# Quiz1 - ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OEM 2009 January 12,2008 QUIZ 8:00-9:00AM Open book This quiz consists of 3 problems

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ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OEM 2009 January 12,2008 QUIZ 8:00-9:00AM Open book This quiz consists of 3 problems Name: UfhtV SJJft4"

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Problem 1: (30 points) Suppose that a fraction 5% of the microchips produced by a leading microchip manufacturer is defective. Historically, given that a microchip is defective, the inspector (wrongly) accepts the chip 10% of the time, thinking it has no defect. If a microchip is not defective, he always correctly accepts it. (a) What is the probability that the inspector accepts a particular microchip? @.O )(0.\0)::: 0·0 leiiV fu-r p-R d O."I50t .00 - ~ / (\itl~ c1iv llc\:iV~ r 'f ,d CCRt~ tet r hd 's" t~ (b) Given that the inspector accepts a microchip, what is the probability)hat it has no defect? (If you were unable to answer (l{), please denote the answer to~ by p). G\ (~) ""3£ --- I OSX6.~) = 0·°15 I ~~ @JjjfJ ·1 5 2
Problem 2: (40 points) The paint department in an automobile factory applies two independent processes when painting cars: (i) painting and (ii) polishing. The painting process is defective 20% of the time, while the polishing process is defective 10% of the time. Each car first goes through the painting and then through the polishing process. Each car is inspected after it has completed the two processes. If either the painting or the polishing is defective, the car is returned to a special station for rework, where the two processes are applied once,again. Rework at the special station is 100% reliable (although it is also very expensive). (a) What is the probability that a car is returned to the special station for rework? p~v = p('6) =: f(A or 0.7-0 ·10 ) - f(A)+f(~)= fii? - p( t1n rr) O'ci / -- (b) Let the random variable X denote the number of cars in a group of 1,000 cars that have painting defects. Determine the (exact) distribution, the expected value, and the standard deviation of X (Do not only specify the type of distribution but also all distribution parameters!) i~ \ ";+[1 ~ThOn e(x/:::- ~ rYX /: /(Jc 3

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(c) Let the random variable Y denote the number of cars in a group of 1,000 cars that have polishing defects. The total number of observed defects is then equal to V = X + Y What is the probability that the total number of observed defects is no more than 325? (Hint: Can you use
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## This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.

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Quiz1 - ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OEM 2009 January 12,2008 QUIZ 8:00-9:00AM Open book This quiz consists of 3 problems

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