One particle performs random walks on the figure shown above (at each step, it moves from its current vertex to a different vertex by choosing one of its neighboring vertices uniformly at random). Note Markov chain (which we shall call X=(Xn : n?0)) is irreducible.

a.)Transition matrix of this Markov chain

b.)Is X reversible? Explain

c.)Equilibrium distribution ? of X.

d.)If the particle starts at vertex A, find the expected time of first return to A.

A D C B E