Suppose a Markov chain has three states, A, B, and C From state A, the process changes randomly to a different state. From state B, the process is equally likely to stay as to change. If it changes, each other state is equally ikely From state C, the process is three times as likely to change as to stay, but it never changes to B P(B-+C)? (a) Carefully set up a transition diagram or transition matrix. What is Give exact answer.) (b) What is P(C- A) Give exact answer.) (c) Right now the process is at state C. What is the probability that the next three states will be ABC (in that order)? Give exact answer.) (d) Right now the process is at state B. What is the probability that in two moves, the process will be at state C? (Give exact answer.)