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## Statistics

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%?

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M998665

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