Problem 2 Answer all the questions based on the following state diagram. 1 0.5 3 0.5 1 (1). How many class(es) does this chain have? Explain your answer. (2). Is this an ergodic chain? Explain your answer. (3). Set up the equations then compute the value of T; for all states j. (4). In this chain, does the Tj represent the limit limn+00 pm)? Why? (5). Now, assume this chain describes a gambling game. The prizes are 5, 1, 10 dollars for the states 1, 2, 3 respectively. Calculate the long-run expected reward per unit time. (6). Set up the equations then compute the expected first passage time mij for all states i and j. (7). Based on the setting in (5), interpret the meaning of m31