Question

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 = $19,792. The mean of the damage in any year is $ 989.6. (Round your response to two decimal places.) The standard deviation of the damage in any year is $ 4313.57 . (Round your response to two decimal places.) 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 Y denote the average damage to these 100 homes in a year. E(), the expected value of the average damage Y, is $ (Round your response to two decimal places.)

Answer 1

Pagena Answey Let'Y' denote the dollar value of damage in any given year. suppose that in 95% of the Year y=$0 but in 5% of the Year y=$19,792 PCy) Y PCY) y² ply) 0.95 | 19492 o-os 989.6 19,586163.2 989-6 1958616 3.2 The Hean ECY) = [ Y P(4) = 989.6 The variance -E(]² 19586163-2 v(Y)= E(42) -[ECY) ECY?)= [y{p(y) v (Y) = ECx2) - [ECY]]? = 19586163.2 - (989-672 i = 19586163-2-979308-16

Pagenol 18,606,855.04 The standard deviation, SD(Y) = July) = 18606855-04 - =4313.56 6395 SDCY) 4313.57 Let y denote the average damage to these homol 100 homes in a year, D şample şi ze meloo 96) The Expected value of the average damange ý iş EC4) 1989.6 Y