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Informationen zum Autor Georges Fiche has worked at Alcatel-Lucent for more than 20 years, where he has acted as Technical Coordinator for Performance Standardization and as Performance Manager for the design of Alcatel products. Gerard Hebuterne has been a member of the research lab at France telecom for 20 years. He is currently a professor and is responsible for the "Network" Department in INT (a French school of higher education). Klappentext This book offers comprehensive coverage of all the mathematical tools needed by engineers in the field of processing and transport of all forms of information, data and images - as well as many other engineering disciplines. It provides essential theories, equations and results in probability theory and statistics, which constitute the basis for the presentation of signal processing, information theory, traffic and queueing theory, and reliability. The mathematical foundations of simulation are also covered. The book's accessible style will enable students, engineers and researches new to this area to advance their knowledge of communication and other engineering technologies; however, it will also serve as a useful reference guide to anyone wishing to further explore this field. Zusammenfassung This book offers comprehensive coverage of all the mathematical tools needed by engineers in the field of processing and transport of all forms of information! data and images - as well as many other engineering disciplines. Inhaltsverzeichnis Preface 15 Chapter 1. Probability Theory 19 1.1. Definition and properties of events 19 1.1.1. The concept of an event 19 1.1.2.Complementary events 21 1.1.2.1. Basic properties 21 1.1.3. Properties of operations on events 21 1.1.3.1.Commutativity 21 1.1.3.2.Associativity 21 1.1.3.3.Distributivity 21 1.1.3.4. Difference 21 1.1.3.5.DeMorgan's rules 22 1.2. Probability 23 1.2.1. Definition 23 1.2.2. Basic theorems and results 23 1.2.2.1. Addition theorem 23 1.2.2.2. Conditional probability 24 1.2.2.3. Multiplication theorem 25 1.2.2.4. The posterior probability theorem 26 1.3. Random variable 27 1.3.1. Definition 27 1.3.2. Probability functions of a random variable 27 1.3.2.1.Notations 27 1.3.2.2.Cumulative distribution function 27 1.3.2.3. Probability density function 27 1.3.3. Moments of a random variable 28 1.3.3.1. Moments about the origin 29 1.3.3.2.Central moments 29 1.3.3.3. Mean and variance 29 1.3.3.4.Example applications 31 1.3.4. Couples of random variables 32 1.3.4.1. Definition 32 1.3.4.2. Joint probability 32 1.3.4.3. Marginal probability of couples of random variables 33 1.3.4.4. Conditional probability of a couple of random variables 34 1.3.4.5. Functions of a couple of random variables 34 1.3.4.6. Sum of independent random variables 36 1.3.4.7. Moments of the sum of independent random variables 37 1.3.4.8. Practical interest 39 1.4.Convolution 40 1.4.1. Definition 40 1.4.2. Properties of the convolution operation 41 1.4.2.1.The convolution is commutative 41 1.4.2.2. Convolution of exponential distributions 41 1.4.2.3. Convolution of normal (Gaussian) distributions 41 1.5.Laplace transform 42 1.5.1. Definition 43 1.5.2. Properties 43 1.5.2.1. Fundamental property 43 1.5.2.2. Differentiation property 43 1.5.2.3. Integration property 44 1.5.2.4. Some common transforms 44 1.6. Characteristic function, generating function, z-transform 47 1.6.1.Characteristic function 47 1.6.1.1. Definition 47 1.6.1.2. Inversion formula 48 1.6.1.3. The concept of event indicator...
