Suppose you work for an insurance company, and you sell an $120,000 _re insurance policy at an annual premium of $1250. Experience has shown that:

the probability of total loss (due to _re) to a house in that area and of the size of your customer's house is .001 (in which case the insurance company will pay the full $120,000 to your customer).

the probability of 50% damage (due to _re) to a house in that area and of the size of your customer's house is .003 (in which case the insurance company will pay only $60,000 to your customer).

(For simplicity, we ignore any other partial losses.)

(a) prepare down the probability distribution of X, the insurance company's annual gain from such a policy (i.e., the amount of money made by the insurance company from such a policy).

(b) What is the mean (expected) annual gain for a policy of this type?

(c) What should be the annual premium (instead of $1250) if the company wants to increase the expected gain from a policy of this type by 10%?