Midterm Exam 2 Practice Problems Econometrics 120A
1. Consider the following ﬁctional joint probability distribution for returns on stocks and bonds. Stock
returns are entered in the left most column and bond returns in the top most row.
Stocks/Bonds

10%
0%
10%

10%
1
6
1
12
1
6
0%
1
12
0
1
12
10%
1
6
1
12
1
6
(a) What is the probability that stock returns are 10%? What is the probability that stock returns
are 0%? What is the probability that stock returns are

10%?
(b) What is the mean of stock returns?
(c) Are stock returns and bond returns independent? Justify your answer.
(d) What is the covariance between stock and bond returns?
(e) Comment on your answers to (c) and (d). Do they contradict each other? What is the relation
ship between covariance and independence?
2. A factory is concerned about the quality of their product. They sample four products from the
production line and let
X
i
= 1 if product #
i
is defective, and
X
i
= 0 otherwise. The probability
that a product is defective is 0.5, that is
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 Spring '10
 Elliot
 Standard Deviation, Probability distribution, Probability theory, stock returns

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