Department of Economics
Professor Dale J. Poirier
University of California, Irvine
October 19, 2010
EXAM
1
ECON
123A
Econometrics I
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.
Let the density of X be unimodal and symmetric around zero with finite third moment.
Define Y = X
2
.
(5)
(a)
Find Cov(X, Y).
(5)
(b)
Are X and Y independent?
2.
Let X and Y be discrete random variables with joint and marginal probabilities given by
x = -1
x = 0
x = 1
f
Y
(y)
y = 0
1/6
0
1/6
1/3
y = 1
0
2/3
0
2/3
f
X
(x)
1/6
2/3
1/6
Answer each of the following.
(7)
(a)
Is X statistically independent of Y?
(6)
(b)
Is X mean-independent of Y?
(6)
(c)
Is Y mean-independent of X?
(6)
(d)
Are X and Y uncorrelated?

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