A Markov chain {Xmas 2 0} with states {0,1,2} has the transition probability matrix P with powers P2 and P3: 1/2 1/4 1/4 5/12 5/24 3/8 25/72 25/144 23/48 F: 2/3 1/3 0 ,P2= 5/9 5/18 1/6 ,P3 25/54 25/108 11/35 0 0 1 0 0 1 0 0 1 (a) Draw the state diagram for this chain. (b) Identify the classes of this Markov chain and determine which states are transient and which are recurrent. Give reasons for your answers