1. There are two types of driver. Good driver makes 75% of the population and in one year have zero claims with probability 0.7, one claim with probability 0.2, and two claims with probability 0.1. Bad drivers makes up 25% of the population and have zero, one, or two claims with probability 0.5, 0.3, 0.2, respectively. For a particular policyholder, suppose we have observed zero claim in year 1 and one claim in year 2. 1) What is the probability that the policyholder is a good driver? 2) What is the probability that the policyholder makes no claims next year? 3) What is the expected number of claims next year? What is the Variance? 2. Insurance policies are often sold with a deductible of d. When the loss x, is at or below d, the insured will not make a claim and the insurance pays nothing. When the loss is above d, the insured will make a claim and the insurance pays the claim amount, x-d. Suppose the losses have an exponential distribution with mean 1000. There is a deductible of 100. 1) What is the expected claim amount? 2) A loss is occurred, what is the probability that the insured will make a claim ? 3) There losses are occurred, assume the losses are independent. What is the probability that exactly one claim is made. 4) One hundred claims are made, assume the losses are independent. What is the probability that the average claim amount is over 1000e^(-0.1). 是否可请各位赐教，并非直接把题目丢上来给各位解答，想了很多天，自己写得答案， 写了又划掉，写了又划掉，每次的想法都不同，所已是否可以请各位帮忙解答一下， 谢谢!! -- --

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