I am having trouble with solving this

P is the (one-step) transition probability matrix of a Markov chain with state Space {0, 1, 2, 3, 4}. 0.5 0.0 0.5 0.0 0.0 0.25 0.5 0.25 0.0 0.0 P = 0.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.5 0.0 0.0 0.0 0.5 0.5 (a) Draw a transition diagram. (b) Suppose the chain starts at time 0 in state 2. That is, X0 = 2. Find E[X1]. (0) Suppose the chain starts at time 0 in any of the states with equal probability. Find E[X1]. ((1) Suppose the chain starts at time 0 in state 1. Find the probability that at time 2, the chain will be in state 0. How about the probability that it will in state 2? (e) Calculate the 4-step transition probability matrix