ECN 329 Study Guide  Final Guide: Conditional Probability, Statistical Significance, Test Statistic
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N
x
N
i
i
∑
=
=
1
µ
n
x
X
n
i
i
∑
=
=
1
( )
N
x
N
i
i
∑
=
−
=
1
2
2
µ
σ
( )
][
1
1
1
1
2
1
2
1
2
2
∑
∑
∑
=
=
=
−
−
=
−
−
=
n
i
n
i
i
i
n
i
i
n
x
x
n
n
Xx
s
Population s.d.: 2
σσ
=
Sample s.d.:
2
ss =
Population coefficient of variation:
µ
σ
=CV Sample coefficient of variation:
X
s
cv =
( )( )
N
yx
N
i
YiXi
XY
∑
=
−−
=
1
µµ
σ
( )( )
1
1
−
−−
=
∑
=
n
YyXx
s
n
i
ii
XY
YX
XY
σσ
σ
ρ
=
YX
XY
ss
s
r=
)(
) and (
)( BP
BAP
BAP =
)(1)( APAP
C
−=
)(1)( BAPBAP
C
−=
)
(
)

(
)
and
(
B
P
B
A
P
B
A
P
=
)
and
(
)
(
)
(
)
or
(
B
A
P
B
P
A
P
B
A
P
−
+
=
∑
=
=
x
)(][
all
xxpXE
µ
Variance:
∑
−==−=
xall
xpµxXEXV
222
)()(])[(][
σµ
Covariance:
∑
∑
−
−
=
=
−
−
xall yall
YXXYYX
yxpyxYXE
),())(( )])([(
µ
µ
σ
µ
µ
Laws of Expected Value: Laws of Variance: Laws of Covariance:
E[c] = c V[c] = 0 COV[X, c] = 0
E[X+c] = E[X] + c V[X+c] = V[X] COV[a+bX, c+dY] = bdCOV[X,Y]
E[cX] = cE[X] V[cX] = c
2
V[X]
E[a+bX+cY] = a + bE[X] + cE[Y] V[a+bX+cY] = b
2
V[X] + c
2
V[Y] + 2bcCOV[X,Y]
Expected
Value
:
Addition
Rule
:
Multiplication
Rule
:
Sample coefficient of
correlation
:
Population coefficient
of correlation
:
Sample
covariance:
Population
covariance:
Population
Mean:
Population
Variance:
Sample
Mean:
Sample
Variance:
Complement Rules:
Conditional Probability:
Sample
covariance
(shortcut):
−
−
=
∑∑
∑
==
=
n
yx
yx
n
s
n
i
i
n
i
i
n
i
iiXY
11
1
1
1