9. Consider a firm with an F rating.

a. What is the probability that after 4 years it will still have an F rating?

b. What is the probability that after 4 years it will have an FF or FFF rating?

c. From examining the transition matrix, are firms tending over time to become rated more or less highly? Why?

For the next two problems, use this information on credit ratings. Suppose there are three credit ratings, F (first-rate), FF (future failure?), and FFF (fading, forlorn, and forsaken).
The transition matrix between ratings looks like this:
Rating to:
Rating from: F FF FFF F 0.9 0.07 0.03 FF 0.15 0.80 0.05 FFF 0.10 0.30 0.6