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Practice Exams and Their Solutions Based on

Practice Exams and Their SolutionsBased onA Course in Probability and StatisticsCopyrightc 2003 5 by Charles J. StoneDepartment of StatisticsUniversity of California, BerkeleyBerkeley, CA 94720-3860 Please email corrections and other comments to (Chapters 1 6) Practice ExamsFirst Practice First Midterm Exam1. Write an essay on variance and standard LetWhave the exponential distribution with mean 1. Explain howWcanbe used to construct a random variableY=g(W) such thatYis uniformlydistributed on{0,1,2}.3. LetWhave the density functionfgiven byf(w) = 2/w3forw >1 andf(w) = 0 forw 1.

4 Probability 9. Let W 1 and W 2 be independent discrete random variables, each having the probability function given by f(0) = 1 2, f(1) = 1 3, and f(2) = 1 6. Set Y = W 1 +W 2. (a) Determine the mean, variance, and standard deviation of Y.

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