Chapter 6.1, Problem 10E

a.

To determine

To construct: A table of the probability distribution of Y .

Explanation of Solution

Given:

Amount spend on insurance = $300

Amount insurance will pay if fire destroys home = $200000

Probability that fire will destroy the home = 0.0002

Calculation:

Using the provided information, the probability distribution is:

Y	300-200000	300
Probability	0.0002	1-0.0002

Thus, the probability distribution is:

Y ($)	199700	300
Probability	0.0002	0.9998

b.

To determine

To find: The expected value and interpret it

Answer to Problem 10E

The expected value is $260

Explanation of Solution

Calculation:

The expected value can be calculated as:

  $\begin{array}{c}\text{E}\left(Y\right)\text{=}{\displaystyle \sum y\times P\left(y\right)}\\ =300\left(0.9998\right)+\left(-199700\right)\left(0.0002\right)\\ =260\end{array}$

The expected value is $260.

The expected gain for the insurance company per homeowner is $260.