How can I read this matrix and identify communicating classes? Our professor explained it, but I was still really confused. I would also appreciate learning how to compute the expectations, probabilities, and distributions, because I'm really struggling with this subject. Thanks in advance!

1. A Markov chain (X, : n 2 0) with states 0, 1, 2, 3, has the transition probability matrix P = NIHJIN ONI WIN O O O (Each part carries 2 points.) a.) Identify the communicating class(es). b.) Compute P(X3 = x Xo = 3) for r = 0, 1, 2, 3. c.) Suppose the initial distribution is given by A = (2, }, },0), i.e., P(X, = r) is given by the r-th element of . Compute the distribution of X3. d.) Compute E(X3). e.) Suppose that a reward function is given by r = (r(x) : x = 0, 1, 2, 3) = (0, 1, 2, 3), compute E(r(X3))