Probability with Statistical Applications

This second edition textbook provides a practical introduction to probability for undergraduates with different backgrounds and applications. It covers the material traditionally required by most undergraduate programs and includes new examples and exercises. It is also suitable for a second course introducing mathematical statistics.

Format: Paperback / softback
Length: 361 pages
Publication date: 28 February 2023
Publisher: Springer Nature Switzerland AG

This second edition textbook provides a comprehensive and practical introduction to probability for undergraduates at various levels, with diverse backgrounds and perspectives on applications. While calculus is a prerequisite for understanding the fundamental concepts, the book is designed with a sensitivity to students' common difficulties with calculus, ensuring that the probability content is thoroughly covered without obscuring it. The first six chapters of this text cover the material traditionally required by most undergraduate programs for a first course in probability in a neat and concise manner.

The comprehensive text includes a wide array of new examples and exercises, with meticulous revisions throughout. Special emphasis is placed on expanding the last three chapters of the book with the addition of an entirely new chapter (9) on Finding and Comparing Estimators. The classroom-tested material presented in this second edition serves as the foundation for a second course introducing mathematical statistics.

The book is organized into nine chapters, each covering a different aspect of probability theory. The first chapter provides an overview of probability concepts and notation, while the second chapter introduces random variables and their distributions. The third chapter explores probability density functions and cumulative distribution functions, which are essential tools in probability analysis.

The fourth chapter introduces conditional probability and Bayes' theorem, which are fundamental tools for making predictions and evaluating evidence. The fifth chapter discusses random processes and stochastic processes, which are used to model real-world phenomena such as weather patterns and financial markets. The sixth chapter explores Markov chains and stochastic processes, which are used to model sequential data and make predictions about future events.

The seventh chapter introduces estimation and hypothesis testing, which are used to make inferences about population parameters and test statistical hypotheses. The eighth chapter discusses random variables with discrete distributions, such as binomial and Poisson distributions, and their applications in probability analysis. The ninth chapter focuses on finding and comparing estimators, which are used to estimate population parameters and make statistical inferences.

Throughout the book, numerous examples and exercises are provided to illustrate the concepts and applications of probability theory. These examples range from simple to complex, and they are designed to help students understand the theoretical principles and apply them to real-world situations. In addition, the book includes a comprehensive glossary of probability terms and symbols, as well as a list of references for further reading.

This second edition textbook is an invaluable resource for undergraduates studying probability theory and mathematical statistics. It provides a solid foundation in probability concepts and tools, and it is written in a clear and accessible style that is suitable for students with a variety of backgrounds and learning styles. Whether you are a first-year student or a advanced undergraduate, this book will help you develop a deeper understanding of probability and its applications in fields such as science, engineering, finance, and social sciences.

Weight: 614g
Dimension: 234 x 156 x 21 (mm)
ISBN-13: 9783030936372
Edition number: 3rd ed. 2022