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Tables of Contents for Probability, Random Variables, and Stochastic Processes
Chapter/Section Title
Page #
Page Count
Preface
ix
 
PART I PROBABILITY AND RANDOM VARIABLES
1
370
The Meaning of Probability
3
12
Introduction
The Definitions
Probability and Induction
Causality Versus Randomness
The Axioms of Probability
15
31
Set Theory
Probability Space
Conditional Probability
Problems
Repeated Trials
46
26
Combined Experiments
Bernoulli Trials
Bernoulli's Theorem and Games of Chance
Problems
The Concept of a Random Variable
72
51
Introduction
Distribution and Density Functions
Specific Random Variables
Conditional Distributions
Asymptotic Approximations for Binomial Random Variable
Problems
Functions of One Random Variable
123
46
The Random Variable g(x)
The Distribution of g(x)
Mean and Variance
Moments
Characteristic Functions
Problems
Two Random Variables
169
74
Bivariate Distributions
One Function of Two Random Variables
Two Functions of Two Random Variables
Joint Moments
Joint Characteristic Functions
Conditional Distributions
Conditional Expected Values
Problems
Sequences of Random Variables
243
60
General Concepts
Conditional Densities, Characteristic Functions, and Normality
Mean Square Estimation
Stochastic Convergence and Limit Theorems
Random Numbers: Meaning and Generation
Problems
Statistics
303
68
Introduction
Estimation
Parameter Estimation
Hypothesis Testing
Problems
PART II STOCHASTIC PROCESSES
371
464
General Concepts
373
62
Definitions
Systems with Stochastic Inputs
The Power Spectrum
Discrete-Time Processes
Continuity, Differentiation, Integration
Shift Operators and Stationary Processes
Problems
Random Walks and Other Applications
435
64
Random Walks
Poisson Points and Shot Noise
Modulation
Cyclostationary Processes
Bandlimited Processes and Sampling Theory
Deterministic Signals in Noise
Bispectra and System Identification
The Poisson Sum Formula
The Schwarz Inequality Problems
Spectral Representation
499
24
Factorization and Innovations
Finite-Order Systems and State Variables
Fourier Series and Karhunen-Loeve Expansions
Spectral Representation of Random Processes
Problems
Spectrum Estimation
523
57
Ergodicity
Spectrum Estimation
Extrapolation and System Identification
The General Class of Extrapolating Spectra and Youla's Parametrization
Minimum-Phase Functions
All-Pass Functions
Problems
Mean Square Estimation
580
49
Introduction
Prediction
Filtering and Prediction
Kalman Filters
Problems
Entropy
629
66
Introduction
Basic Concepts
Random Variables and Stochastic Processes
The Maximum Entropy Method
Coding
Channel Capacity
Problems
Markov Chains
695
78
Introduction
Higher Transition Probabilities and the Chapman-Kolmogorov Equation
Classification of States
Stationary Distributions and Limiting Probabilities
Transient States and Absorption Probabilities
Branching Processes
Mixed Type Population of Constant Size
Structure of Periodic Chains
Problems
Markov Processes and Queueing Theory
773
62
Introduction
Markov Processes
Queueing Theory
Networks of Queues
Problems
Bibliography
835
2
Index
837