Econ 141: Problem Set 1: Answers
Fall 2007
1. You ask 1000 people in a neighborhood (the total population of the neighborhood)
about their education and employment status. The responses can be divided up into the
following four categories:
Unemployed, Noncollege grads : 42 people
Employed, Noncollege grads : 694 people
Unemployed, College grads : 9 people
Employed, College grads : 255 people
You decide to deﬁne the random variable
X
as 0 if the person is not a college grad and 1 if
the person is, and the random variable
Y
as 0 if the person is unemployed and 1 if employed.
What is E[
X
]? E[
Y
]? What is E[
Y

X
= 0]? E[
Y

X
= 1]?
Answer:
E[
X
] = 0
*
(42 + 694)
/
1000 + 1
*
(9 + 255)
/
1000 = 263
/
1000 =
.
263
E[
Y
] = 0
*
(42 + 9)
/
1000 + 1
*
(694 + 255)
/
1000 = 949
/
1000 =
.
949
E[
Y

X
= 0] = 0
*
42
/
(42 + 694) + 1
*
694
/
(42 + 694) = 694
/
736 =
.
943
E[
Y

X
= 1] = 0
*
9
/
(9 + 255) + 1
*
255
/
(9 + 255) = 255
/
264 =
.
966
2. We think that stock prices react to expectations about the future regulatory environ
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 Spring '08
 MCCULLOUGH
 Variance, Dow Jones & Company, Dow Jones Indexes, Yi x

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