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A customer buys a $1000 deductible policy on her $31,000
Chapter 3, Problem 14E(choose chapter or problem)
Problem 14E
A customer buys a $1000 deductible policy on her $31,000 car. The probability of having an accident in which the loss is greater than $1000 is 0.03, and then that loss, as a fraction of the value of the car minus the deductible, has the pdf f (x) = 6(1 − x)5, 0 < x < 1.
(a) What is the probability that the insurance company must pay the customer more than $2000?
(b) What does the company expect to pay?
Questions & Answers
QUESTION:
Problem 14E
A customer buys a $1000 deductible policy on her $31,000 car. The probability of having an accident in which the loss is greater than $1000 is 0.03, and then that loss, as a fraction of the value of the car minus the deductible, has the pdf f (x) = 6(1 − x)5, 0 < x < 1.
(a) What is the probability that the insurance company must pay the customer more than $2000?
(b) What does the company expect to pay?
ANSWER:
Solution 14E
Step1 of 3:
We have car policy problem that is A customer buys a $1000 deductible policy on her $31,000 car.
P(having an accident in which the loss is greater than $1000) = 0.03.
The probability density function is .
We need to find,
(a) P(the insurance company must pay the customer more than $2000) = ?
(b) What does the company expect to pay?
Step2 of 3:
a).
The probability that the insurance company must pay the customer more than $2000 is given by
= ………..(1)
Where,
Let
Then,