Question

A customer for a $50,000 fire insurance policy has a home in an area that may sustain a total loss in a given year with a probability of 0.001 and a 50% loss with a probability of 0.01. There is a 0.989 chance that the customer will make no claim in the coverage year. This same customer also wants a $20,000 renter’s insurance policy. The probability of a total loss is 0.005, the probability of a 50% loss is 0.015, and the probability of no loss is 0.98.

Let X be the company's loss on the fire policy and Y be the company's loss on the renter's policy.

Suppose the customer wants to increase the payout of the fire policy by 10% and the renter's insurance policy by 20%.

Find the variance of the combined policy, P = V(1.1X + 1.2Y), assuming the policy payouts are independent.

Answer 1

Expected value of X, E[X] = 0.001*$50,000 + 0.01*0.5*$50,000 = $300

Variance of X ,V[X] = = 8,660,000

Similarly, Variance of Y , V[Y] =

=

= 3,437,500

Variance of the combined policy , P = V(1.1X + 1.2Y)

= = 15,248,600