Question 1: Objective Risk Analysis (20 points)

Consider the following fire loss experience of Nopay Limited over the last 10 years.

Both Nopay Limited and the insurance company believe that the future fire loss will follow the same distribution.

1. a) Determine the expected amount of fire loss for next year. (4 points) (b) Determine the standard deviation of the amount of fire loss for next year. (4 points) (c) Determine the pure premium for the following insurance policies that cover the company for firm losses:

2. i. An insurance policy that provides full coverage. (2 points)

   ii. An insurance policy with $1,000,000 deductible, 50% coinsurance policy up to $2,500,000, and full coverage beyond $2,500,000. (2 points) (d) Suppose Nopay wanted to setup a risk capital that will protect it against fire loss above the expected loss level 95% of the time. Nopay will buy fire insurance to cover the amount of fire loss over the risk capital. Determine the 95% risk capital. (4 points) (e) Explain the meaning of the maximum probable yearly loss. (4 points)

Annual Dollar Losses	Relative Frequency
$0	0.60
1,000,000	0.20
2,500,000	0.10
5,000,000	0.05
8,000,000	0.05