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

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Stat 5102 First Midterm Exam February 24, 2010 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.] For the following data 1.5 2.0 2.5 3.0 4.5 7.0 11.5 16 (a) Find the mean of the empirical distribution. (b) Find a median of the empirical distribution. 1

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(c) Find a 0.25 quantile of the empirical distribution. 2. [20 pts.] The function F θ ( x ) = ( 0 , x 1 1 - x - θ , x > 1 is a distribution function (note: DF not PDF) when the parameter θ is any positive real number. Find the asymptotic distribution of the sample median of an independent and identically distributed (IID) sample having this distribution.
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t1 - Stat 5102 First Midterm Exam Name Student ID 1 The...

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