說明 
xvi, 135 pages : illustrations ; 23 cm 

text rdacontent 

unmediated rdamedia 

volume rdacarrier 
系列 
Communications and signal processing collection, 23774231


Communications and signal processing collection

附註 
Includes bibliographical references (pages 127129) 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 Twodimensional 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, selfcontained 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

