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 0.82, 0.08, 0.08, 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?

The premium amount should it charge is $690

Explanation:

The X values would be 0 1,000 5,000 10,000

Since, we have to deduct the $500 and add the premium amount

So, new X values would be 100 600 4,600 9,600

And, the probability would be 0.82, 0.08, 0.08, and 0.02

So, the premium amount would be equal to

= 100 * 0.82 + 600 * 0.08 + 4,600 * 0.08 + 9,600 * 0.02

= 82 + 48 + 368 + 192

= $690