Textbook in PDF format

This textbook explores probability and stochastic processes at a level that does not require any prior knowledge except basic calculus. It presents the fundamental concepts in a step-by-step manner, and offers remarks and warnings for deeper insights. The chapters include basic examples, which are revisited as the new concepts are introduced. To aid learning, figures and diagrams are used to help readers grasp the concepts, and the solutions to the exercises and problems. Further, a table format is also used where relevant for better comparison of the ideas and formulae. The first part of the book introduces readers to the essentials of probability, including combinatorial analysis, conditional probability, and discrete and continuous random variable. The second part then covers fundamental stochastic processes, including point, counting, renewal and regenerative processes, the Poisson process, Markov chains, queuing models and reliability theory. Primarily intended for undergraduate engineering students, it is also useful for graduate-level students wanting to refresh their knowledge of the basics of probability and stochastic processes.
Table of contents
Combinatorial Analysis
Basic Concepts, Axioms and Operations in Probability
Conditional Probability, Bayes’ Formula, Independent Events
Introduction to Random Variables
Discrete Random Variables
Continuous Random Variables
Other Selected Topics in Basic Probability
A Brief Introduction to Stochastic Processes
A Brief Introduction to Point Process, Counting Process, Renewal Process, Regenerative Process, Poisson Process
Poisson Process
Renewal Process
An Introduction to Markov Chains
Special Discrete-Time Markov Chains
Continuous-Time Markov Chains
An Introduction to Queueing Models
Introduction to Brownian Motion
Basics of Martingales
Basics of Reliability Theory