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Middle East Technical University
20102011 Fall
Department of Economics
ECON 206
Instructor: Ozan ERUYGUR
Research Assistant: Pelin AKÇAGÜN
PROBLEM SET 03
CENTRAL LIMIT THEOREM
PROBLEM 1
Let
denote the sample variance for a random sample of ten ln(LC50) values for
copper, and let
denote the sample variance for a random sample of eight ln(LC50)
values for lead, both samples using the same species of fish. The population variance
for measurements on copper is assumed to be twice the corresponding population
variance for measurements on lead. Assume
to be independent of
.
2
1
S
2
2
S
2
1
S
2
2
S
a)
Find a number
b
such that
2
1
2
2
.95
S
Pb
S
⎛⎞
≤=
⎜⎟
⎝⎠
b)
Find a number
a
such that
2
1
2
2
.95
S
Pa
S
[
Hint
: Notice that
()
( )
12
21
//
PU U
k
k
≤
1
/
].
c)
If
a
and
b
are as in the previous parts, find
2
1
2
2
S
b
S
≤
≤
.
PROBLEM 2
Let
be a random sample of size 5 from a normal population with mean 0
and variance 1, and let
,
5
,
...,
YY
Y
5
1
1/5
i
i
Y
=
=
Y
∑
. Let
be another independent observation
from the same population. Let
6
Y
Y
5
2
1
1
i
W
=
=
∑
, and let
( )
2
5
1
i
i
UY
Y
=
=−
∑
. What is the
distribution of
U
22
6
25
/
+
? Why?
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This note was uploaded on 03/22/2012 for the course ECON 106 taught by Professor Kücüksenel during the Spring '12 term at Middle East Technical University.
 Spring '12
 Kücüksenel
 Economics

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