Consider a simple random walk on the following graph.

a. Suppose that the walker begins in state 3. What is the expected number of visits to state 2 before the walker visits state 1?
b. Suppose again that the walker begins in state 3. What is the expected number of steps until the walker reaches state 1?
c. Now suppose that the walker starts in state 1. What is the probability that the walker reaches state 3 before reaching state 2?

Transcribed Image Text:

4 2 3