Test Bank For An Introduction to Management Science 13th Edition By Anderson Sweeney Williams Martin

Chapter 16—Markov Processes


MULTIPLE CHOICE

1. In Markov analysis, we are concerned with the probability that the
a. state is part of a system.
b. system is in a particular state at a given time.
c. time has reached a steady state.
d. transition will occur.
ANS: B PTS: 1 TOP: Introduction

2. For a situation with weekly dining at either an Italian or Mexican restaurant,
a. the weekly visit is the trial and the restaurant is the state.
b. the weekly visit is the state and the restaurant is the trial.
c. the weekly visit is the trend and the restaurant is the transition.
d. the weekly visit is the transition and the restaurant is the trend.
ANS: A PTS: 1 TOP: Market share analysis

3. A transition probability describes
a. the probability of a success in repeated, independent trials.
b. the probability a system in a particular state now will be in a specific state next period.
c. the probability of reaching an absorbing state.
d. None of the alternatives is correct.
ANS: B PTS: 1 TOP: Introduction

4. The probability of going from state 1 in period 2 to state 4 in period 3 is
a. p12
b. p23
c. p14
d. p43
ANS: C PTS: 1 TOP: Market share analysis

5. The probability that a system is in a particular state after a large number of periods is
a. independent of the beginning state of the system.
b. dependent on the beginning state of the system.
c. equal to one half.
d. the same for every ending system.
ANS: A PTS: 1 TOP: Market share analysis

6. At steady state
a. p1(n+1) > p1(n)
b. p1 = p2
c. p1 + p2 ³ 1
d. p1(n+1) = p1
ANS: D PTS: 1 TOP: Market share analysis

7. Analysis of a Markov process
a. describes future behavior of the system.

, b. optimizes the system.
c. leads to higher order decision making.
d. All of the alternatives are true.
ANS: A PTS: 1 TOP: Introduction

8. If the probability of making a transition from a state is 0, then that state is called a(n)
a. steady state.
b. final state.
c. origin state.
d. absorbing state.
ANS: D PTS: 1 TOP: Absorbing states

9. Absorbing state probabilities are the same as
a. steady state probabilities.
b. transition probabilities.
c. fundamental probabilities.
d. None of the alternatives is true.
ANS: D PTS: 1 TOP: Fundamental matrix

10. The probability of reaching an absorbing state is given by the
a. R matrix.
b. NR matrix.
c. Q matrix.
d. (I - Q)-1 matrix
ANS: B PTS: 1 TOP: Fundamental matrix


TRUE/FALSE

1. Markov processes use historical probabilities.

ANS: T PTS: 1 TOP: Market share analysis

2. All entries in a matrix of transition probabilities sum to 1.

ANS: F PTS: 1 TOP: Transition probabilities

3. All Markov chain transition matrices have the same number of rows as columns.

ANS: T PTS: 1 TOP: Transition probabilities

4. A unique matrix of transition probabilities should be developed for each customer.

ANS: F PTS: 1 TOP: Transition probabilities

5. The probability that the system is in state 2 in the 5th period is p5(2).

ANS: F PTS: 1 TOP: Market share analysis

6. The fundamental matrix is used to calculate the probability of the process moving into each absorbing
state.

, ANS: T PTS: 1 TOP: Fundamental matrix, absorbing state

7. Steady state probabilities are independent of initial state.

ANS: T PTS: 1 TOP: Steady-state probabilities

8. A Markov chain cannot consist of all absorbing states.

ANS: F PTS: 1 TOP: Absorbing states

9. If an absorbing state exists, then the probability that a unit will ultimately move into the absorbing
state is given by the steady state probability.

ANS: F PTS: 1 TOP: NR matrix

10. All Markov chains have steady-state probabilities.

ANS: F PTS: 1 TOP: Steady-state probabilities

11. All entries in a row of a matrix of transition probabilities sum to 1.

ANS: T PTS: 1 TOP: Transition probabilities

12. A state i is a transient state if there exists a state j that is reachable from i, but the state i is not
reachable from state j.

ANS: T PTS: 1 TOP: Transition probabilities

13. A state i is an absorbing state if pii = 0.

ANS: F PTS: 1 TOP: Absorbing states

14. When absorbing states are present, each row of the transition matrix corresponding to an absorbing
state will have a single 1 and all other probabilities will be 0.

ANS: T PTS: 1 TOP: Absorbing states

15. For Markov processes having the memoryless property, the prior states of the system must be
considered in order to predict the future behavior of the system.

ANS: F PTS: 1 TOP: First-order Markov processes

16. The sum of the probabilities in a transition matrix equals the number of rows in the matrix.

ANS: T PTS: 1 TOP: Transition matrix

17. Transition probabilities are conditional probabilities.

ANS: T PTS: 1 TOP: Transition probabilities

18. A state, i, is an absorbing state if, when i = j, pij = 1.

ANS: T PTS: 1 TOP: Absorbing states

, 19. If a Markov chain has at least one absorbing state, steady-state probabilities cannot be calculated.

ANS: T PTS: 1 TOP: Steady-state probabilities

20. State j is an absorbing state if pij = 1.

ANS: F PTS: 1 TOP: Absorbing states


SHORT ANSWER

1. What assumptions are necessary for a Markov process to have stationary transition probabilities?

ANS:
Answer not provided.

PTS: 1 TOP: Market share analysis

2. Explain the concept of memorylessness.

ANS:
Answer not provided.

PTS: 1 TOP: Notes and comments

3. Give two examples of how Markov analysis can aid decision making.

ANS:
Answer not provided.

PTS: 1 TOP: Establishing the allowance for doubtful accounts

4. Where is a fundamental matrix, N, used? How is N computed?

ANS:
Answer not provided.

PTS: 1 TOP: Fundamental matrix

5. Why is a computer necessary for some Markov analyses?

ANS:
Answer not provided.

PTS: 1 TOP: Fundamental matrix


PROBLEM

1. Calculate the steady state probabilities for this transition matrix.