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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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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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
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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