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# pfinal2 - 36-226 INTRO TO PROBABILITY STATISTICS II N08...

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36-226 INTRO TO PROBABILITY & STATISTICS II N08 PRACTICE FINAL EXAM You must show your work and/or explain your steps in order to get full credit or be considered for partial credit. This is a closed book/closed notes exam. You may use a one–sided sheet of notes (8.5 by 11 inches) and a non-programmable calculator. You may not share a calculator, pencil, paper or anything else during the exam. Your ANDREW ID: Your First Name: Your Last Name: Your Signature: Grader use: Problem Total Correct 1 30 2 15 3 10 4 15 5 10 6 10 7 10 Total 100 *** Do not turn this page until instructed to do so.*** 1

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PLEASE CHECK THAT YOU HAVE PAGES 1 THROUGH 12 1. Let X 1 , X 2 , . . . , X n be a random sample from the following distribution: f X ( x ; θ ) = θ 2 xe - θx x > 0 θ > 0 0 otherwise Note : This is a Ga (2 , 1 θ ) distribution. Useful Facts: If Y Gamma( α , β ), then E ( Y ) = α · β V ( Y ) = α · β 2 (a) (8 points) Find the maximum likelihood estimator for θ (be sure to verify that it is indeed maximum ).
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pfinal2 - 36-226 INTRO TO PROBABILITY STATISTICS II N08...

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