This book covers fundamental concepts in probability, random processes, and statistical analysis. A central theme in this book is the interplay between probability theory and statistical analysis. The book will be suitable to graduate students majoring in information sciences and systems in such departments as Electrical and Computer Engineering, Computer Science, Operations Research, Economics and Financial Engineering, Applied Mathematics and Statistics, Biology, Chemistry and Physics. The instructor and the reader may opt to skip some chapters or sections and focus on chapters that are relevant to their fields of study. At the end of this preface, we provide suggested course plans for various disciplines.

Organization of the book

Before we jump into a mathematical description of probability theory and random processes, we will provide in Chapter 1, Introduction, specific reasons why the subjects of this book pertain to study and research across diverse fields or disciplines: (i) communications, information and control systems, (ii) signal processing, (iii) machine learning, (iv) bioinformatics and related fields, (v) econometrics and mathematical finance, (vi) queueing and loss systems, and (vii) other applications. We will then provide a brief but fascinating historical review of the development of (a) classical probability theory, (b) modern probability theory, (c) random processes, and (d) statistical analysis and inference. This historical review also serves as an overview of various topics discussed in this volume.