LEADER 03441nam 22005895 450 001 9910835058303321 005 20240619185727.0 010 $a3-031-49830-5 024 7 $a10.1007/978-3-031-49830-5 035 $a(MiAaPQ)EBC31150948 035 $a(Au-PeEL)EBL31150948 035 $a(DE-He213)978-3-031-49830-5 035 $a(CKB)30362856500041 035 $a(EXLCZ)9930362856500041 100 $a20240213d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMeasure-Theoretic Probability $eWith Applications to Statistics, Finance, and Engineering /$fby Kenneth Shum 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (262 pages) 225 1 $aCompact Textbooks in Mathematics,$x2296-455X 311 $a3-031-49832-1 311 $a3-031-49829-1 327 $aPreface -- 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. 330 $aThis textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector?s problem, Monte Carlo integration in finance, data compression in information theory, and more. Measure-Theoretic Probability is ideal for a one-semester course and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study. Prerequisites include a basic knowledge of probability and elementary concepts from real analysis. 410 0$aCompact Textbooks in Mathematics,$x2296-455X 606 $aProbabilities 606 $aMeasure theory 606 $aProbability Theory 606 $aApplied Probability 606 $aMeasure and Integration 606 $aTeoria de la mesura$2thub 608 $aLlibres electrònics$2thub 615 0$aProbabilities. 615 0$aMeasure theory. 615 14$aProbability Theory. 615 24$aApplied Probability. 615 24$aMeasure and Integration. 615 7$aTeoria de la mesura 676 $a519.2 700 $aShum$b Kenneth$01741670 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910835058303321 996 $aMeasure-Theoretic Probability$94167788 997 $aUNINA