Probability, Random Variables, Statistics, and Random Processes
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English

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.

English

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.

English

Preface

Acknowledgments

About the companion website

Part I PROBABILITY

Chapter 1 Basic Concepts of Probability Theory

1.1 Statistical Regularity and Relative Frequency

1.2 Set Theory and Its Applications to Probability

1.3 The Axioms and Corollaries of Probability

1.4 Joint Probability and Conditional Probability

1.5 Statistically-Independent Events and Mutually-Exclusive Events

1.6 Law of Total Probability and Bayes’ Theorem

Chapter 2 Applications in Probability

2.1 Odds and Risk

2.2 Gambler’s Ruin Problem

2.3 Systems Reliability

2.4 Medical Diagnostic Testing

2.5 Bayesian Spam Filtering

2.6 Monty Hall Problem

2.7 Digital Transmission Error

2.8 How to Make the Best Choice Problem

2.9 The Viterbi Algorithm

2.10 All Eggs in One Basket

Chapter 3 Counting Methods and Applications

3.1 Basic Rules of Counting

3.2 Permutations and Combinations

3.3 Multinomial Counting

3.4 Special Arrangements and Selections

3.5 Applications

Part II RANDOM VARIABLES

Chapter 4 One Random Variable: Fundamentals

4.1 Types of Random Variables

4.2 The Cumulative Distribution Function

4.3 The Probability Mass Function

4.4 The Probability Density Function

4.5 Expected Values

4.6 Conditional Distributions

4.7 Functions of a Random Variable

4.8 Transform Methods

4.9 Upper Bounds on Probability

Chapter 5 Special Probability Distributions and Applications

5.1 Special Discrete Random Variables

5.2 Special Continuous Random Variables

5.3 Applications

Chapter 6 Multiple Random Variables

6.1 Pairs of Random Variables

6.2 The Joint Cumulative Distribution Function of Two Random Variables

6.3 The Joint Probability Mass Function of Two Random Variables

6.4 The Joint Probability Density Function of Two Random Variables

6.5 Expected Values of Functions of Two Random Variables

6.6 Independence of Two Random Variables

6.7 Correlation between Two Random Variables

6.8 Conditional Distributions

6.9 Distributions of Functions of Two Random Variables

6.10 Random Vectors

Chapter 7 The Gaussian Distribution

7.1 The Gaussian Random Variable

7.2 The Standard Gaussian Distribution

7.3 Bivariate Gaussian Random Variables

7.4 Jointly Gaussian Random Vectors

7.5 Sums of Random Variables

7.6 The Sample Mean

7.7 Approximating Distributions with the Gaussian Distribution

7.8 Probability Distributions Related to the Gaussian Distribution

Part III STATISTICS

Chapter 8 Descriptive Statistics

8.1 Overview of Statistics

8.2 Data Displays

8.3 Measures of Location

8.4 Measures of Dispersion

8.5 Measures of Shape

Chapter 9 Estimation

9.1 Parameter Estimation

9.2 Properties of Point Estimators

9.3 Maximum Likelihood Estimators

9.4 Bayesian Estimators

9.5 Confidence Intervals

9.6 Estimation of a Random Variable

9.7 Maximum A posteriori Probability Estimation

9.8 Minimum Mean Square Error Estimation

9.9 Linear Minimum Mean Square Error Estimation

9.10 Linea MMSE Estimation Using a Vector of Observations

Chapter 10 Hypothesis Testing

10.1 Significance Testing

10.2 Hypothesis Testing for Mean

10.3 Decision Tests

10.4 Bayesian Test

10.5 Neyman-Pearson Test

Part IV RANDOM PROCESSES

Chapter 11 Introduction to Random Processes

11.1 Classification of Random Processes

11.2 Characterization of Random Processes

11.3 Moments of Random Processes

11.4 Stationary Random Processes

11.5 Ergodic Random Processes

11.6 Gaussian Processes

11.7 Poisson Processes

Chapter 12 Analysis and Processing of Random Processes

12.1 Stochastic Continuity, Differentiation, and Integration

12.2 Power Spectral Density

12.3 Noise

12.4 Sampling of Random Signals

12.5 Optimum Linear Systems

Bibliography

Index

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