03441nam 22005895 450 991083505830332120240619185727.03-031-49830-510.1007/978-3-031-49830-5(MiAaPQ)EBC31150948(Au-PeEL)EBL31150948(DE-He213)978-3-031-49830-5(CKB)30362856500041(EXLCZ)993036285650004120240213d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierMeasure-Theoretic Probability With Applications to Statistics, Finance, and Engineering /by Kenneth Shum1st ed. 2023.Cham :Springer International Publishing :Imprint: Birkhäuser,2023.1 online resource (262 pages)Compact Textbooks in Mathematics,2296-455X3-031-49832-1 3-031-49829-1 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.Compact Textbooks in Mathematics,2296-455XProbabilitiesMeasure theoryProbability TheoryApplied ProbabilityMeasure and IntegrationTeoria de la mesurathubLlibres electrònicsthubProbabilities.Measure theory.Probability Theory.Applied Probability.Measure and Integration.Teoria de la mesura519.2Shum Kenneth1741670MiAaPQMiAaPQMiAaPQBOOK9910835058303321Measure-Theoretic Probability4167788UNINA