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IE 300/GE 331 Lecture 16
Negar Kiyavash, UIUC
1
Announcements:
• No Class on March 31
st
.
• Second exam in less than a month: April 23
rd
.
• Ample time to study over the break.
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Negar Kiyavash, UIUC
2
Quiz 4
The random variable X has the PDF:
Let A be the event
X>2, find conditional PDF of
X given A.
{
)
(
3
1
4
0
≤
≤
=
x
x
else
x
f
IE 300/GE 331 Lecture 16
Negar Kiyavash, UIUC
3
Covariance
• An statistical measure of how two random
variable vary with respect to each other.
Y
μ
X
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Negar Kiyavash, UIUC
4
Covariance
• Covariance
measures
linear relationship
between two r.v.’s
X
and
Y
)
(
)
(
)
,
cov(
)
(
)]
)(
[(
)
,
cov(
2
2
X
V
X
E
X
X
XY
E
Y
X
E
Y
X
X
Y
X
Y
X
XY
=
−
=
−
=
−
−
=
=
μ
σ
IE 300/GE 331 Lecture 16
Negar Kiyavash, UIUC
5
Covariance (cont)
X
μ
Y
)
)(
(
Y
X
Y
X
−
−
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Negar Kiyavash, UIUC
6
Correlation
•
Correlation
also measures
linear relationship
between r.v.’s
X
and
Y
: easier to interpret
• Satisfies
Y
X
XY
XY
Y
V
X
V
Y
X
Y
X
corr
σ
ρ
=
=
=
)
(
)
(
)
,
cov(
)
,
(
1
1
≤
≤
−
XY
IE 300/GE 331 Lecture 16
Negar Kiyavash, UIUC
7
Independence
• If X and Y are independent E(XY)=E(X)E(Y)
• If
X
and
Y
are independent,
• Independence
Î
zero covariance.
Not
vice versa
0
)
(
)
(
)
(
)
,
cov(
=
−
=
Y
E
X
E
XY
E
Y
X
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Negar Kiyavash, UIUC
8
Linear functions of r.v.s
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This note was uploaded on 09/08/2009 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.
 Spring '09
 NegarKayavash

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