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＜E-Book＞
Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / by Kenneth Shum
(Compact Textbooks in Mathematics. ISSN:2296455X)

Edition	1st ed. 2023.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2023
Language	English
Size	XV, 259 p. 33 illus., 25 illus. in color : online resource
Authors	*Shum, Kenneth author SpringerLink (Online service)
Subjects	LCSH:Probabilities LCSH:Measure theory FREE:Probability Theory FREE:Applied Probability FREE:Measure and Integration
Notes	Preface -- Beyond discrete and continuous random variables -- Probability spaces -- Lebesgue–Stieltjes measures -- Measurable functions and random variables -- Statistical independence -- Lebesgue integral and mathematical expectation -- Properties of Lebesgue integral and convergence theorems -- Product space and coupling -- Moment generating functions and characteristic functions -- Modes of convergence -- Laws of large numbers -- Techniques from Hilbert space theory -- Conditional expectation -- Levy’s continuity theorem and central limit theorem -- References -- Index This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector’s problem, Monte Carlo integration in finance, data compression in information theory, and more. Measure-Theoretic Probability is ideal for a one-semester course and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study. Prerequisites include a basic knowledge of probability and elementary concepts from real analysis HTTP:URL=https://doi.org/10.1007/978-3-031-49830-5

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