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240301  eng 
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a 9783031498305

100 
1 

a Shum, Kenneth

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0 
0 
a MeasureTheoretic Probability
h Elektronische Ressource
b With Applications to Statistics, Finance, and Engineering
c by Kenneth Shum

250 


a 1st ed. 2023

260 


a Cham
b Birkhäuser
c 2023, 2023

300 


a XV, 259 p. 33 illus., 25 illus. in color
b online resource

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0 

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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a Measure theory

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a Probability Theory

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a Applied Probability

653 


a Measure and Integration

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a Probabilities

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0 
7 
a eng
2 ISO 6392

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b Springer
a Springer eBooks 2005

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0 

a Compact Textbooks in Mathematics

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a 10.1007/9783031498305

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u https://doi.org/10.1007/9783031498305?nosfx=y
x Verlag
3 Volltext

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0 

a 519.2

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a This textbook offers an approachable introduction to measuretheoretic 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. MeasureTheoretic Probability is ideal for a onesemester 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 measuretheoretic probability, it is also suitable for selfstudy. Prerequisites include a basic knowledge of probability and elementary concepts from real analysis
