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Economics 140
Professor Enrico Moretti
02/08/10
Lecture 4
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ANNOUNCEMENTS:
Problem set 2 is due today. Please turn your
problem set in to your GSI. There is no class next
Monday because of the holiday, but discussion will
still be held. I will send an email on whether a
problem set will be assigned or not.
LECTURE
Recall that the definition of
expected value
is:
For one variable
E(x) =
∑
x
ּ
pr(x)
For two variables
E(x) =
∑
over x
∑
over y
x
ּ
f(xy) =
∑
over x
x
∑
over y
f(xy) =
∑
over x
f(x)
Some
properties of expected value
are:
If x
1
, x
2
, x
3
,…x
n
are random variables then the
E(x
1
+x
2
+x
3
…+x
n
) = E(x
1
) +E(x
2
) +
E(x
3
)…+E(x
n
).
If a is a number then E(a
1
x
1
+ a
2
x
2
+a
3
x
3
…+a
n
x
n
)
= a
1
E(x
1
)+ a
2
E(x
2
)+ a
3
E(x
3
)+… a
n
E(x
n
).
Measures of association
, such as covariance,
describes how much two random variables move
together.
For ex:
1)Y
X
X and Y have positive covariance because if you
increase X, you’re likely (on average) to increase Y.
There is positive association between the two
variables.
2)
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