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quiz2BS-M1_f10

quiz2BS-M1_f10 - Econ 506 Section M1 Quiz 2B Sept 30 2010...

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Econ 506, Section M1 NAME:_ SOLUTION_ _____ Quiz 2B, Sept. 30, 2010 Total points: 50 I. The probability that you find a defective machine in a warehouse is 0.2. A company selects the machines randomly. a. (4 points) the company repairs the defective ones at a cost of \$50 each. Find the mean and variance of the total repair cost, if the company selects 5 machines. let Y = # of defective machine selected in 5 machines E (50 Y ) = 50 E ( Y ) = 50[5 ( 29 10 2 ] = \$50. Furthermore, V (50 Y ) = 2500 V ( Y ) = 2500[5 ( 29 10 8 10 2 ] = 2000. b. (5 points) what is the probability that the third defective machine is found on the selection of the fifth machine? let Y = # of machine selected until third defective is found. Therefore, Y is negative binomial where r = 3 and p = 0.4. Then, P ( Y = 5) = ( 29 ( 29 083 . 6 . 0 4 . 0 2 4 3 3 = . II. Let Y be a continuous random variable, with the following probability density function: = elsewhere

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quiz2BS-M1_f10 - Econ 506 Section M1 Quiz 2B Sept 30 2010...

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