pfinal2 - 36-226 INTRO TO PROBABILITY &...

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Unformatted text preview: 36-226 INTRO TO PROBABILITY & STATISTICS II N08PRACTICE FINAL EXAMYou 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 aonesidedsheet of notes (8.5 by 11inches) and a non-programmable calculator. You may not share a calculator, pencil, paperor anything else during the exam.Your ANDREW ID:Your First Name:Your Last Name:Your Signature:Grader use:ProblemTotalCorrect130215310415510610710Total100*** Do not turn this page until instructed to do so.***1PLEASE CHECK THAT YOU HAVE PAGES 1 THROUGH 121. LetX1,X2,...,Xnbe a random sample from the following distribution:fX(x;) =2xe-xx > >otherwiseNote:This is aGa(2,1)distribution.Useful Facts:IfYGamma( , ), thenE(Y) =V(Y) =2(a) (8 points) Find the maximum likelihood estimator for(be sure to verify that it isindeedmaximum).2(b) (7 points) Find a large-sample approximate100(1-)%confidence interval forbased on the MLE....
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pfinal2 - 36-226 INTRO TO PROBABILITY &...

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