作者lyndonxxx (lyndon)
看板CFAiafeFSA
标题[请益] SOA EXAM/P 考题
时间Thu Jul 28 13:44:37 2011
题目如下
A family buys two policies from the same insurance company.
Losses under the two policies are independent and have continuous
uniform distributions on the interval from 0 to 10.
One policy has a deductible of 1 and the other has a deductible of 2.
The family experiences exactly one loss under each policy.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Calculate the probability that the total benefit paid to the family
does not exceed 5.
我的解法
设 X and Y ~ U(0,10)
X' = X-1 , X > 1 and P = 9/10
Y' = Y-2 , Y > 2 and P = 4/5
P(X'+Y'< 5) = P(X+Y<8,X>1,Y>2) = 0.125
而详解是
P(0<X<6,0<Y<2) + P(0<X<1,2<Y<7) + P(1<X<6,2<Y<8-X) = 0.295
deductible的意思不是说在额度以下自付，超过的部份才由保险支付吗?
还是我对题目的理解有误?
还有文中标示的那段有用吗?
thanks
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 118.171.210.33
※ 编辑: lyndonxxx 来自: 118.171.210.33 (07/28 13:45)
1F：推 joewusuper:文章的那一句话~应该是每张保单都一定有一个理赔发生 07/28 14:12
2F：→ joewusuper:详解:X第一张保单损失在0~5元~第二章没损失 07/28 14:13
3F：→ joewusuper:+第一章没损失第二章损失在0~5元 07/28 14:13
4F：→ joewusuper:+第一章损失损失在X元(5元之下)~第二章5-X元 07/28 14:14
5F：→ joewusuper:你的答案~应该只考虑到详解的第三个部份~前两各没考虑 07/28 14:15
6F：→ lyndonxxx:那如果考虑那段话，应该要从X>1,Y>1开始吗? 07/28 19:55
7F：推 how155031:这种题目 画图去想 会是最安全的解法．． 07/29 00:28
8F：推 louis0407:先从各只有一张保单赔偿算起 也就是X与Y其中一个要大过 08/02 20:12
9F：→ louis0407:deductible 再计算两个都大过之後的情况 08/02 20:13
10F：推 louis0407:你一开始是先假设两张保单都有赔偿发生 所以漏了一部分 08/02 20:17