True/False Quizzes for
Finite Mathematics
Topic: Markov Systems
(Chapter 9)

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1. A Markov system can be in several states at one time.
2. The (1,3) entry in the transition matrix is the probability of going from state 1 to state 3 in two steps.
3. The (6,5) entry in the transition matrix is the probability of going from state 6 to state 5 in one step.
4. The entries in each row of the transition matrix add to zero.
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.
6. To find the probability of going from state 3 to state 5 in six steps, we take the (3,5) entry in P6.
7. Given the initial distribution vector [10, 23, 77, 1] and a 44 transition matrix P, the distribution 4 steps later is given by [10, 23, 77, 1]P4.
8. Given the initial distribution vector [10, 23, 77, 1] and a 44 transition matrix P, the distribution 4 steps later is given by [10, 23, 77, 1]P.P.P.P.
9. The entries in a distribution vector add to the same number before and after multiplication on the right by P.
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.
11. The rows in the steady state transition matrix Pinfinity give the fractions of time the system spends in each of the states.
12. Every system with one or more absorbing states is an absorbing system.
13. No regular system can be absorbing.
14. No absorbing system can be regular.
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.
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.
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.
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.
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.
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.

Last Updated: July, 2000
Copyright © 2000 Stefan Waner & Steven R. Costenoble