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A Markov system can be in several states at one time. |
2. |
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The (1,3) entry in the transition matrix is the probability of going from state 1 to state 3 in two steps. |
3. |
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The (6,5) entry in the transition matrix is the probability of going from state 6 to state 5 in one step. |
4. |
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The entries in each row of the transition matrix add to zero. |
5. |
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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. |
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To find the probability of going from state 3 to state 5 in six steps, we take the (3,5) entry in P6. |
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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. |
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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. |
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The entries in a distribution vector add to the same number before and after multiplication on the right by P. |
10. |
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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. |
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The rows in the steady state transition matrix Pinfinity give the fractions of time the system spends in each of the states. |
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Every system with one or more absorbing states is an absorbing system. |
13. |
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No regular system can be absorbing. |
14. |
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No absorbing system can be regular. |
15. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |