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作者 Alencar, Marcelo Sampaio de., author
書名 Probability theory / Marcelo Sampaio de Alencar and Raphael Tavares de Alencar
出版項 New York, NY : Momentum Press, 2016
國際標準書號 9781606507483 eBook
9781606507476
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 資訊所圖書室圖書區  G3 A368    在架上    30330000232525
說明 xvi, 135 pages : illustrations ; 23 cm
text rdacontent
unmediated rdamedia
volume rdacarrier
系列 Communications and signal processing collection, 2377-4231
Communications and signal processing collection
附註 Includes bibliographical references (pages 127-129) and index
1. Advanced set theory -- 1.1 Set theory -- 1.2 Basic set theory -- 1.3 The axioms of set theory -- 1.4 Operations on sets -- 1.5 Families of sets -- 1.6 An algebra of sets -- 1.7 The Borel algebra --
2. Fundamentals of measure theory -- 2.1 A short history of measure -- 2.2 Measure in an algebra of sets -- 2.3 The Riemann integral -- 2.4 The Lebesgue integral --
3. Axiomatic theory of probability -- 3.1 Basic probability theory -- 3.2 The axioms of probability -- 3.3 Bayes' theorem --
4. Random variables -- 4.1 The concept of a random variable -- 4.2 Cumulative distribution function -- 4.3 Moments of a random variable -- 4.4 Functions of random variables -- 4.5 Discrete distributions -- 4.6 Characteristic function -- 4.7 Conditional distribution -- 4.8 Useful distributions and applications --
5. Joint random variables -- 5.1 An extension of the concept of random variables -- 5.2 Properties of probability distributions -- 5.3 Moments in two dimensions -- 5.4 Conditional moments -- 5.5 Two-dimensional characteristic function -- 5.6 Function of joint random variables -- 5.7 Complex random variables --
6. Fundamental inequalities -- 6.1 The world of inequalities -- 6.2 Tchebychev's inequality -- 6.3 Markov's inequality -- 6.4 Bienaymé's inequality -- 6.5 Jensen's inequality -- 6.6 Chernoff 's inequality -- 6.7 Kolmogorov's inequality -- 6.8 Schwarz' inequality -- 6.9 Hölder's inequality -- 6.10 Lyapunov's inequality -- 6.11 Minkowsky's inequality -- 6.12 About arguments and proofs --
7. Convergence and the law of large numbers -- 7.1 Forms of convergence in probability theory -- 7.2 Types of convergence -- 7.3 Relationships between the types of convergence -- 7.4 Weak law of large numbers -- 7.5 Strong law of large numbers -- 7.6 Central limit theorem -- References -- Index
Probability Theory is a classic topic in any course of exact sciences that evolved from the amalgamation of different areas of Mathematics, including set and measure theory. An axiomatic treatment of probability is presented in the book. The main idea is to present a seamless connection between the more abstract advanced set theory, the fundamental concepts from measure theory and integration and probability, filling in the gaps from previous books and leading to an interesting, robust and, hopefully, self-contained exposition of Probability Theory. This book presents the historical evolution of Probability Theory. It deals with the advanced concepts of set and measure theory, along with the axioms of probability. Random variables, in one and two dimensions, are discussed. The fundamental inequalities are deduced. The book also presents the main convergence theorems and the law of large numbers. It targets graduate students who may not have taken basic courses in these specific topics, and can provide a quick and concise way of obtaining the knowledge they need to succeed in advanced courses
Also available in print
Mode of access: World Wide Web
System requirements: Adobe Acrobat reader
Title from PDF title page (viewed on May 14, 2016)
主題 Probabilities
Electronic books. local
Alt Author Alencar, Raphael Tavares de., author
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