7.40. A random walk on a graph goes from vertex to adjacent vertex by walking along...

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7.40. A random walk on a graph goes from vertex to adjacent vertex by walking along the connecting edge. It chooses the edge at random: all edges connecting to that vertex are equally likely. Consider a random walk on the graph below. (a) Find the long-term proportion of time spent at vertex 0. (b) Find the expected return time to 0. (c) Find the probability that a random walk from vertex e hits 0 before hitting either a or b. (d) Suppose the random walk starts at 0. Find the expected time to reach {a Ub}. [Hint: Make use of symmetry!] A 7.40. A random walk on a graph goes from vertex to adjacent vertex by walking along the connecting edge. It chooses the edge at random: all edges connecting to that vertex are equally likely. Consider a random walk on the graph below. (a) Find the long-term proportion of time spent at vertex 0. (b) Find the expected return time to 0. (c) Find the probability that a random walk from vertex e hits 0 before hitting either a or b. (d) Suppose the random walk starts at 0. Find the expected time to reach {a Ub}. [Hint: Make use of symmetry!] A