1. An insurance policy is being issued for a loss with the following discrete distribution: X = 2, with probability = 0.4 20, with probability = 0.6 (a) Find the expected payment by the insurer. ( b ) An actuary has to set up deductible d for this policy so that the expected payment by the insurer is 6. Find d. 2. A policyholder's loss, X, follows a distribution with density function: 2 f( x) = 1x3' for x > 1 0 , otherwise What is the expected value of the benefit paid under the insurance policy if the insurance policy reimburses the loss (a) up to a benefit limit of 10? (b) with a deductible of 5? 3. An insurance policy is written to cover a loss, X, where X has a uniform on [0, 1000]. At what level must a deductible be set in order for the expected payment to be 25% of what it would be with no deductible? 4. An insurance policy covers losses due to theft, with a deductible of 3. Theft losses are uniformly distributed on [0, 10]. Determine the moment generating function, M((), for t # 0, of the claim payment on a theft. 5. Losses covered by a flood insurance policy are uniformly distributed on the interval [0, 2]. The insurer pays the amount of the loss in excess of a deductible d. The probability that the insurer pays at least 1.20 on a random loss is 0.30. Calculate the probability that the insurer pays at least 1.44 on a random loss. 6. Losses due to accidents at an amusement park are exponentially distributed. An insurance company offers the park owner two different policies, with different premiums, to insure against losses due to accidents at the park. Policy A has a deductible of 1.44. For a random loss, the probability is 0.640 that under this policy, the insurer will pay some money to the park owner. Policy B has a deductible of d. For a random loss, the probability is 0.512 that under this policy, the insurer will pay some money to the park owner. Calculate d