Basics of Probability and Stochastic Processes

Description

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. Front Matter ....Pages i-ix Front Matter ....Pages 1-1 Combinatorial Analysis (Esra Bas)....Pages 3-14 Basic Concepts, Axioms and Operations in Probability (Esra Bas)....Pages 15-26 Conditional Probability, Bayes’ Formula, Independent Events (Esra Bas)....Pages 27-38 Introduction to Random Variables (Esra Bas)....Pages 39-53 Discrete Random Variables (Esra Bas)....Pages 55-69 Continuous Random Variables (Esra Bas)....Pages 71-93 Other Selected Topics in Basic Probability (Esra Bas)....Pages 95-122 Front Matter ....Pages 123-123 A Brief Introduction to Stochastic Processes (Esra Bas)....Pages 125-129 A Brief Introduction to Point Process, Counting Process, Renewal Process, Regenerative Process, Poisson Process (Esra Bas)....Pages 131-147 Poisson Process (Esra Bas)....Pages 149-161 Renewal Process (Esra Bas)....Pages 163-178 An Introduction to Markov Chains (Esra Bas)....Pages 179-198 Special Discrete-Time Markov Chains (Esra Bas)....Pages 199-215 Continuous-Time Markov Chains (Esra Bas)....Pages 217-231 An Introduction to Queueing Models (Esra Bas)....Pages 233-252 Introduction to Brownian Motion (Esra Bas)....Pages 253-263 Basics of Martingales (Esra Bas)....Pages 265-272 Basics of Reliability Theory (Esra Bas)....Pages 273-292 Back Matter ....Pages 293-307