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6. (15 pts.) Consider the discrete time Markov chain Xn with state space S = {0, 1, 2, 3, 4, 5} and transition matrix 0 1 2 3 4 5 0 [ 0.5 0 0 0 0.5 0 ] 1 [ 0 0.1 0 0.2 0.3 0.4] P = 2 [ 0 0 0.9 0 0 0.1] 3 [ 0 0.3 0 0.7 0 0 ] 4 [ 0.4 0 0 0 0.6 0 ] 5 [ 0 0.6 0 0.4 0 0 ] (a) Write down all the communication classes. Which classes are recurrent? Which classes are transient?

          6. (15 pts.) Consider the discrete time Markov chain Xn with state space S = {0, 1, 2, 3, 4, 5} and transition matrix

      0   1   2   3   4   5
0 [ 0.5   0   0   0  0.5  0 ]
1 [  0   0.1  0  0.2 0.3 0.4]
P = 2 [  0    0  0.9  0   0  0.1]
3 [  0   0.3  0  0.7  0   0 ]
4 [ 0.4   0   0   0  0.6  0 ]
5 [  0   0.6  0  0.4  0   0 ]

(a) Write down all the communication classes. Which classes are recurrent? Which classes are transient?

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6. (15 pts.) Consider the discrete time Markov chain Xn with state space S = 0, 1, 2, 3, 4, 5 and transition matrix

0 1 2 3 4 5
0 [ 0.5 0 0 0 0.5 0 ]
1 [ 0 0.1 0 0.2 0.3 0.4]
P = 2 [ 0 0 0.9 0 0 0.1]
3 [ 0 0.3 0 0.7 0 0 ]
4 [ 0.4 0 0 0 0.6 0 ]
5 [ 0 0.6 0 0.4 0 0 ]

(a) Write down all the communication classes. Which classes are recurrent? Which classes are transient?

Added by Marcos A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sanchit Jain

Step 1

5 & 0.5 & 0 & 0 & 0 & 0 \\ 0.1 & 0.2 & 0.3 & 0.4 & 0 & 0 \\ 0 & 0.3 & 0.5 & 0.2 & 0 & 0 \\ 0 & 0 & 0.4 & 0.6 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ Now, let's find the communication classes. Two states i and j communicate Show more…

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Consider the discrete time Markov chain Xn with state space S = {0, 1, 2, 3, 4, 5} and transition matrix Write down all the communication classes. Which classes are recurrent? Which classes are transient?

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