Let (X,)n>o be a Markov chain on a state space I = {0, 1, 2, 3, ...} with stochastic matrix given by: (1 – )10-3, if i = 0, j e {0,1, 2, ..., 10} if i e {1,2, ..., 10}, j= i + 1 if i e {1,2,..., 10}, j = i – 1 P1, 1- P1» (P)ij= P2, if i e {11, 12, ...},j=i+1 1- P2, if i e {11, 12, ...}, j=i – 1 otherwise where 0 < Y, P1, P2 < 1. How many communicating classes exist for this Markov chain?

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O 2
|I|
Transcribed Image Text:O 2 |I|
Let (X„)n>o be a Markov chain on a state space I = {0, 1, 2,3, ...} with stochastic
matrix given by:
)(1– )10-3, if i = 0, j € {0, 1, 2,..., 10}
if i e {1,2, ..., 10}, j= i + 1
if i e {1,2,..., 10}, j = i – 1
P1,
1- P1»
(P)ij=
if i e {11, 12, ...},j=i+1
if i e {11, 12,...},j=i – 1
P2,
1- P2,
otherwise
where 0 < Y,P1, P2 < 1.
How many communicating classes exist for this Markov chain?
O 4
O 5
O 2!
O 10
O 2" – 1
O 3
O 1
O 2"
Transcribed Image Text:Let (X„)n>o be a Markov chain on a state space I = {0, 1, 2,3, ...} with stochastic matrix given by: )(1– )10-3, if i = 0, j € {0, 1, 2,..., 10} if i e {1,2, ..., 10}, j= i + 1 if i e {1,2,..., 10}, j = i – 1 P1, 1- P1» (P)ij= if i e {11, 12, ...},j=i+1 if i e {11, 12,...},j=i – 1 P2, 1- P2, otherwise where 0 < Y,P1, P2 < 1. How many communicating classes exist for this Markov chain? O 4 O 5 O 2! O 10 O 2" – 1 O 3 O 1 O 2"
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