Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $$270,$ the probability of a fire is $0\mathrm{.}1\%,$ and in the event of a fire, the insured damages $($the payout on the policy$)$ will be $$260,000.$

Required:

a$.$ Make a table of the two possible payouts on each policy with the probability of each. $($Negative answers should be indicated with a minus sign.$)$

b$.$ Suppose you own the entire firm, and the company issues only one policy. What are the expected value, variance, and standard deviation of your profit? $($Do not round intermediate calculations. Round your standard deviation to the nearest whole number.$)$

c$.$ Now suppose your company issues two policies. The risk of fire is independent across the two policies. Make a table of the three possible payouts along with their associated probabilities. $($Negative answers should be indicated with a minus sign. Round your "Probability" answers to $4$ decimal places.$)$

d$.$ What are the expected value, variance, and standard deviation of your profit? $($Do not round intermediate calculations. Round your standard deviation to the nearest whole number.$)$Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $$270,$ the probability of a fire is $0\mathrm{.}1\%,$ and in

the event of a fire, the insured damages $($the payout on the policy$)$ will be $$260,000.$

Required:

a$.$ Make a table of the two possible payouts on each policy with the probability of each. $($Negative answers should be indicated with a

minus sign.$)$

b$.$ Suppose you own the entire firm, and the company issues only one policy. What are the expected value, variance, and standard

deviation of your profit? $($Do not round intermediate calculations. Round your standard deviation to the nearest whole number.$)$