Deck 16: Markov Processes

Question 1

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.

Answer 1

D

Question 2

Steady state probabilities are independent of initial state.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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 5

At steady state

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

Question 6

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

Question 7

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.

Question 8

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.

Question 9

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.

Question 10

A Markov chain cannot consist of all absorbing states.

Question 11

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 12

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 13

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 14

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 15

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

Question 16

Markov processes use historical probabilities.

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 chains have steady-state probabilities.

Question 19

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

Question 20

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

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

Rent-To-Keep rents household furnishings by the month. At the end of a rental month a customer can: a) rent the item for another month, b) buy the item, or c) return the item. The matrix below describes the month-to-month transition probabilities for 32-inch stereo televisions the shop stocks.
What is the probability that a customer who rented a TV this month will eventually buy it?

Question 27

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 28

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 29

State j is an absorbing state if p_ij = 1.

Question 30

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 31

Transition probabilities are conditional probabilities.