practicemidterm

practicemidterm - 36-226 INTRO TO PROBABILITY&...

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Unformatted text preview: 36-226 INTRO TO PROBABILITY & STATISTICS II N08PRACTICE MIDTERMYou must show your work and/or explain your steps in order to get full credit or be consideredfor partial credit.This is a closed book/closed notes exam. You may use aone–sidedsheet of notes (8.5 by11 inches) and a calculator. You may not share a calculator, pencil, paper or anything elseduring the exam.Your ANDREW ID:Your First Name:Your Last Name:Your Signature:Grader use:ProblemTotalCorrect1492373648Total100*** Do not turn this page until instructed to do so.***1PLEASE CHECK THAT YOU HAVE PAGES 1 THROUGH 71. LetX1,X2,...,Xnbe i.i.d. from aGamma(2, θ)distribution, which has the followingdensity function:fX(x;θ) =xe-x/θθ2x >θ >otherwiseFor this problem it will be useful to know that:X1,X2,...,Xni.i.d∼Gamma(2, θ) =⇒∑ni=1Xi∼Ga(2n, θ)(a) (8 points) Find a sufficient statistic forθusing the factorization theorem....
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practicemidterm - 36-226 INTRO TO PROBABILITY&...

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