Question 1

Describe the situation of the existence of an equilibrium condition in a Markov analysis.

Accepted Answer

state probabilities

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

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)S1U1B1 S1U1B0
-Using the data in Table 14-1,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 4

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 5

Equilibrium state probabilities may be estimated by using Markov analysis for a large number of periods.

Accepted Answer

A) True 
 B)False

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)fu

Question 7

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 8

In Markov analysis,the transition probability Pij represents the conditional probability of being in state i in the future given the current state of j.

Accepted Answer

A) True 
 B)False

Question 9

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 10

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,what is the long run number of employees expected in location C?

Accepted Answer

A) 1400 
B) 1000 
C) 800 
D) 750 
E) 700 
A) 1400 
B) 1000 
C) 800 
D) 750 
E) 700

Question 11

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 12

When absorbing states exist,the fundamental matrix is used to compute equilibrium conditions.

Accepted Answer

A) True 
 B)False

Question 13

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 B one year from now?

Accepted Answer

A) 1000 
B) 1400 
C) 1500 
D) 800 
E) 700 
A) 1000 
B) 1400 
C) 1500 
D) 800 
E) 700

Question 14

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

Accepted Answer

A) 0%. 
B) 25%. 
C) 50%. 
D) 75%. 
E) 100%. 
A) 0%. 
B) 25%. 
C) 50%. 
D) 75%. 
E) 100%.

Question 15

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 16

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

Accepted Answer

Collectively exhaust

Question 17

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

Question 18

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 19

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 20

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

Describe the situation of the existence of an equilibrium condition in a Markov analysis.

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

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

Equilibrium state probabilities may be estimated by using Markov analysis for a large number of periods.

In Markov analysis,the transition probability Pij represents the conditional probability of being in state i in the future given the current state of j.

In the long run,in Markov analysis,

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.

When absorbing states exist,the fundamental matrix is used to compute equilibrium conditions.

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

The initial values for the state probabilities

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

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

At equilibrium,

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Exam 14: Markov Analysis

Describe the situation of the existence of an equilibrium condition in a Markov analysis.

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

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

Equilibrium state probabilities may be estimated by using Markov analysis for a large number of periods.

In Markov analysis,the transition probability Pij represents the conditional probability of being in state i in the future given the current state of j.

In the long run,in Markov analysis,

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

When absorbing states exist,the fundamental matrix is used to compute equilibrium conditions.

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

The initial values for the state probabilities

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

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

At 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,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.