t1 - Stat 5102 First Midterm Exam February 25, 2009 Name...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

t1 - Stat 5102 First Midterm Exam February 25, 2009 Name...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online