2. Suppose a transition diagram is given as follows: 1/2 1/4 For this chain, there are two recurrent classes R1 = {6,7} and R2 = {1,2,5}, and one transient class R3 = {3, 4}. 1/2 (a) Find the period of state 3 and the probability that, starting at state 3, the state 3 is eventually reentered (i.e., I33). (b) Assuming X0 = 3, nd the probability that the chain gets absorbed in R1. (c) Assuming X" = 3, nd the expected time (number of steps) until the chain gets absorbed in R1 or R2. More specically, let T be the absorption time, i.e., the rst time the chain visits a state in R1 or R2. We would like to nd E[T|Xo = 3]