Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $$170,$ 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 $$160,000.$

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.$)$

Answer is complete and correct.

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.$)$

Answer is complete and correct.

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.$)$

e$.$ Compare your answers to $($b$)$ and $($d$).$ Did risk pooling increase or decrease the variance of your profit?

Answer is complete and correct.

$\backslash$table$[[$Risk pooling,increased,the total variance of profit.$]]$

f$.$ Continue to assume the company has issued two policies, but now assume you take on a partner, so that you each

own one$-$half of the firm. Make a table of your share of the possible payouts the company may have to make on the

two policies, along with their associated probabilities. $($Negative answers should be indicated with a minus sign.

Round your "Probability" answers to $4$ decimal places.$)$g$.$ What are the expected value and variance of your profit?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.$)$