Consider the Markov chain of Problem 16. Again assume X₀ = 4. We would like to find the expected time (number of steps) until the chain gets absorbed in R₁ or R₂. More specifically, let T be the absorption time, i.e., the first time the chain visits a state in R₁ or R₂. We would like to find E[T|X₀ = 4].

Problem 16

Consider the Markov chain in Figure 11.32. There are two recurrent classes, R₁ = {1, 2}, and R₂ = {5, 6, 7}. Assuming X₀ = 4, find the probability that the chain gets absorbed to R₁.

Transcribed Image Text:

1 S AL 1 1 Figure 11.32 - A state transition diagram.