In a year, weather can impose storm damage to a home. From year to year the damage is random. Let Y be the dollar value of damage in a given year. Assume that 95% of the year's Y=$1,000, and 5% of the years, Y=$15,000.
a. Calculate the mean and standard deviation of the damage in any year.
b. Consider an 'insurance pool' of 100 sufficiently dispersed homes, which implies the damage to dissimilar homes can be viewed as separately distributed as random variables. If ? is the average damage to those 100 homes in a year, (i) what is the expected value of the average damage? (ii) What is the probability that ? exceeds $2000?