Let (Xn)n be a Markov chain on a nite state space S with transition probabilities pmy. Suppose a is absorbing and that all other states are transient. Find the minimal non negative solution h of the system { 2&3 Express h in its simplest form. 1 Pm + ZyESpwyh(y)a 23 7 0'- Optional. Show that the above system has a unique nonnegative solution. Hint. Let g be a solution to the above system, I: = g h, M = maxmes k(a:) and B = {3: E S : k(:13) = M}, and then reason by contradiction