Department of Economics
Professor Dale J. Poirier
University of California, Irvine
December 8, 2009
FINAL
EXAM
ECON 220A
Statistics and Econometrics I
(open book)
Directions
: You must answer each of the following questions. Points (out of 100) are allocated
as noted to the left of each question. Allocate your time according to these points. To receive any
partial credit, you
must
show your work.
1.
Suppose that the random variables
Y
1
and
Y
2
have the joint density function
f(y
1
, y
2
)
= 3(
)/2, for 0
#
y
1
#
1 and 0
#
y
2
#
1.
(5)
(a)
Are Y
1
and Y
2
exchangeable?
(5)
(a)
Are Y
1
and Y
2
independent?
(20)
2.
Suppose X
1
and X
2
are i.i.d. with p.d.f.
Is W =
R
n(X
1
)/
R
n(X
2
) an ancillary statistic?
3.
Let Y
t
(t =1, 2, ..., T) be i.i.d. N(
2
,
2
2
),
2
> 0. Denote the usual sample mean and
variance estimators by

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