# Exam P Practice Problem 96 – Expected Insurance Payment

Problem 96-A

An insurance policy is purchased to cover a random loss subject to a deductible of 1. The cumulative distribution function of the loss amount $X$ is:

$\displaystyle F(x) = \left\{ \begin{array}{ll} \displaystyle 0 &\ \ \ \ \ \ x<0 \\ \text{ } & \text{ } \\ \displaystyle \frac{3}{25} \ x^2 - \frac{2}{125} \ x^3 &\ \ \ \ \ \ 0 \le x<5 \\ \text{ } & \text{ } \\ 1 &\ \ \ \ \ \ 5

Given a random loss $X$, determine the expected payment made under this insurance policy?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 0.50$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 1.54$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 1.72$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 4.63$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 6.26$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

Problem 96-B

An insurance policy is purchased to cover a random loss subject to a deductible of 2. The density function of the loss amount $X$ is:

$\displaystyle f(x) = \left\{ \begin{array}{ll} \displaystyle \frac{3}{8} \biggl(1- \frac{1}{4} \ x + \frac{1}{64} \ x^2 \biggr) &\ \ \ \ \ \ 0

Given a random loss $X$, what is the expected benefit paid by this insurance policy?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 0.51$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 0.57$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 0.63$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 1.60$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 2.00$

_______________________________________________

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

_______________________________________________

$\copyright \ 2016 - \text{Dan Ma}$