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Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 3 - Problem 30e
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 3 - Problem 30e

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# An individual who has automobile insurance from a certain

ISBN: 9780321629111 32

## Solution for problem 30E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 30E

An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is a.? ?Compute E(Y). b. ?Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge. Step-by-Step Solution: Step 1 of 3 Answer: Step1: An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is Y 0 1 2 3 p(y) 0.6 0.25 0.1 0.05 Step2: a). To compute E(Y). E(y) = y p(y) = 0×0.6 + 1×0.25 + 2×0.1+ 3×0.05 = 0.6 Therefore, E(y) = 0.6 Step3: 2 b). Suppose an individual with Y violations incurs a surcharge of$100Y . To calculate the expected amount of the surcharge. The surcharge is the expected value of 100 dollars times the expected value of the square of ‘y’. Therefore, 2 Surcharge = E(100Y ) dollars. E(100Y ) = 100 E(Y ) 2 = 100(0 ×0.6 + 1 ×0.25 + 2 ×0.1+ 3 ×0.05) = 100(0.25 + 0.4 + 0.45) 2 E(100Y ) = 110

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