# quiz3BS-M_f10 - Section M ECON 506 Section M Quiz 3 Version...

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Section M Quiz 3 Version B ECON 506, Section M Solution NAME: ___Ali Toossi_________________ Quiz 3, Version B November 11 2010 NetID: ______________________________ Total points: 50 I. (5 points) Suppose that a company has determined that the number of jobs per week, N , varies from week to week and has a Poisson distribution with mean λ. The number of hours to complete each job Y i , is gamma distributed with parameters α and β. The total time to complete all jobs in a week is = = N i i Y T 1 . What is E (T | N = n ) and E (T)? [Use iterated expectation]. Solution: = = = = = = = = n i n i i n i i n Y E Y E n N T E 1 1 1 ) ( ) ( ) | ( αβ λαβ = = = = = ) ( ) ( )] | ( [ ) ( n E n E n N T E E T E II. Let 40 2 1 , , , X X X denotes a random sample of size 40 from the uniform distribution U (0, 1). Suppose X is the mean of this sample. Let 30 2 1 , , , Y Y Y denotes a random sample of size 30 from the standard normal distribution. (a) (5 points)

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quiz3BS-M_f10 - Section M ECON 506 Section M Quiz 3 Version...

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