Probability, Random Variables, and Random Processes - Theory and Signal Processing Applications

Informationen zum Autor JOHN J. SHYNK, PhD, is Professor of Electrical and Computer Engineering at the University of California, Santa Barbara. He was a Member of Technical Staff at Bell Laboratories, and received degrees in systems engineering, electrical engineering, and statistics from Boston University and Stanford University. Klappentext Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background.The book has the following features:* Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy.* Unlike most books on probability, numerous figures have been included to clarify and expand upon important points. Over 600 illustrations and MATLAB plots have been designed to reinforce the material and illustrate the various characterizations and properties of random quantities.* Sufficient statistics are covered in detail, as is their connection to parameter estimation techniques. These include classical Bayesian estimation and several optimality criteria: mean-square error, mean-absolute error, maximum likelihood, method of moments, and least squares.* The last four chapters provide an introduction to several topics usually studied in subsequent engineering courses: communication systems and information theory; optimal filtering (Wiener and Kalman); adaptive filtering (FIR and IIR); and antenna beamforming, channel equalization, and direction finding. This material is available electronically at the companion website.Probability, Random Variables, and Random Processes is the only textbook on probability for engineers that includes relevant background material, provides extensive summaries of key results, and extends various statistical techniques to a range of applications in signal processing. Zusammenfassung Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. Inhaltsverzeichnis PREFACE xxi NOTATION xxv 1 Overview and Background 1 1.1 Introduction 1 1.1.1 Signals, Signal Processing, and Communications 3 1.1.2 Probability, Random Variables, and Random Vectors 9 1.1.3 Random Sequences and Random Processes 11 1.1.4 Delta Functions 16 1.2 Deterministic Signals and Systems 19 1.2.1 Continuous Time 20 1.2.2 Discrete Time 25 1.2.3 Discrete-Time Filters 29 1.2.4 State-Space Realizations 32 1.3 Statistical Signal Processing with MATLAB® 35 1.3.1 Random Number Generation 35 1.3.2 Filtering 38 Problems 39 Further Reading 45 PART I Probability, Random Variables, and Expectation 2 Probability Theory 49 2.1 Introduction 49 2.2 Sets and Sample Spaces 50 2.3 Set Operations 54 2.4 Events and Fields 58 2.5 Summary of a Random Experiment 64 2.6 Measure Theory 64 2.7 Axioms of Probability 68 2.8 Basic Probability Results 69 2.9 Conditional Probability 71 2.10 Independence 73 2.11 Bayes' Formula 74 2.12 Total Probability 76 ...

List of contents

PREFACE xxi
 
NOTATION xxv
 
1 Overview and Background 1
 
1.1 Introduction 1
 
1.2 Deterministic Signals and Systems 19
 
1.3 Statistical Signal Processing with MATLAB(r) 35
 
Problems 39
 
Further Reading 45
 
PART I Probability, Random Variables, and Expectation
 
2 Probability Theory 49
 
2.1 Introduction 49
 
2.2 Sets and Sample Spaces 50
 
2.3 Set Operations 54
 
2.4 Events and Fields 58
 
2.5 Summary of a Random Experiment 64
 
2.6 Measure Theory 64
 
2.7 Axioms of Probability 68
 
2.8 Basic Probability Results 69
 
2.9 Conditional Probability 71
 
2.10 Independence 73
 
2.11 Bayes' Formula 74
 
2.12 Total Probability 76
 
2.13 Discrete Sample Spaces 79
 
2.14 Continuous Sample Spaces 83
 
2.15 Nonmeasurable Subsets of R 84
 
Problems 87
 
Further Reading 90
 
3 Random Variables 91
 
3.1 Introduction 91
 
3.2 Functions and Mappings 91
 
3.3 Distribution Function 96
 
3.4 Probability Mass Function 101
 
3.5 Probability Density Function 103
 
3.6 Mixed Distributions 104
 
3.7 Parametric Models for Random Variables 107
 
3.8 Continuous Random Variables 109
 
3.9 Discrete Random Variables 151
 
Problems 173
 
Further Reading 176
 
4 Multiple Random Variables 177
 
4.1 Introduction 177
 
4.2 Random Variable Approximations 177
 
4.3 Joint and Marginal Distributions 183
 
4.4 Independent Random Variables 186
 
4.5 Conditional Distribution 187
 
4.6 Random Vectors 190
 
4.7 Generating Dependent Random Variables 201
 
4.8 Random Variable Transformations 205
 
4.9 Important Functions of Two Random Variables 218
 
4.10 Transformations of Random Variable Families 226
 
4.11 Transformations of Random Vectors 229
 
4.12 Sample Mean X and Sample Variance S2 232
 
4.13 Minimum, Maximum, and Order Statistics 234
 
4.14 Mixtures 238
 
Problems 240
 
Further Reading 243
 
5 Expectation and Moments 244
 
5.1 Introduction 244
 
5.2 Expectation and Integration 244
 
5.3 Indicator Random Variable 245
 
5.4 Simple Random Variable 246
 
5.5 Expectation for Discrete Sample Spaces 247
 
5.6 Expectation for Continuous Sample Spaces 250
 
5.7 Summary of Expectation 253
 
5.8 Functional View of the Mean 254
 
5.9 Properties of Expectation 255
 
5.10 Expectation of a Function 259
 
5.11 Characteristic Function 260
 
5.12 Conditional Expectation 265
 
5.13 Properties of Conditional Expectation 267
 
5.14 Location Parameters: Mean, Median, and Mode 276
 
5.15 Variance, Covariance, and Correlation 280
 
5.16 Functional View of the Variance 283
 
5.17 Expectation and the Indicator Function 284
 
5.18 Correlation Coefficients 285
 
5.19 Orthogonality 291
 
5.20 Correlation and Covariance Matrices 294
 
5.21 Higher Order Moments and Cumulants 296
 
5.22 Functional View of Skewness 302
 
5.23 Functional View of Kurtosis 303
 
5.24 Generating Functions 304
 
5.25 Fourth-Order Gaussian Moment 309
 
5.26 Expectations of Nonlinear Transformations 310
 
Problems 313
 
Further Reading 316
 
PART II Random Processes, Systems, and Parameter Estimation
 
6 Random Processes 319
 
6.1 Introduction 319
 
6.2 Characteriz

Product details

• Authors: Jj Shynk, John J Shynk, John J. Shynk, SHYNK JOHN J, Shynk John J.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 07.12.2012
• EAN: 9780470242094
• ISBN: 978-0-470-24209-4
• No. of pages: 794
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Elektrotechnik, Statistics, Signalverarbeitung, Angewandte Mathematik, Signal Processing, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Statistik in den Ingenieurwissenschaften, Engineering Statistics, Numerische Methoden u. Algorithmen, Numerical Methods & Algorithms