A textbook for an introductory undergraduate course in probability theory, first published in 1970, and revised in 1976. The novelty of the approach is its basis on the subject's expectation rather than on probability measures. Assumes a fair degree of mathematical sophistication. Annotation copyrighted by Book News, Inc., Portland, OR

This book has exerted a continuing appeal since its original publication in 1970. It develops the theory of probability from axioms on the expectation functional rather than on probability measure, demonstrates that the standard theory unrolls more naturally and economically this way, and that applications of real interest can be addressed almost immediately. A secondary aim of the original text was to introduce fresh examples and convincing applications, and that aim is continued in this edition, a general revision plus the addition of chapters giving an economical introduction to dynamic programming, that is then applied to the allocation problems represented by portfolio selection and the multi-armed bandit. The investment theme is continued with a critical investigation of the concept of risk-free'trading and the associated Black-Sholes formula, while another new chapter develops the basic ideas of large deviations. The book may be seen as an introduction to probability for students with a basic mathematical facility, covering the standard material, but different in that it is unified by its theme and covers an unusual range of modern applications.

This book has exerted a continuing appeal since its original publication in 1970. It develops the theory of probability from axioms on the expectation functional rather than on probability measure, demonstrates that the standard theory unrolls more naturally and economically this way, and that applications of real interest can be addressed almost immediately. A secondary aim of the original text was to introduce fresh examples and convincing applications, and that aim is continued in this edition, a general revision plus the addition of chapters giving an economical introduction to dynamic programming, that is then applied to the allocation problems represented by portfolio selection and the multi-armed bandit. The investment theme is continued with a critical investigation of the concept of risk-free'trading and the associated Black-Sholes formula, while another new chapter develops the basic ideas of large deviations. The book may be seen as an introduction to probability for students with a basic mathematical facility, covering the standard material, but different in that it is unified by its theme and covers an unusual range of modern applications.

This book of problems is designed to challenge students learning probability. Each chapter is divided into three parts: Problems, Hints, and Solutions. All Problems sections include expository material, making the book self-contained. Definitions and statements of important results are interlaced with relevant problems. The only prerequisite is basic algebra and calculus.

Probability and Conditional Expectations bridges the gap between books on probability theory and statistics by providing the probabilistic concepts estimated and tested in analysis of variance, regression analysis, factor analysis, structural equation modeling, hierarchical linear models and analysis of qualitative data. The authors emphasize the theory of conditional expectations that is also fundamental to conditional independence and conditional distributions. Probability and Conditional Expectations Presents a rigorous and detailed mathematical treatment of probability theory focusing on concepts that are fundamental to understand what we are estimating in applied statistics. Explores the basics of random variables along with extensive coverage of measurable functions and integration. Extensively treats conditional expectations also with respect to a conditional probability measure and the concept of conditional effect functions, which are crucial in the analysis of causal effects. Is illustrated throughout with simple examples, numerous exercises and detailed solutions. Provides website links to further resources including videos of courses delivered by the authors as well as R code exercises to help illustrate the theory presented throughout the book.

This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.

The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.