Probability: An Introduction Through Theory and Exercises

This textbook provides a comprehensive one-semester course in probability, covering measure theory, random variables, laws, convergence, conditioning, discrete time martingales, and computer simulation. It is designed for teaching in parallel with a first course in measure theory and is ideal for preparing for further courses in statistics or probability.

Format: Paperback / softback
Length: 389 pages
Publication date: 16 January 2024
Publisher: Springer International Publishing AG

This comprehensive textbook serves as an all-encompassing one-semester course in probability, providing a thorough foundation for further exploration in the fields of probability and statistics. The book commences by reviewing the fundamental principles of measure theory and integration, laying the groundwork. Probability measures, random variables, and their governing laws are introduced, accompanied by essential analytic tools for their investigation. Several applications to statistics are also presented, highlighting the practical significance of these concepts. The discussion then turns to convergence, leading to classical results such as the law of large numbers and the central limit theorem, which have profound applications in statistical analysis and beyond. Conditioning, a crucial topic, is explored in depth, followed by a comprehensive introduction to discrete-time martingales. Some attention is also given to computer simulation, offering practical insights into the computational aspects of probability theory. Throughout the text, over 150 meticulously crafted exercises with comprehensive solutions serve not only to reinforce the presented concepts but also to enhance students' problem-solving abilities. This textbook is designed to be suitable for guided self-study, making it an invaluable resource for both instructors and students alike. With a wealth of teaching experience behind the author, the clear presentation of material and thoughtfully selected exercises reflect their expertise. The book assumes a foundational understanding of measure and integration theory, as well as elementary notions of probability, making it particularly well-suited for teaching in parallel with a first course in measure theory. As a comprehensive guide for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic, this textbook, offers ideal preparation and enrichment for students seeking to delve deeper into the world of probability and statistics.

Weight: 611g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031384912
Edition number: 1st ed. 2023