Economics 390, Midterm #2 Page 1
Economics 390
Midterm #2
180 Points
75 Minutes
Instructions:
Answer the following questions as clearly as you can.
Circle your answers
.
Also, show
your work.
You do not need to write out every detail, but give a clear indication of how you are making
your calculations.
This is for your benefit, as we can give partial credit if, say, you make a mistake early
in the problem that otherwise would make a correct final answer wrong.
You may use any type of handheld calculator.
All other electronic devices are prohibited.
Several question I consider to be a little more challenging than the others.
I’ve identified these with
an asterisk *.
Suggestions:
There are 18 problems.
Do not get stuck on any one problem.
The questions vary in
difficulty, and you should be sure to get done the ones you feel strong about.
The most difficult part of
any question is going to be determining where the question fits into the class as a whole
.
If you can do
that, and you understand the formulas in the formula sheet, then translating the problem into the formulas
and executing the calculations is going to be relatively straightforward.
Name: ___________________________________
ID:
___________________________________
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View Full DocumentEconomics 390, Midterm #2 Page 2
1.
(10 points) Consider two random variables X and Y, where Cov(X,Y)>0. Then, all
else equal, when the standard deviation of X increases, the correlation coefficient ρ
also increases.
True or False, and explain your answer.
(Explanation exclusively
determines grade.)
False.
( , )
X
Y
Cov X Y
ρ
σ σ
=
.
If σ
X
increases, then ρ must fall.
2.
(10 points) Consider two continuous distributions for the random variables R and S.
R has a
PDF given by the function f
R
(R), and S has a PDF given by the function f
S
(S). If f
R
(1)>f
S
(1),
then the probability that R=1equals the probability that S=1.
True or False, and explain your
answer.
(Explanation exclusively determines grade.)
True.
The key here is the fact that for a
continuous
RV, as opposed to a discrete RV, the
probability that the RV takes on
any
particular value is exactly 0, regardless of the value of
the PDF.
Thus, P(R=1)=P(S=1)=0.
3.
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 Fall '08
 GOLDSTEIN,DANIELWILLIAMS,MARLONL
 Economics, Normal Distribution, Standard Deviation, Variance

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