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Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 3.4 - Problem 14e
Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 3.4 - Problem 14e

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# A customer buys a \$1000 deductible policy on her \$31,000

ISBN: 9780321923271 41

## Solution for problem 14E Chapter 3.4

Probability and Statistical Inference | 9th Edition

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Problem 14E

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?

Step-by-Step Solution:
Step 1 of 3

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, =

Substitute  value in above equation (1) we get

=

=

= 0.0198.

Therefore,P(the insurance company must pay the customer more than \$2000) = 0.0198.

Step3 of 3:

b).

Consider,

= 900

Let

Then,

Now,

= 5400

= 5400

=

= 128.57

Therefore, 128.57.

Conclusion:

Therefore,

a).P(the insurance company must pay the customer more than \$2000) = 0.0198.

b). 128.57.

Step 2 of 3

Step 3 of 3

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