Probability, Statistics, and Stochastic Processes (PDF)

A mathematical and intuitive approach to probability,
statistics, and stochastic processes

This textbook provides a unique, balanced approach to
probability, statistics, and stochastic processes. Readers gain a
solid foundation in all three fields that serves as a stepping
stone to more advanced investigations into each area. This text
combines a rigorous, calculus-based development of theory with a
more intuitive approach that appeals to readers' sense of reason
and logic, an approach developed through the author's many years of
classroom experience.

The text begins with three chapters that develop probability
theory and introduce the axioms of probability, random variables,
and joint distributions. The next two chapters introduce limit
theorems and simulation. Also included is a chapter on statistical
inference with a section on Bayesian statistics, which is an
important, though often neglected, topic for undergraduate-level
texts. Markov chains in discrete and continuous time are also
discussed within the book.

More than 400 examples are interspersed throughout the text to
help illustrate concepts and theory and to assist the reader in
developing an intuitive sense of the subject. Readers will find
many of the examples to be both entertaining and thought provoking.
This is also true for the carefully selected problems that appear
at the end of each chapter.

This book is an excellent text for upper-level undergraduate
courses. While many texts treat probability theory and statistical
inference or probability theory and stochastic processes, this text
enables students to become proficient in all three of these
essential topics. For students in science and engineering who may
take only one course in probability theory, mastering all three
areas will better prepare them to collect, analyze, and
characterize data in their chosen fields.