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

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 14E Chapter 3.4

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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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, =...

Step 2 of 3

Chapter 3.4, Problem 14E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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

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