Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications - Ali Grami

. .

Auteur(s) : Ali Grami

Editeur : Wiley

Langue : Anglais

Parution : 31/03/2019

Nombre de pages : 416

Expédition : 794

Dimensions : 23.1 x 15.5 x 2.8

ISBN : 1119300819

Résumé :

Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this book is on the basic principles and practical applications of the fundamental concepts that are extensively used in various Engineering disciplines as well as in a variety of programs in Life and Social Sciences. The text provides students with the requisite building blocks of knowledge they require to understand and progress in their areas of interest. With a simple, clear-cut style of writing, the intuitive explanations, insightful examples, and practical applications are the hallmarks of this book.

The text consists of twelve chapters divided into four parts. Part-I, Probability (Chapters 1 - 3), lays a solid groundwork for probability theory, and introduces applications in counting, gambling, reliability, and security. Part-II, Random Variables (Chapters 4 - 7), discusses in detail multiple random variables, along with a multitude of frequently-encountered probability distributions. Part-III, Statistics (Chapters 8 - 10), highlights estimation and hypothesis testing. Part-IV, Random Processes (Chapters 11 - 12), delves into the characterization and processing of random processes. Other notable features include:

• Most of the text assumes no knowledge of subject matter past first year calculus and linear algebra
• With its independent chapter structure and rich choice of topics, a variety of syllabi for different courses at the junior, senior, and graduate levels can be supported
• A supplemental website includes solutions to about 250 practice problems, lecture slides, and figures and tables from the text?

Given its engaging tone, grounded approach, methodically-paced flow, thorough coverage, and flexible structure, Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications clearly serves as a must textbook for courses not only in Electrical Engineering, but also in Computer Engineering, Software Engineering, and Computer Science.

...

Biographie:

Ali Grami is a founding faculty member at the University of Ontario Institute of Technology (UOIT), Canada. He holds B.Sc., M.Eng., and Ph.D. degrees in Electrical Engineering from the University of Manitoba, McGill University and the University of Toronto, respectively. Before joining academia, he was with the high-tech industry for many years, where he??was the principal designer of the first North-American broadband access satellite system. He has taught at the University of Ottawa and Concordia University. At UOIT, he has also led the development of programs toward bachelor's, master's, and doctoral degrees in Electrical and Computer Engineering....

Sommaire:

Preface xiii

Acknowledgments xv

About the Companion Website xvii

Part I Probability 1

1 Basic Concepts of Probability Theory 3

1.1 Statistical Regularity and Relative Frequency 3

1.2 Set Theory and Its Applications to Probability 5

1.3 The Axioms and Corollaries of Probability 12

1.4 Joint Probability and Conditional Probability 18

1.5 Statistically Independent Events and Mutually Exclusive Events 21

1.6 Law of Total Probability and Bayes' Theorem 28

1.7 Summary 32

Problems 32

2 Applications in Probability 37

2.1 Odds and Risk 37

2.2 Gambler's Ruin Problem 41

2.3 Systems Reliability 43

2.4 Medical Diagnostic Testing 47

2.5 Bayesian Spam Filtering 50

2.6 Monty Hall Problem 51

2.7 Digital Transmission Error 54

2.8 How to Make the Best Choice Problem 56

2.9 The Viterbi Algorithm 59

2.10 All Eggs in One Basket 61

2.11 Summary 63

Problems 63

3 Counting Methods and Applications 67

3.1 Basic Rules of Counting 67

3.2 Permutations and Combinations 72

3.2.1 Permutations without Replacement 73

3.2.2 Combinations without Replacement 73

3.2.3 Permutations with Replacement 74

3.2.4 Combinations with Replacement 74

3.3 Multinomial Counting 77

3.4 Special Arrangements and Selections 79

3.5 Applications 81

3.5.1 Game of Poker 81

3.5.2 Birthday Paradox 83

3.5.3 Quality Control 86

3.5.4 Best-of-Seven Championship Series 86

3.5.5 Lottery 89

3.6 Summary 90

Problems 90

Part II Random Variables 95

4 One Random Variable: Fundamentals 97

4.1 Types of Random Variables 97

4.2 The Cumulative Distribution Function 99

4.3 The Probability Mass Function 102

4.4 The Probability Density Function 104

4.5 Expected Values 107

4.5.1 Mean of a Random Variable 107

4.5.2 Variance of a Random Variable 110

4.5.3 Moments of a Random Variable 113

4.5.4 Mode and Median of a Random Variable 114

4.6 Conditional Distributions 116

4.7 Functions of a Random Variable 120

4.7.1 pdf of a Function of a Continuous Random Variable 121

4.7.2 pmf of a Function of a Discrete Random Variable 123

4.7.3 Computer Generation of Random Variables 124

4.8 Transform Methods 125

4.8.1 Moment Generating Function of a Random Variable 125

4.8.2 Characteristic Function of a Random Variable 126

4.9 Upper Bounds on Probability 127

4.9.1 Markov Bound 127

4.9.2 Chebyshev Bound 128

4.9.3 Chernoff Bound 128

4.10 Summary 131

Problems 131

5 Special Probability Distributions and Applications 137

5.1 Special Discrete Random Variables 137

5.1.1 The Bernoulli Distribution 137

5.1.2 The Binomial Distribution 138

5.1.3 The Geometric Distribution 140

5.1.4 The Pascal Distribution 142

5.1.5 The Hypergeometric Distribution 143

5.1.6 The Poisson Distribution 144

5.1.7 The Discrete Uniform Distribution 146

5.1.8 The Zipf (Zeta) Distribution 147

5.2 Special Continuous Random Variables 148

5.2.1 The Continuous Uniform Distribution 148

5.2.2 The Exponential Distribution 149

5.2.3 The Gamma Distribution 151

5.2.4 The Erlang Distribution 152

5.2.5 The Weibull Distribution 152

5.2.6 The Beta Distribution 153

5.2.7 The Laplace Distribution 154

5.2.8 The Pareto Distribution 155

5.3 Applications 156

5.3.1 Digital Transmission: Regenerative Repeaters 156

5.3.2 System Reliabili...