Neighborhood Insurance sells fire insurance policles to local homeowners. The premium is $$110,$ the probability of a fire is $0\mathrm{.}1\%$ and in the event of a fire, the insured damages $($the payout on the policy$)$ will be $$100,000$

Requlred:

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

a minus s$|$gn$.)$

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

b$.$ Suppose you own the entire firm, and the company issues only one policy. What are the expected value, varlance, and standard deviation of your pr ofif $($Do not round Intermedlate calculatlons. Round your standard devlation to the nearest whole number.$)$

$\backslash$table$[[\backslash$table$[[$Expected$],[$Return$]],$Variance,$\backslash$table$[[$Standard$],[$Deviation$]]],[,,]]$

c$.$ Now suppose your company issues wo policies. The risk of fire is independent across the two policles. Make a table of the inree possible payouts along with their associated probabililes. $($Negatlve answers should be Indicated with a minus sign. Round your "probability" answers to $4$ decimal places.l

$\backslash$table$[[,\backslash$table$[[$Outcome$],[$No Fire$]],\backslash$table$[[$Outcome$],[$One Fire$]],\backslash$table$[[$Outcome$],[$Two Fires$]],,],[$Payout$,,,,,],[$Probability$,,$$$,,\%,]]$

d$.$ What are the expected value, varlance, and standard deviation of your profit? $($Do not round Imermedlate calculat lons. Round your standard deviation to the nearest whole number.t

$\backslash$table$[[\backslash$table$[[$Expeted$],[$Return$]],$Variance,$\backslash$table$[[$Standard$],[$Deviation$]]],[,,]]$

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

Risk pooting

The total variance of profit

Continue to ascume the company has is sued two policles, but now as sume you take on a partner, so that you each own one haif of the firm. Make a table of your share of the possible payouts the company may have to make on the two policles, along wath their assoclated probabilines. INegative answers should be Inclicated with a minus sign. Round your "Probability" answers to $4$ derlmel places.l

$\backslash$table$[[,\backslash$table$[[$Outcomes$],[$Ho Fire$]],\backslash$table$[[$Outcomes$],[$One Fire$]],\backslash$table$[[$Outcomes$],[$Two Fires$]],],[$Payout$,,,,],[$Probability$,,,,]]$

g$.$ What are the expected value and varlance of your profir?

$\backslash$table$[[\backslash$table$[[$Expected$],[$Return$]],$Variance,$\backslash$table$[[$Standard$],[$Deviatinn$]]],[,,]]$