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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 Spring '03
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 Normal Distribution, positive real number

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