Use the given information below in order to solve questions #2 & #3:

Joy owns a $250,000 house, which has a 2% chance of experiencing a fire in any given year. Assume that if a fire occurs, the house is completely destroyed.

For the peril of Joys house burning down the Expected Loss (P*) = $5,000

The amount of risk that Joy faces for the peril of her house burning down, as measured by the Measures of Dispersion that we learned about back in Topic #4, is as follows:

• Variance = $1,225,000,000 squared
• Standard Deviation = $35,000
• Coefficient of Variation = 7.00 or 700%
• Expected Loss (P*) = $5,000

Joy purchases full insurance from Schwartz Insurance Company to insure her home against the peril of fire. Assume that the premium charged by Schwartz Insurance Company is equal to the actuarially fair premium (AFP)

• Meaning, the quote from Schwartz Insurance Company = Joys Expected Loss (P*)
• In turn, the quote from Schwartz Insurance Company = $5,000

Question #2:

Assume Joys best friend Kate owns the same exact type of house (worth $250,000) and faces the same exact probability of her house burning down to the ground (2%). We assume that the two houses are independent of each other. In other words, if one house has a fire, this has no impact on the probability of the other house having a fire.

Like Joy, Kate also purchases full insurance from Schwartz Insurance Company.

Schwartz Insurance Company determines the possible outcomes and corresponding probabilities that could occur if it sells full insurance contracts to BOTH Joy AND Kate:

Outcome	Loss $ Amount	Probability
Both houses do NOT burn down	$0	0.98 * 0.98 = 0.9604
Joys house burns down; AND Kates house does not burn down	$250,000	0.02 * 0.98 = 0.0196
Kates house burns down; AND Joys house does not burn down	$250,000	0.02 * 0.98 = 0.0196
Both houses burn down	$500,000	0.02 * 0.02 = 0.0004
		1.00

Schwartz Insurance Company then calculates the following Probability Distribution for the possible loss outcomes that could occur if it sells full insurance contracts to BOTH Joy AND Kate:

Loss $ Amount	Probability
$0	0.9604
$250,000	0.0392
$500,000	0.0004

1. What is the expected loss or expected payout for Schwartz Insurance Company if it sells full insurance contracts to both Joy and Kate? [2 points]

Expected loss P* = ($0*0.9604) + ($250,000*0.0392) + ($500,000*0.0004)=

($0) + ($9,800) + ($200)

= $10,000

2. Schwartz Insurance Company calculates that a risk pool containing BOTH Joy and Kate has a variance = $2,450,000,000 squared (that is not a typo the number is that large).

Schwartz Insurance Company are professionals, so you can rest assured that the calculated variance is 100% accurate (meaning you do NOT need to calculate it!)

What is the amount of risk Schwartz Insurance Company faces if it sells full insurance contracts to BOTH Joy AND Kate? [2 points]

(Hint: remember how we measure risk, as we learned back in Topic #4!)

3. Briefly explain the benefit(s) to Schwartz Insurance Company as the number of insurance contracts sold increases? Use your calculations from Part B to justify your answer.[2 points]

4. What type of risk pool is the risk pool containing Joy and Kate an example of? [1 point]