Question 1

A state that when entered, cannot be left is called

Accepted Answer

A)  transient. 
B)  recurrent. 
C)  absorbing. 
D)  steady. 
E)  None of the above 
A)  transient. 
B)  recurrent. 
C)  absorbing. 
D)  steady. 
E)  None of the above

Question 2

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. 
E)  None of the above 
A)  using the simplex solution method. 
B)  analyzing currently known probabilities. 
C)  statistical sampling. 
D)  the minimal spanning tree. 
E)  None of the above

Question 3

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 4

The initial values for the state probabilities ________.

Accepted Answer

A)  are always greater than the equilibrium state probabilities 
B)  are always less than the equilibrium state probabilities 
C)  do not influence the equilibrium state probabilities 
D)  heavily influence the equilibrium state probabilities 
E)  None of the above 
A)  are always greater than the equilibrium state probabilities 
B)  are always less than the equilibrium state probabilities 
C)  do not influence the equilibrium state probabilities 
D)  heavily influence the equilibrium state probabilities 
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 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 6

A certain firm has noticed that employees' salaries from year to year can be modeled by Markov analysis. The matrix of transition probabilities follows.   (a) Set up the matrix of transition probabilities in the form:   (b) Determine the fundamental matrix for this problem.
(c) What is the probability that an employee who has received a raise will eventually quit?
(d) What is the probability that an employee who has received a raise will eventually be fired?

Accepted Answer

(a) @#IMG-DLM& (b) f

Question 7

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, determine Company 2's estimated market share in the next period.

Accepted Answer

A)  0.26 
B)  0.27 
C)  0.28 
D)  0.29 
E)  None of the above 
A)  0.26 
B)  0.27 
C)  0.28 
D)  0.29 
E)  None of the above

Question 8

The vector of state probabilities for any period is equal to the vector of state probabilities for the preceding period multiplied by the matrix of transition probabilities.

Accepted Answer

A) True 
 B)False

Question 9

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. If the probability that it was raining yesterday is 0.25, what is the probability that it will rain today?

Accepted Answer

A)  0.1 
B)  0.3 
C)  0.4 
D)  0.7 
E)  None of the above 
A)  0.1 
B)  0.3 
C)  0.4 
D)  0.7 
E)  None of the above

Question 10

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 11

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 12

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

Accepted Answer

A) True 
 B)False

Question 13

Creating the fundamental matrix requires a partition of the matrix of transition.

Accepted Answer

A) True 
 B)False

Question 14

The matrix of transition probabilities gives the conditional probabilities of moving from one state to another.

Accepted Answer

A) True 
 B)False

Question 15

A Markov process could be used as a model of how a disease progresses from one set of symptoms to another.

Accepted Answer

A) True 
 B)False

Question 16

There is a 60% chance that 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 is the long run percentage of the target market that will own smart phones?

Accepted Answer

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

Question 17

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 18

At equilibrium,

Accepted Answer

A)  state probabilities for the next period equal the state probabilities for this period. 
B)  the state probabilities are all equal to each other. 
C)  the matrix of transition probabilities is symmetrical. 
D)  the vector of state probabilities is symmetrical. 
E)  the fundamental matrix is the same as the matrix of transition probabilities. 
A)  state probabilities for the next period equal the state probabilities for this period. 
B)  the state probabilities are all equal to each other. 
C)  the matrix of transition probabilities is symmetrical. 
D)  the vector of state probabilities is symmetrical. 
E)  the fundamental matrix is the same as the matrix of transition probabilities.

Question 19

Markov analysis assumes that there are a limited number of states in the system.

Accepted Answer

A) True 
 B)False

Question 20

Given the following matrix of transition probabilities, write three equations that, when solved, will give the equilibrium state values.
P =

Accepted Answer

π₁ + π₂ = 1

A state that when entered, cannot be left is called

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

To find the equilibrium state in Markov analysis,

The initial values for the state probabilities ________.

The vector of state probabilities for any period is equal to the vector of state probabilities for the preceding period multiplied by the matrix of transition probabilities.

In Markov analysis, we also assume that the sates are

In a matrix of transition probabilities,

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

Creating the fundamental matrix requires a partition of the matrix of transition.

The matrix of transition probabilities gives the conditional probabilities of moving from one state to another.

A Markov process could be used as a model of how a disease progresses from one set of symptoms to another.

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

At equilibrium,

Markov analysis assumes that there are a limited number of states in the system.

Given the following matrix of transition probabilities, write three equations that, when solved, will give the equilibrium state values. P =

Introduction to Quantitative Analysis

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Exam 15: Markov Analysis

A state that when entered, cannot be left is called

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

To find the equilibrium state in Markov analysis,

The initial values for the state probabilities ________.

The vector of state probabilities for any period is equal to the vector of state probabilities for the preceding period multiplied by the matrix of transition probabilities.

In Markov analysis, we also assume that the sates are

In a matrix of transition probabilities,

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

Creating the fundamental matrix requires a partition of the matrix of transition.

The matrix of transition probabilities gives the conditional probabilities of moving from one state to another.

A Markov process could be used as a model of how a disease progresses from one set of symptoms to another.

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

At equilibrium,

Markov analysis assumes that there are a limited number of states in the system.

Given the following matrix of transition probabilities, write three equations that, when solved, will give the equilibrium state values. P =

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