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Unformatted text preview: McGill University Probability Theory (Math 323) Sample MidTerm Question 1. Accident records collected by an automobile insurance com pany give the following information. The probability that an insured driver has an automobile accident is 0.15. If an accident has occurred, the damage to the vehicle amounts to 20% of its market value with a probability of 0.80, to 60% of its market value with a probability of 0.12, and to a total loss with a probability of 0.08. What premium should the company charge on a $10,000 car so that the expected gain by the company is zero? Solution: Let G be the premium that the company needs to charge on a $10,000 car, and Y represents the gain by the company on a $10,000 car. Then Y = G with 0.85 chance G . 2(10 , 000) with (0.15)(0.80)=0.140 G . 6(10 , 000) with (0.15)(0.12)=0.018 G 10 , 000 with (0.15)(0.08)=0.014 Then E ( Y ) = G (0 . 85)+( G 2 , 000)(0 . 14)+( G 6 , 000)(0 . 018)+( G 10 , 000)(0 . 014) = 0 , which can be simplified to...
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This note was uploaded on 02/16/2011 for the course MATH 323 taught by Professor Vahid during the Spring '11 term at McGill.
 Spring '11
 Vahid
 Probability

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