A credit union classifies automobile loans into one of four categories: the loan has been paid in full (F), the account is in good standing (G) with all payments up to date, the account is in arrears (A) with one or more missing payments, or the account has been classified as a bad debt (B) and sold to a collection agency. Past records indicate that each month 10% of theaccounts in good standing pay the loan in full, 80% remain in good standing, and 10% become
in arrears. Furthermore, 10% of the accounts in arrears are paid in full, 40% become accounts in good standing, 40% remain in arrears, and 10% are classified as bad debts.
(a) Give the transition matrix for the described Markov Chain.
(b) What is the probability that an account currently in arrears will eventually be paid in full?
(c) What is the probability that an account in good standing will end up becoming a bad debt that is sold to a collection agency?