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＜電子ブック＞
Probability : An Introduction Through Theory and Exercises / by Paolo Baldi
(Universitext. ISSN:21916675)

版	1st ed. 2023.
出版者	Cham : Springer International Publishing : Imprint: Springer
出版年	2023
本文言語	英語
大きさ	IX, 389 p. 32 illus : online resource
著者標目	*Baldi, Paolo author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Measure theory FREE:Probability Theory FREE:Measure and Integration
一般注記	1 Elements of Measure Theory -- 2 Probability -- 3 Convergence -- 4 Conditioning -- 5 Martingales -- 6 Complements -- 7 Solutions This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics. The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study. Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic HTTP:URL=https://doi.org/10.1007/978-3-031-38492-9

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