3. Suppose that {Xx}ken is a MC with state space S = {1, 2,3} and transition matrix: 0 0 P = 1/4 1/2 1/4 . 0 0 1 (a) Calculate Pij for all n > 1 and i, j = 1, 2,3, and hence write down P() and pn. (b) Find the limitation of P" as n -> co. Does the chain have a limit distribution? (c) Show that this MC has more than one stationary distributions. (d) Assuming Xo = 2, find the probability that the chain gets absorbed in 1. (e) Assuming Xo = 2, find the expected time (number of steps) until the chain gets absorbed in 1 or 3. More specifically, let T be the absorption time, i.c., the first time the chain visits a state in 1 or 3. We would like to find E[TIXo = 2]