推 david529d:東吳商數的解答在市面上都找不到 11/11 11:20
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).
是否可請各位賜教，並非直接把題目丟上來給各位解答，想了很多天，自己寫得答案，
寫了又劃掉，寫了又劃掉，每次的想法都不同，所已是否可以請各位幫忙解答一下，
謝謝!!
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