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Statistics for
Economists
Lecture 7
Kata Bognar
UCLA
Expectations
Chebyshev’s
Inequality
Linear Functions
of Independent
Random Variables
Statistics for Economists
Lecture 7
Kata Bognar
UCLA
October 19, 2010
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View Full Document Statistics for
Economists
Lecture 7
Kata Bognar
UCLA
Expectations
Chebyshev’s
Inequality
Linear Functions
of Independent
Random Variables
Announcements
•
Answer key for the midterm is online.
•
Homework 3 will be posted on Thursday.
Statistics for
Economists
Lecture 7
Kata Bognar
UCLA
Expectations
Chebyshev’s
Inequality
Linear Functions
of Independent
Random Variables
Last Lecture
•
Special discrete distributions
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View Full Document Statistics for
Economists
Lecture 7
Kata Bognar
UCLA
Expectations
Chebyshev’s
Inequality
Linear Functions
of Independent
Random Variables
Today’s Outline
1
Expectations
2
Chebyshev Theorem
3
Linear functions of random variables
4
Readings: TH, Chapter 2.2, 2.5
5
Readings for next class: TH, Chapter 2.4
Statistics for
Economists
Lecture 7
Kata Bognar
UCLA
Expectations
Chebyshev’s
Inequality
Linear Functions
of Independent
Random Variables
Functions of a Random Variable
•
Let
X
be a discrete random variable with p.m.f.
f
(
x
)
.
•
Then
Y
=
u
(
X
) is a random variable that takes the value
u
(
x
) 
for all
x
in the support of
X
 with a probability
f
(
x
)
.
•
Example:
•
X
has a p.m.f.
f
(
x
) =
x
6
for
x
= 1
,
2
,
3
.
•
Y
= 2
X
takes
y
= 2
,
4
,
6 with probabilities
1
6
,
2
6
,
3
6
.
•
Y
has a p.m.f.
g
(
y
) =
y
12
for
y
= 2
,
4
,
6
.
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View Full Document Statistics for
Economists
Lecture 7
Kata Bognar
UCLA
Expectations
Chebyshev’s
Inequality
Linear Functions
of Independent
Random Variables
Functions of a Random Variable
X
Y
= 2
X
x
f
(
x
)
1
1/6
2
2/6
3
3/6
=
⇒
y
g
(
y
)
2
1/6
4
2/6
6
3/6
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This note was uploaded on 12/28/2010 for the course ECON 41 taught by Professor Guggenberger during the Fall '07 term at UCLA.
 Fall '07
 Guggenberger

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