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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. SetY= + W, where >0. In terms of and ,determine(a) the distribution function ofY;(b) the density function ofY;(c) the quantiles ofY;(d) the mean ofY;(e) the variance LetYbe a random variable having mean and suppose thatE[(Y )4] this information to determine a good upper bound toP(|Y | 10).5. LetUandVbe independent random variables, each uniformly distributed on[0,1].

Practice Exams First Practice First Midterm Exam 1. Write an essay on variance and standard deviation. 2. Let W have the exponential distribution with mean 1. Explain how W can be used to construct a random variable Y = g(W) such that Y is uniformly distributed on {0,1,2}. 3. Let W have the density function f given by f(w) = 2/w3 for w > 1 and

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