Exercise 5. In financial markets, banks (for example, JP Morgan) receive grades from various ratings agencies (for example, the Moody's investor services). The ratings are complicated but are based on letter grades. Sup- pose for simplicity that a bank can recieve a grade A, a grade B or a grade D. Grade D means the bank is filing for bankrupcy and ratings agencies typi- cally use CTMCs to model bankrupcy events. Let X = {X1}120 be CMTC on the states S = {A, B, D}. Suppose that rA and rp are the positive rates at which the chain X transitions out of states A and B. The bank files for bankrupcy with probability Pa given it has an A rating and probability PB given it has a B rating. Given Xo = A compute the expected time until the bank files for bankrupcy (i.e., find E(T) where T = inf{t > 0: X, = D}). Exercise 5. In financial markets, banks (for example, JP Morgan) receive grades from various ratings agencies (for example, the Moody's investor services). The ratings are complicated but are based on letter grades. Sup- pose for simplicity that a bank can recieve a grade A, a grade B or a grade D. Grade D means the bank is filing for bankrupcy and ratings agencies typi- cally use CTMCs to model bankrupcy events. Let X = {X1}120 be CMTC on the states S = {A, B, D}. Suppose that rA and rp are the positive rates at which the chain X transitions out of states A and B. The bank files for bankrupcy with probability Pa given it has an A rating and probability PB given it has a B rating. Given Xo = A compute the expected time until the bank files for bankrupcy (i.e., find E(T) where T = inf{t > 0: X, = D})