1. Suppose that Jack and Mary face an independent and identical risk of car accident as follows: Loss amount Probability S 0 70% S 30,000 20% 5 90,000 10% C. Now suppose that, once a claim is submitted, the insurer can investigate it by incurring a cost $10,000. From the investigation, the insurer can tell whether the loss occurs or not, but it is still unable to observe the actual loss amount (i.e., $30,000 vs. $90,000). If the insurer investigates all claims and refuses to pay "verified\" fraudulent claims, what is the minimum premium that the insurer is willing to charge on a full coverage policy? (Hint: For the insurer to break even, the expected investigation cost must be included in the premium.) (10 points) How does your answer in (c) change if the investigation allows the insurer to verify the occurrence of $90,000 loss only (i.e., it does not tell whether the minor loss $30,000 actually occurs)? (10 points)