Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications

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.

Keywords:

Electrical engineering; computer engineering; software engineering; computer science; information technology; life sciences; probability; random variables; statistics; random processes; Set Theory; Definitions of Probability; Axioms of Probability; Marginal Probability; Conditional Probability; Joint Probability; Statistically-Independent Events; Mutually-Exclusive Events; Law of Total Probability; A priori Probability; Cumulative Distribution Function; Probability Mass Function; Probability Density Function; Mean; Median; Mode; Variance; Moment; Expected Value; Conditional Distribution; Descriptive Statistics; Population Parameter; Sample Statistic; Histogram; Bar; Pareto and Pie Charts; Quantiles; Quartiles; Percentiles; Boxplot; Coefficient of Variation; Continuous and Discrete Processes; Sample Functions; Distributions of Time Samples; Autocorrelation and Autocovariance Functions; Cross-correlation and Cross-covariance Functions; Gaussian Processes