that it will be working 2 days from now?

Accepted Answer

A)  0.16 
B)  0.17 
C)  0.34 
D)  0.66 
E)  None of the above 
A)  0.16 
B)  0.17 
C)  0.34 
D)  0.66 
E)  None of the above

Question 10

(n+1) = nP

Accepted Answer

A) True 
 B)False

Question 11

In Markov analysis, the row elements of the transition matrix must sum to 1.

Accepted Answer

A) True 
 B)False

Question 12

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

Question 13

Table 15-1
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 15-1, and assuming that the transition probabilities do not change, in the long run what market share would Company 2 expect to reach? (Rounded to two decimal places.)

Accepted Answer

A)  0.30 
B)  0.32 
C)  0.39 
D)  0.60 
E)  None of the above 
A)  0.30 
B)  0.32 
C)  0.39 
D)  0.60 
E)  None of the above

Question 14

There is a 30% chance that any current client of company A will switch to company B this year. There is a 40% chance that any client of company B will switch to company A this year. If these probabilities are stable over the years, and if company A has 500 clients and company B has 300 clients,
(a) how many clients will each company have next year?
(b) how many clients will each company have in two years?

Accepted Answer

(a) Company A will have 470; C

Question 15

In Markov analysis, the likelihood that any system will change from one period to the next is revealed by the

Accepted Answer

A)  cross-elasticities. 
B)  fundamental matrix. 
C)  matrix of transition probabilities. 
D)  vector of state probabilities. 
E)  state of technology. 
A)  cross-elasticities. 
B)  fundamental matrix. 
C)  matrix of transition probabilities. 
D)  vector of state probabilities. 
E)  state of technology.

Question 16

Table 15-2
The following data consists of a matrix of transition probabilities (P) of three competing retailers, the initial market share π(0). Assume that each state represents a retailer (Retailer 1, Retailer 2, Retailer 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 given in Table 15-2, find the market shares for the three retailers in month 2.

Accepted Answer

A)  π(2) = (0.30, 0.60, 0.10) 
B)  π(2) = (0.55, 0.33, 0.12) 
C)  π(2) = (0.44, 0.43, 0.12 
D)  π(2) = (0.55, 0.12, 0.33) 
E)  π(2) = (0.47, 0.40, 0.13) 
A)  π(2) = (0.30, 0.60, 0.10) 
B)  π(2) = (0.55, 0.33, 0.12) 
C)  π(2) = (0.44, 0.43, 0.12 
D)  π(2) = (0.55, 0.12, 0.33) 
E)  π(2) = (0.47, 0.40, 0.13)

Question 17

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

Question 18

The vector of state probabilities for period n is (0.4, 0.6).
The accompanying matrix of transition probabilities is:   Calculate the vector of state probabilities for period n+1.

Accepted Answer

The answer of The vector of state probabilities for period...

Question 19

Table 15-2
The following data consists of a matrix of transition probabilities (P) of three competing retailers, the initial market share π(0). Assume that each state represents a retailer (Retailer 1, Retailer 2, Retailer 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 given in Table 15-2, what is the equilibrium market share?

Accepted Answer

A)  (0.30, 0.60, 0.10) 
B)  (0.55, 0.33, 0.12) 
C)  (0.44, 0.43, 0.11) 
D)  (0.55, 0.12, 0.33) 
E)  (0.47, 0.40, 0.13) 
A)  (0.30, 0.60, 0.10) 
B)  (0.55, 0.33, 0.12) 
C)  (0.44, 0.43, 0.11) 
D)  (0.55, 0.12, 0.33) 
E)  (0.47, 0.40, 0.13)

Question 20

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

Accepted Answer

A) True 
 B)False

Describe the concept of "collectively exhaustive" in the context of Markov analysis.

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

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

Markov analysis assumes that while a member of one state may move to a different state over time, the overall makeup of the system will remain the same.

What do we do when solving for equilibrium conditions?

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 not working today, what is the probability that it will be working 2 days from now?

(n+1) = nP

In Markov analysis, the row elements of the transition matrix must sum to 1.

In the long run, in Markov analysis,

In Markov analysis, the likelihood that any system will change from one period to the next is revealed by the

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

The vector of state probabilities for period n is (0.4, 0.6). The accompanying matrix of transition probabilities is: Calculate the vector of state probabilities for period n+1.

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

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Exam 15: Markov Analysis

Describe the concept of "collectively exhaustive" in the context of Markov analysis.

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

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

Markov analysis assumes that while a member of one state may move to a different state over time, the overall makeup of the system will remain the same.

What do we do when solving for equilibrium conditions?

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 not working today, what is the probability that it will be working 2 days from now?

(n+1) = nP

In Markov analysis, the row elements of the transition matrix must sum to 1.

In the long run, in Markov analysis,

In Markov analysis, the likelihood that any system will change from one period to the next is revealed by the

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

The vector of state probabilities for period n is (0.4, 0.6). The accompanying matrix of transition probabilities is: Calculate the vector of state probabilities for period n+1.

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

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 and Assignment Models

Integer Programming, Goal Programming, and Nonlinear Programming

Network Models

Project Management

Waiting Lines and Queuing Theory Models

Simulation Modeling

Statistical Quality Control

Filters