3-(24 points) consider a Markov process with 4 states (1, 2, 3, 4) and the following Transitional Probability Matrix and initial PMF: [0.5 0.2 0.3 0 0 0.4 0.6 0 P = = ' 0 0.2 0.6 0.2 °[0.5 0.3 0.2 0] 0 0 0.5 0.5 a) What is the steady state probability? b) What is the probability that X3 = 4? c) Let N be the consecutive number of times that you can be at state 1. Find the PMF of N. d) What is the average time of returning to state 4, once you leave it?