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?

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,

Now,

=

=

=

=

=

=

Hence, =...