Probability, Random Variables and Stochastic Processes

by Papoulis, Athanasios; Pillai, S

• ISBN13: 9780073660110
• ISBN10: 0073660116
• Edition: 4th
• Format: Hardcover
• Copyright: 2001-10-25
• Publisher: McGraw-Hill Education

Summary

* Treats probability theory and stochastic processes as a deductive discipline and illustrates them with basic engineering applications* Approximately 1/3 of the text is new with new material on: Parameter Estimation, Random Walks, Markov Chains, and Queuing Theory

Author Biography

Athanasios Papoulis: University Professor Polytechnic University S. Unnikrishna Pillai: Professor of Electrical and Computer Engineering Polytechnic University

Table of Contents

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