PROBABILITY,
RANDOM
VARIABLES,
AND
STOCHASTIC
PROCESSES
FOURTH
EDITION
Athanasios
Papoulis
<
University
Professor
Polytechnic
University
s.
Unnikrishna
Pillai
Professor
of
Electrical
and
Computer
Engineering
Polytechnic
University
Boston
Burr
Ridge,
IL
Dubuque,
IA
Madison,
WI
N~w
York
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Francisco
St.
Louis
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Lumpur
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PROBABIUTY.
RANDOM
VARIABLES,
AND
STOCHASTIC
PROCESSES.
FOUR11:l
EDmoN
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Library
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Data
Papoulis.
Atbanasios.
1921-
Probability,
random
variables.
and
stochastic
processes
I
Atbanasios
Papoulis.
S.
Unnikrishna
PlIlai.
-
4th
ed.
p.em.
Includes
bibliographical
references
and
index.
ISBN
0-07-366011-6 -
ISBN
0-07-112256-7
(ISE)
1.
Probabilities.
2.
Random
variables.
3.
Stochastic
processes.
l.
Pillai.
S.
U~bna,
1955
-.
II.
TIde.
QA273
.P2
2002
5
19.2---dc21
INTERNATIONAL
EDmON
ISBN
0-07-112256-7
2001044139
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www.mhhe.com
CONTENTS
Preface
ix
PART I
PROBABILITY
AND
RANDOM
VARIABLES
1
Chapter!
The Meaning of Probability 3
1-1
Introduction
I
1-2
The
Definitions
I
1-3
Probability
and
Induction
I
1-4
Causality
Versus
Randomness
Chapter 2
The
Axioms
of Probability
15
2-1
Set
Theory
I
2-2
Probability
Space
I
2-3
Conditional
Probability
I
Problems
Chapter 3
Repeated Trials
46
3-1
Combined
Experiments
I
3-2
Bernoulli
Trials
I
3-3
Bernoulli's
Theorem
and
Games
of
Chance
I
Problems
Chapter 4
The Concept of a Random
Variable
72
4-1
Introduction
I
4-2
Distribution
and
Density
Functions
I
4-3
Specific
Random
Variables
I
4-4
Conditional
Distributions
I
4-5
Asymptotic
Approximations
for
Binomial
Random
Variable
I
Problems
ChapterS Functions of
One
Random
Variable
123
5-1
The
Random
Variable
g(x) I
5-2
The
Distribution
"
of
g(x)
I
5-3
Mean
and
Variance
I
5-4
Moments
I
5-5
Characteristic
Functions
I
Problems
Chapter 6
Two
Random
Variables
169
6-1
Bivariate
Distributions
I
6-2
One
Function
of
Two
Random
Variables
I
6-3
Two
Functions
of
Two
Random
Variables
I
6-4
Joint
Moments
I
6-5
Joint
Characteristic
Functions
I
6-6
Conditional
Distributions
I
6-7
Conditional
Expected
Values
I
Problems
vi
CONTENTS
Chapter 7
Sequences
of
Random
'Variables
7-1
General
Concepts /
7-2
Conditional Densities,
Characteristic
Functions,
and
Normality I
7-3
M~
Square
Estimation I
7-4
Stochastic
Convergence
and
Limit
Theorems
I
7-5
Random
Numbers:
Meaning
and
Generation
I Problems
Chapter 8 Statistics
8-1
Introduction I
8-2
Estimation I
8-3
Parameter
Estimation I
8-4
Hypothesis Testing I
Problems
PART
II
STOCHASTIC
PROCESSES
Chapter 9
General
Concepts
9-1
Definitions I
9-2
Systems with Stochastic
Inputs
I
9-3
The Power
Spectrum
I 9-4 Discrete-Time
Processes
I
Appendix
9A
Continuity,
Differentiation, Integration I
Appendix
9B
Shift Operators
and
Stationary
Processes
I Problems
243
303
371
373
Chapter
10
Random
Walks
and
Other Applications
435
10-1
Random
Walks
I
10-2
Poisson Points
and
Shot
Noise I
10-3
Modulation I
10-4
Cyclostationary
Processes
I
10-5
Bandlimited Processes
and
Sampling
Theory I
10-6
Deterministic Signals in
Noise
I
10-7
Bispectra
and
System Identification I Appendix
lOA
The
Poisson
Sum
Formula
I Appendix
lOB
The
Schwarz
Inequality
I
Problems
Chapter
11
Spectral Representation
499
11-1
Factorization
and
Innovations
I
11-2
Finite-Order
Systems
and
State Variables I
11-3
Fourier Series
and
Karhunen-Loeve
Expansions
I
11-4
Spectral Representation of
Random
Processes
I
Problems
Chapter
12
Spectrum
Estimation
12-1
Ergodicity I
12-2
Spectrum
Estimation
I
12-3
Extrapolation
and
System
Identification I
12-4
The
GeQeral
Class of Extrapolating Spectra
and
Youla's Parametrization I
Appendix
12A
Minimum-Phase
Functions
I
Appendix
12B
All-Pass Functions I
Problems
Chapter
13
Mean
Square Estimation
13-1
Introduction I
13-2
Prediction I
13-3
Filtering
and
Prediction I
13-4
Kalman
Filters I
Problems
Chapter
14
Entropy
14-1
Introduction I
14-2
Basic
Concepts I
14-3
Random
Variables
and
Stochastic Processes I
14-4
The
Maximum
Entropy
Method I
14-5
Coding I
14-6
Channel
Capacity I Problems
523
580
629
CONTENTS
vii
Chapter
15
Markov
Chains
15-1
InlI'Oduction
I
15-2
Higher Transition Probabilities
and
the
Chapman-Kolmogorov Equation I
15-3
Classification of
StaleS
I 15-4 Stationary Distributions
and
Limiting
Probabilities I IS-S Transient States
and
Absorption
Probabilities I
15-6
Branching
Processes
I
Appendix
15A
Mixed
Type
Population of Constant Size I
Appendix.
ISB
Structure of Periodic Chains I
Problems
Chapter
16
Markov
Processes
and
Queueing
Theory
16-1
Introduction I
16-2
Markov
Processes I
16-3
Queueing
Theory
I
16-4
Networks
of
Queues
I
Problems
Bibliography
Index
695
773
835
837
