Question

Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.83, 0.10, 0.05, and 0.02, respectively. A particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge?

Answer 1

$150

Explanation:

In this case, we have a random variable with four possible outcomes

0, 1000, 5000 and 10000

and four possible probabilities of occurrence

0.83, 0.10, 0.05 and 0.02

respectively.

The expectation of this random variable is (* means multiplication),

0.83*0 + 0.10*1000 + 0.05*5000 + 0.02*10000 = 100 + 250 + 200 = 550

This represents the amount of money the company expects to pay a customer in a given year.

As the deductible is $500, the customer would pay $500 in case of an accident, so the company would only have to pay

$550 - $500 = $50.

So, if the company wishes a profit of $100, the premium amount should be $150.