11. Let L be a random variable that takes the value S500 with probability 999/ 1000, otherwise, L = $200,000. Suppose that L represents a loss that you are facing. You are considering buying insurance. a) Compute E[L],-00 (b) Compute E[(L-1000)+], (200 Dop-10-r) x.01 (c) If you buy full coverage insurance, the premium charged by the in- surance company is twice the expected loss. How much would full coverage cost? (d) If you "self-insure," what is your expected cost? (e) To lower your average cost, you consider buying insurance with a $1,000 deductible. With a deductible d, you incur the first d 2 0 of any loss and the insurance company incurs any loss above d. That is, the loss L is split into two parts: LA d and (L - d)+. Show that these two pieces add up to L. (f) If d = $1,000 and the insurance company charges you double the expected loss that they will incur, what is the premium? (g) What is your total expected cost, which would be the premium plus the expected cost of the loss you incur assuming a $1,000 deductible? (h) Under what circumstances would a $1,000 deductible be better than either full coverage or self-insuring? By the way, even though the numbers here are made up, the idea of reducing your expected cost but also avoiding a catastrophic loss through a large deductible is often a wise strategy