Please show me the work thank you very much

Problem 5.3 (10 points) Consider a Markov chain (Xn)n=0,1,2,... with state space 8 = {1, 2,3} and transition probability matrix 3/10 2/10 5/10 P= 1/10 7/10 2/10 2/10 4/10 4/10 The initial distribution is given by aT = (1 /4, 5/8, 1/8). Compute (a) IP[X2 = k] for each k = 1,2,3; ('0) E[X2]~ Does the distribution of X2 computed in (a) depend on the initial distribution a? Does the expected value of X2 computed in (b) depend on the initial distribution a? Give a reason for both of your answers