Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $$280,$ the probability of a fire is $0\mathrm{.}1\%,$ and in the event of a fire, the insured damages $($the payout on the policy$)$ will be $$270,000.$

Required:

a$.$ Make a table of the two possible payouts on each policy with the probability of each.

Note: Negative answers should be indicated with a minus sign.

$\backslash$table$[[$Payout$,,,,\backslash$table$[[$come B:$],[$Fire$!]]],[$$$,280,$$$,(269,720)$

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $$280,$ the probability of a fire is $0\mathrm{.}1\%,$ and in the event of a fire, the insured damages $($the payout on the policy$)$ will be $$270,000.$

Required:

a$.$ Make a table of the two possible payouts on each policy with the probability of each.

Note: Negative answers should be indicated with a minus sign.

$\backslash$table$[[,\backslash$table$[[$Outcome A:$],[$No Fire$]],\backslash$table$[[$

Outcome B:$],[$Fire$!]]],[$Payout$,280,$$$,(269,720)$

Please also answer D$,$ E$,$F$,$ &G

D$.$ What are the expected value,variance, and standard deviation of your profit?

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

F$.$ Continue to assume the company has issued two policies, but now assume you take on a partner, so that each own one$-$half of the firm. Make a tabke of your share of the possible payouts the company may have to make on the two policies, along with thier associated probabilities.

G$.$ what are the expected value and variance of your profit?