True/False Quiz for Chapter 8

Markov Systems

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1. A Markov system can be in several states at one time. True False

2. The (1,3) entry in the transition matrix is the probability of going from state 1 to state 3 in two steps. True False

3. The (6,5) entry in the transition matrix is the probability of going from state 6 to state 5 in one step. True False

4. The entries in each row of the transition matrix add to zero. True False

5. To find the probability of going from state 3 to state 5 in six steps, we take the sixth power of the (3,5) entry in P. True False

6. To find the probability of going from state 3 to state 5 in six steps, we take the (3,5) entry in P⁶. True False

7. Given the initial distribution vector [10, 23, 77, 1] and a 4 x 4 transition matrix P, the distribution 4 steps later is given by [10, 23, 77, 1]P⁴. True False

8. Given the initial distribution vector [10, 23, 77, 1] and a 4 x 4 transition matrix P, the distribution 4 steps later is given by [10, 23, 77, 1]P.P.P.P. True False

9. The entries in a distribution vector add to the same number before and after multiplication on the right by P. True False

10. The entries in a steady state distribution vector of a regular Markov system give the fractions of time the system spends in each of the states. True False

11. The rows in the steady state transition matrix P^infinity give the fractions of time the system spends in each of the states. True False

12. Every system with one or more absorbing states is an absorbing system. True False

13. No regular system can be absorbing. True False

14. No absorbing system can be regular. True False

15. In an absorbing system, if the (2,3) entry of the fundamental matrix is 4, this means that, starting in state 2, you can expect the system to be in state 3 four times prior to absorption. True False

16. In an absorbing system, if the (3,3) entry of the fundamental matrix is 5, this means that, starting in state 3, you can expect the system to be in state 3 five more times prior to absorption. True False

17. In an absorbing system, if the (3,3) entry of the fundamental matrix is 5, this means that, starting in state 3, you can expect the system to be in state 3 four more times prior to absorption. True False

18. The sum of the entries in row number 4 of the fundamental matrix is the total number of time steps you expect the system to be in state 4 prior to absorption. True False

19. The sum of the entries in column number 4 of the fundamental matrix is the total number of time steps you expect the system to be in state 4 prior to absorption. True False

20. The sum of the entries in row number 4 of the fundamental matrix is the total number of steps you expect the system to take until absorption if it starts in state 4. True False