(10 pts) You have recently joined a retail credit risk management team. After looking at some historical data, your coworkers have concluded that loan applicants (for the 1 year loan your group offers) can be grouped into three types: No-risk borrowers: who are certain to repay their loans (i.e., their default probability is zero) Moderate Risk Borrowers: these borrowers will default on average 6 percent of the time High Risk Borrowers: who are certain to default on their loans Your data indicates that a 40 % of loan applicants are no risk types, 40 % are moderate risk types and 20 % are high risk types. If a borrower defaults, the recovery rate is 0 (i.e., LGD is 100%). You have been told that the internal charge for one dollar of funds in 5%. However, since your group is small compared to the rest of the bank, you can treat this supply of funds as perfectly elastic (i.e., you can access as much funds to lend out as you wish so long as you can make a case that lending is profitable. The interest rate on the one-year loan your group offers is fixed as 10%. This is a simple loan, where a face value of $X is borrowed a today, in exchange for repaying $X(1+r) in one year. All applicants report a single credit score. The high risk applicants report credit scores uniformly distributed on the interval [a,b], the mid- dle risk applicants are uniformly distributed on (c,d) and the no risk r = borrowers credit scores are uniformly distributed on the interval [e,f]. a