Question

1 - Consider a Markov chain on the six states 1, 2, ..., 6 with transition matrix P given by ? 0.5 0.1 0.1 0 0.3 0 ? | 0 1 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 1 0 0 0 | | 0.15 0.15 0.15 0.2 0.15 0.15 | ? 0 0 0.2 0.8 0 0 ? a) Which states are accessible from state 1? and From which states is state 1 accessible? b) Do states 1 and 6 communicate? c) Identify the communication classes for this Markov chain. d) Which states are transient? Which states are recurrent? Which states are aperiodic?

          1 - Consider a Markov chain on the six states 1, 2, ..., 6 with transition matrix P given by

? 0.5   0.1   0.1   0   0.3   0 ?
|  0     1     0     0    0    0 |
|  0     0     0     0    0    1 |
|  0     0     1     0    0    0 |
| 0.15  0.15  0.15  0.2  0.15  0.15 |
?  0     0    0.2   0.8   0    0 ?

a) Which states are accessible from state 1? and From which states is state 1 accessible?

b) Do states 1 and 6 communicate?

c) Identify the communication classes for this Markov chain.

d) Which states are transient? Which states are recurrent? Which states are aperiodic?

1 - Consider a Markov chain on the six states 1, 2, ..., 6 with transition matrix P given by

? 0.5 0.1 0.1 0 0.3 0 ?
| 0 1 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 1 0 0 0 |
| 0.15 0.15 0.15 0.2 0.15 0.15 |
? 0 0 0.2 0.8 0 0 ?

a) Which states are accessible from state 1? and From which states is state 1 accessible?

b) Do states 1 and 6 communicate?

c) Identify the communication classes for this Markov chain.

d) Which states are transient? Which states are recurrent? Which states are aperiodic?

Added by Carla S.

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