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Record Nr. |
UNINA9910835058303321 |
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Autore |
Shum Kenneth |
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Titolo |
Measure-Theoretic Probability : With Applications to Statistics, Finance, and Engineering / / by Kenneth Shum |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2023 |
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ISBN |
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Edizione |
[1st ed. 2023.] |
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Descrizione fisica |
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1 online resource (262 pages) |
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Collana |
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Compact Textbooks in Mathematics, , 2296-455X |
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Disciplina |
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Soggetti |
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Probabilities |
Measure theory |
Probability Theory |
Applied Probability |
Measure and Integration |
Teoria de la mesura |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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. |
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