Question

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $110, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $100,000.

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

Outcome A: No Fire	Outcome B: Fire!
Payout

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. (Round your "Probability" answers to 4 decimal places.)

Outcome: No Fire		Outcome: One Fire		Outcome: Two Fires
Payout
Probability		%		%	0.0001	%

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

Answer 1

a.

Probability of fire = 0.1% = 0.001

Probability of no fire = 1-0.001 = 0.999

Given that in case of fire sum insured $100,000 which is equal to payout

Outcomes	NO FIRE	FIRE
Payout	$0	$100,000
Probability	0.999	0.001

c.

Given the company issues two policies

Let us now calculate the probabilities

Probability of 0 fire = 0.999 *0.999 = 0.998001

Probability of 1 fire = 2* 0.001 *0.999 = 0.001998

Probability of 2 = 0.001 *0.001 = 0.000001

Outcomes	NO FIRE	ONE FIRE	TWO FIRES
Payout	$0	$100,000	$200,000
Probability	0.998001	0.001998	0.000001

d.

let us first calculate the profits in each outcome

Profit for No fire = $110 + $110 = $220        

Profit for One fire = $220 - $100,000 = - 99780     

Profit for two fire   = $220- $200,000 = -$199780

	A	B	C=A*B	D= B-20	E= D^2	F= E*A
	Probabilities	Profit	Probability *Profit	Deviation from expected return	Square of deviation	Probability * Square of deviation
NO FIRE	0.998001	220	219.56022	200	40000	39920.04
ONE FIRE	0.001998	-99780	-199.36044	-99800	9960040000	19900159.92
TWO FIRES	0.000001	-199780	-0.19978	-199800	39920040000	39920.04
			Total = 20			Total = 19980000

Expected return = $20

Variance = $19,980,000

Standard deviation = square root of deviation = $4469.899328 = $4,469.9