Question 1

If the probability of making a transition from a state is 0, then that state is called a(n)

Accepted Answer

A)   steady state.
B)   final state.
C)   origin state.
D)   absorbing state. D

Question 2

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

Accepted Answer

A) True 
 B)False  True

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

Transition probabilities are conditional probabilities.

Accepted Answer

A) True 
 B)False  True

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

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.

Accepted Answer

A) True 
 B)False

Question 8

A Markov chain cannot consist of all absorbing states.

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

At steady state

Accepted Answer

A)    π\piπ 1(n+1)  >   π\piπ 1(n) 
B)     π\piπ 1 =   π\piπ 2
C)     π\piπ 1 +   π\piπ 2  ≥\ge≥  1
D)     π\piπ 1(n+1)  =   π\piπ 1

Question 11

In Markov analysis, we are concerned with the probability that the

Accepted Answer

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 12

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

Accepted Answer

A) True 
 B)False

Question 13

Markov processes use historical probabilities.

Accepted Answer

A) True 
 B)False

Question 14

State j is an absorbing state if pij = 1.

Accepted Answer

A) True 
 B)False

Question 15

Steady state probabilities are independent of initial state.

Accepted Answer

A) True 
 B)False

Question 16

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.

Accepted Answer

A) True 
 B)False

Question 17

The probability of reaching an absorbing state is given by the

Accepted Answer

A)   R matrix.
B)   NR matrix.
C)   Q matrix.
D)   (I -Q)  - 1 matrix

Question 18

For a situation with weekly dining at either an Italian or Mexican restaurant,

Accepted Answer

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 19

The probability that a system is in a particular state after a large number of periods is

Accepted Answer

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 20

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

Accepted Answer

A) True 
 B)False

Exam 16: Markov Processes

If the probability of making a transition from a state is 0, then that state is called a(n)

Correct AnswerverifiedD

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

Correct AnswerverifiedTrue

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Transition probabilities are conditional probabilities.

Correct AnswerverifiedTrue

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

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

A Markov chain cannot consist of all absorbing states.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

At steady state

Correct AnswerverifiedShow Answer

In Markov analysis, we are concerned with the probability that the

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Markov processes use historical probabilities.

Correct AnswerverifiedShow Answer

State j is an absorbing state if pij = 1.

Correct AnswerverifiedShow Answer

Steady state probabilities are independent of initial state.

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

The probability of reaching an absorbing state is given by the

Correct AnswerverifiedShow Answer

For a situation with weekly dining at either an Italian or Mexican restaurant,

Correct AnswerverifiedShow Answer

The probability that a system is in a particular state after a large number of periods is

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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D

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True

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

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True

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State j is an absorbing state if p_ij = 1.

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

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