exam p sample test 150求助

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题目如下

150. An automobile insurance company issues a one-year policy with a deductible of 500. The probability is 0.8 that the insured automobile has no accident and 0.0 that the automobile has more than one accident. If there is an accident, the loss before application of the deductible is exponentially distributed with mean 3000.

Calculate the 95th percentile of the insurance company payout on this policy.

(A) 3466

(B) 3659

(C) 4159

(D) 8487

(E) 8987

解答是这样的

                                                                                               

150. Solution: B

The 95th percentile is in the range when an accident occurs. It is the 75th percentile of the payout, given that an accident occurs, because (0.95 - 0.80)/(1 - 0.80) = 0.75. Letting x be the 75th

3000

percentile of the given exponential distribution, F(x) = 0.75, so x = 4159. Subtracting

the deductible of 500 gives 3659 as the (unconditional) 95th percentile of the insurance company payout.

我对这个解答感到很费解，求学霸们指教。

                               
                       
               

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关键词：Sample Exam P AMPL test Exam automobile insurance company before issues

刚过p 过来献丑一下希望给楼主的杀p之旅加点油。

解答：
注意题目中If there is an accident, the loss before application of the deductible is exponentially distributed with mean 3000.
所以这个exponential function是在发生了accident的条件下产生的(conditional)， 而95th percentile是unconditional = 正常无任何限制的,所以为了用这个exponential function去计算loss, 你得把这个95th percentile转换成conditional的： "there is an accident"的概率是1-0.80，percentile转换过来也就是解答中给的(0.95 - 0.80)/(1 - 0.80) = 0.75。然后你就可以愉快的把0.75带去cdf里算出来了。记得减去deductible 500就是保险公司付的钱了。

希望对题主有帮助 :)