Problem Set 2

Due Tuesday 09/23/08
Econ 319  Introduction to Probability and Statistics
Fall 2008
Cornell University
Prof. Molinari
This was Test 1 for this class during one of the semesters in which I taught it. As you will see,
the exam consisted of TWO parts totaling 100 points. I will maintain the same structure for the
Test 1 that I am preparing for your class. The exam will be a CLOSED BOOK exam. However,
useful formulas will be provided on pages 4+. Calculators are permitted °but graphic calculators
are prohibited. You will have 75 minutes
to complete the exam. SHOW ALL your work as partial
credit will be given. Answers without explanations might NOT be given (full) credit even if they
are correct.
Part 1
°
25 points (5 points each)
In
WORDS
, brie±y
(1 paragraph maximum) describe the following:
1. Sample Space.
2. Independence of two events.
3. Independence of two random variables.
4. Conditional Probability.
5. Expected Value.
1
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Part 2
°
75 points (Each subquestion has the number of corresponding points in brackets)
1. Given three events
A
,
B
and
C;
is
Pr (
A
j
B
\
C
) + Pr (
A
0
j
B
\
C
) = 1?
If your answer is yes,
give a proof; if your answer is no, give a counterexample. Is
Pr (
A
j
B
\
C
)+Pr (
A
j
B
0
[
C
0
) =
1?
If your answer is yes, give a proof; if your answer is no, give a counterexample.
(5 points)
2. Suppose Cornell²s rowing team has a group of four scullers (i.e., rowers who row each with
two oars), being considered to form the Quadruple in the U.S. National Rowing Team. The
coach of the National Team has decided to test the athletes on how fast each of them can
complete a 2,000 meter distance alone, on a so called ³single boat.´Each of the four athletes²
performance on the test is independent of the others. Let
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 Fall '07
 HONG
 Probability distribution, Probability theory, probability density function, national team

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