In any year, the weather can inflict storm damage to a home. from year to year, the damage is random. let y denote the dollar value of damage in any given year: suppose that in 95% of the years y = $0, but in 5% of the years y = $2.
a. what is the mean and the standard deviation of the damage to a home in any given year?
b. consider an "insurance pool" of 100 people whose homes are sufficiently dispersed so that, in any given year, the damage to different homes are viewed as independently distributed random variables. let y denote the average damage to these 100 homes in a year. (i) what is the expected value of the average damage y ? (ii) what is the probability that y exceeds $2000?