Probability, statistics, and random processes for engineers

Preface 11
Chapter1 Introduction to Probability 13
1.1 Introduction: Why Study Probability? 13
1.2 The Different Kinds of Probability 14
Probability as Intuition 14
Probability as the Ratio of Favorable to Total Outcomes (Classical Theory) 15
Probability as a Measure of Frequency of Occurrence 16
Probability Based on an Axiomatic Theory 17
1.3 Misuses, Miscalculations, and Paradoxes in Probability 19
1.4 Sets, Fields, and Events 20
Examples of Sample Spaces 20
1.5 Axiomatic Definition of Probability 27
1.6 Joint, Conditional, and Total Probabilities; Independence 32
Compound Experiments 35
1.7 Bayes’ Theorem and Applications 47
1.8 Combinatorics 50
Occupancy Problems 54
Extensions and Applications 58
1.9 Bernoulli Trials—Binomial and Multinomial Probability Laws 60
Multinomial Probability Law 66
1.10 Asymptotic Behavior of the Binomial Law: The Poisson Law 69
1.11 Normal Approximation to the Binomial Law 75
Summary 77
Problems 78
References 89
Chapter2 Random Variables 91
Chapter3 Functions of Random Variables 163
Chapter4 Expectation and Moments 227
Chapter5 Random Vectors 307
Chapter6 Statistics: Part 1 Parameter Estimation 352
Chapter7 Statistics: Part 2 Hypothesis Testing 402
Chapter8 Random Sequences 453
Chapter 9 Random Processes 555
Chapters 10 Advanced Topics in Random Processes
Chapter11 Applications to Statistical Signal Processing 712
Appendix A Review of Relevant Mathematics A-1
Appendix B Gamma and Delta Functions B-1
Appendix C Functional Transformations and Jacobians C-1
Appendix D Measure and Probability D-1
Appendix E Sampled Analog Waveforms and Discrete-time Signals E-1
Appendix F Independence of Sample Mean and Variance for Normal Random Variables F-1
Appendix G Tables of Cumulative Distribution Functions: the Normal, Student t, Chi-square, and F G-1
Index I-1