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240301 ||| eng |
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|a 9783031498305
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|a Shum, Kenneth
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| 245 |
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|a Measure-Theoretic Probability
|h Elektronische Ressource
|b With Applications to Statistics, Finance, and Engineering
|c by Kenneth Shum
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| 250 |
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|a 1st ed. 2023
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| 260 |
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|a Cham
|b Birkhäuser
|c 2023, 2023
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| 300 |
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|a XV, 259 p. 33 illus., 25 illus. in color
|b online resource
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| 505 |
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|a 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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| 653 |
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|a Measure theory
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| 653 |
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|a Probability Theory
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| 653 |
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|a Applied Probability
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| 653 |
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|a Measure and Integration
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| 653 |
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|a Probabilities
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Compact Textbooks in Mathematics
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| 028 |
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|a 10.1007/978-3-031-49830-5
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| 856 |
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|u https://doi.org/10.1007/978-3-031-49830-5?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 519.2
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| 520 |
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|a 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
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