Exam P Practice Problem 54 – Expected Insurance Payment

Problem 54-A

An insurance policy is purchased to reimburse a loss that is modeled by the following probability density function:

      \displaystyle f(x)=\frac{30}{1024} \ x^2 \ (4-x)^2 \ \ \ \ \ \ \ 0<x<4

This insurance policy has a deductible of 1 with an additional provision that any loss that exceeds the deductible will be paid in full to the policyholder.

When there is a loss, what is the expected amount paid to the policyholder under this policy?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 1.028

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 1.598

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 1.836

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 1.925

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 2.000

\text{ }

\text{ }

\text{ }

\text{ }

Problem 54-B

An insurance policy is purchased to reimburse a loss that is modeled by the following probability density function:

      \displaystyle f(x)=\frac{5}{256} \ x^3 \ (4-x) \ \ \ \ \ \ \ 0<x<4

This insurance policy has a deductible of 2 with an additional provision that any loss that exceeds the deductible will be paid in full to the policyholder.

When there is a loss, what is the expected amount paid to the policyholder under this policy?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.750

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 2.375

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 2.667

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 3.375

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 3.667

________________________________________________________

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

________________________________________________________

Answers

________________________________________________________

\copyright \ 2013

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: