Question: In any year, the weather can inflict damage to a home. From year to year, the damage is random. Let Y denote the dollar value of damage in a given year. Suppose that in 95% of the years Y =$0, but in 5% of the years Y = $20,000.

1. What are the mean and standard deviation of the damage in any year? (2 points)
2. Consider an insurance pool of 100 people whose homes are sufficiently dispersed so that, in any year, the damage to different homes can be viewed as independently distributed random variables. Let \(\bar{Y}\) denote the average damage to these 100 homes in a year.

1. What is the expected value of the average damage \(E\left( {\bar{Y}} \right)\) ?
2. What is the probability that \(\bar{Y}\) exceeds $2,000?
3. How would you use economic theory to determine the maximum amount a homeowner would pay to insure against the potential $20,000 damage? (1 point)

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