Please show the work, Thank you !

Problem 7.1 (10 points) Let (Xn)n>0 denote a Markov chain with state space 8 = {1, 2, 3, 4} and transition probability matrix H pi o o | NIH '3 ONIHONIH H O'U O Ownno O Where p 6 [0,1] is some arbitrary probability. (a) (3 points) Provide the transition graph. (b) (7 points) Determine all communication classes. Which states are transient / recurrent? Hint: You need to do a casebycase analysis depending on the value of p