# Probability Problem

## Transcribed Text

2/3 L-X 1+ X l 2/37 3 6 1/3 1/3 3+X 2 4 1/3 5 7 3-X 1) When X = 1/3 (such that the transition arrow from state 7 to state 2 would be gone), identify the communicating classes. Which states are transient? Which states are recurrent? Which states are aperiodic? 2) When X = - 1/3 (such that some transition arrows on the graph would be gone), identify the communicating classes. Which states are transient? Which states are recurrent? Which states are aperiodic? 3) For what values of X is the Markov chain irreducible? Explain why. (Note that in the first place such X should make the transition probabilities meaningful.)

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