Deck 16: Markov Processes

Question 1

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.

Answer 1

A

Question 2

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.

Answer 2

False

Question 3

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.

Answer 3

B

Question 4

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

Question 5

All Markov chains have steady-state probabilities.

Question 6

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

Question 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.

Question 8

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.

Question 9

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

Question 10

The probability that the system is in state 2 in the 5th period is $\pi$ ₅(2).

Question 11

At steady state

A) $\pi$ ₁(n+1) > $\pi$ ₁(n)
B) $\pi$ ₁ = $\pi$ ₂
C) $\pi$ ₁ + $\pi$ ₂ > 1
D) $\pi$ ₁(n+1) = $\pi$ ₁

Question 12

Steady state probabilities are independent of initial state.

Question 13

A Markov chain cannot consist of all absorbing states.

Question 14

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.

Question 15

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

Question 16

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

Question 17

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.

Question 18

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

Question 19

Absorbing state probabilities are the same as

A)steady state probabilities.
B)transition probabilities.
C)fundamental probabilities.
D)None of the alternatives is true.

Question 20

Markov processes use historical probabilities.

Question 21

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

Question 22

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.

Question 23

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.

Question 24

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.

Question 25

A state i is an absorbing state if p_ii = 0.