A 4-state Markov chain {Xo, X1, ..., Xn, ...} has a transition probability matrix as follows. The states are 0, 1, 2, and 3. ONIHAHA 10 NIH ORICOPIN PIHAIH O O AIHAIHO O (a) (10) Specify the classes of the Markov chain. (b) (10) Determine for each class, whether it is transient or recurrent. (c) (10) Find P{X2 = 1, X3 =0 | Xo = 0}, i.e., the probability that X2 = 1 and X3 = 0 given that Xo = 0. (d) (10) Find the expected number of visits to state 2 given that the Markov chain starts in state 3 (Xo = 3). (e) (10) Find the probability the Markov chain ever makes a transition into state 2 given that it starts in state 3