midterm-sample

midterm-sample - McGill University Probability Theory (Math...

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Unformatted text preview: McGill University Probability Theory (Math 323) Sample Mid-Term 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.

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midterm-sample - McGill University Probability Theory (Math...

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