Key Topics
Introduction to Econometrics
Mathematical Concepts
Understand and verify the following properties
°
P
J
j
=1
x
j
p
j
=
x
1
p
1
+
x
2
p
2
+
± ± ±
+
x
J
p
J
°
P
J
j
=1
(
x
j
+
z
j
)
p
j
=
P
J
j
=1
x
j
p
j
+
P
J
j
=1
z
j
p
j
°
°
P
J
j
=1
x
j
p
j
±
2
=
P
J
j
=1
P
J
k
=1
x
j
x
k
p
j
p
k
=
P
J
j
=1
x
2
j
p
2
j
+
P
J
j
=1
P
J
k
=1
j
6
=
k
x
j
x
k
p
j
p
k
You should know this from prior coursework, but it is covered in the Random
Variables lecture
Probability Concepts
Understand that for discrete random variables
X
, which takes
J
distinct values,
and
U
, which takes
K
distinct values,
°
E
(
X
) =
P
J
j
=1
x
j
±
P
(
X
=
x
j
) :=
°
X
°
V ar
(
X
) :=
E
(
X
²
°
X
)
2
=
P
J
j
=1
(
x
j
²
°
X
)
2
±
P
(
X
=
x
j
)
°
Cov
(
X; U
) :=
E
[(
X
²
°
X
) (
U
²
°
U
)]
=
P
J
j
=1
P
K
k
=1
(
x
j
²
°
X
) (
u
k
²
°
U
)
±
P
(
X
=
x
j
; U
=
u
k
)
°
E
(
U
j
X
=
x
j
) =
P
K
k
=1
u
k
±
P
(
U
=
u
k
j
X
=
x
j
)
°
V ar
(
U
j
X
=
x
j
) :=
P
K
k
=1
[
u
k
²
E
(
U
j
X
=
x
j
)]
2
±
P
(
U
=
u
k
j
X
=
x
j
)
You should know this from prior coursework, but it is covered in the Random
Variables lecture
Understand and verify the following implications
°
E
(
U
j
X
) = 0
means
E
(
U
j
X
=
x
j
) = 0
for all
(
x
1
; : : : ; x
J
)
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°
E
(
U
j
X
) = 0
)
²
E
(
U
) = 0
Cov
(
X; U
) = 0
°
E
(
U
2
j
X
) =
±
2
)
E
(
U
2
) =
±
2
This is covered in the Random Variables lecture
Statistical Concepts
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 Fall '08
 Staff
 Econometrics, Regression Analysis, pj, xj xk pj, xj pj, ut xt

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