Please help on this applied stochastic process problem part (c) and (d)

7. (15 points) Six Avengers (Iron Man (1), Doctor Strange (D), Star-Lord (L), Drax (R), Mantis (M), and Spider-Man (8)) take turns attacking Thanos every second. Let (X,,),j','?'={J be the stationary discrete time Markov chain where X\" represents the Avenger that is attacking Thanos at time n. The attacks are governed by the transition matrix P 1/2 1/6 0 0 0 1/3 0 4/5 0 0 1/5 0 P = 0 1 0 0 o 0 1 0 0 0 o 0 o 0 1/3 0 2/3 0 1/2 0 0 1/2 0 0 with state space S = {1, D,L,R, M, S}. (a) Show the transition graph. Find the communication classes and classify them as open or closed. (b) Find the period of each state. exactly 5 seconds. ((1) Find the average rest time for Doctor Strange between his attacks on Thanos. That is, nd ]E[pp I X0 = D] where pp is the rest time for Doctor Strange. Depending on how you do the problem, you may want to use: 22:0 1" = and Eliot-1" = g for M