# t1 - Stat 5102 First Midterm Exam Name Student ID 1 The...

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February 25, 2009 Name Student ID The exam is closed book and closed notes. You may use one 8 1 2 × 11 sheet of paper with formulas, etc. You may also use the handouts on “brand name distributions” and Greek letters. Put all of your work on this test form (use the back if necessary). Show your work or give an explanation of your answer. No credit for numbers with no indication of where they came from. The points for the questions total to 100. There are 5 pages and 5 prob- lems. 1. [20 pts.] The function f μ ( x ) = 2 π ( e x - μ + e - ( x - μ ) ) , -∞ < x < is a probability density function (PDF), where the parameter μ can be any real number. The mean and variance of this distribution are E ( X ) = μ var( X ) = π 2 4 You do not have to prove any of the above. Given that information, ﬁnd the asymptotic relative eﬃciency (ARE) of the sample mean and sample median of an independent and identically distributed (IID) sample from this distribution, both considered as estimators of μ . 1

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## This note was uploaded on 10/28/2010 for the course STAT 2102 taught by Professor Geyer during the Spring '09 term at Minnesota.

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t1 - Stat 5102 First Midterm Exam Name Student ID 1 The...

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