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s230.as3.F09-1 - Then check your answer using E X 1 X 2 E X...

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Probability Statistics 230, Fall 2009 Assignment 3 Please indicate your name, ID number an instructor/section on your submission. 1. The life of a compact fluorescent light bulb (CFL) is modeled by an exponential distribution, with a median life of 9000 hrs. (a) Find the mean life of CFLs. (b) You have 2 CFLs and replace the first immediately with the second bulb when it fails. Let X be the total life of these 2 bulbs. (i) Derive the p.d.f. of X . (ii) Using this p.d.f., find
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Unformatted text preview: . Then check your answer using E X 1 X 2 E X 1 E X 2 . 2. Let f ( x ) k for 0 x 1 k / x for1 x e otherwise (a) Find the constant k , E X and the c.d.f., F x . (b) Let y 1 , y 2 , K , y n be n independent random numbers from a U [0,1) distribution. Show how to transform these n y i values into n x i values from the distribution of X given above....
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