SOA EXAM/P 考題 - 金融分析師

題目如下

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.
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Calculate the probability that the total benefit paid to the family

does not exceed 5.

我的解法

設 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


而詳解是

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的意思不是說在額度以下自付，超過的部份才由保險支付嗎?

還是我對題目的理解有誤?

還有文中標示的那段有用嗎?

thanks









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