The Theory of Probability
Explorations and Applications
Book Details:
Pages: | 827 |
Published: | Nov 08 2012 |
Posted: | May 10 2017 |
Language: | English |
Book format: | PDF |
Book size: | 5.79 MB |
Book Description:
From classical foundations to advanced modern theory, this self-contained and comprehensive guide to probability weaves together mathematical proofs, historical context and richly detailed illustrative applications. A theorem discovery approach is used throughout, setting each proof within its historical setting and is accompanied by a consistent emphasis on elementary methods of proof. Each topic is presented in a modular framework, combining fundamental concepts with worked examples, problems and digressions which, although mathematically rigorous, require no specialised or advanced mathematical background. Augmenting this core material are over 80 richly embellished practical applications of probability theory, drawn from a broad spectrum of areas both classical and modern, each tailor-made to illustrate the magnificent scope of the formal results. Providing a solid grounding in practical probability, without sacrificing mathematical rigour or historical richness, this insightful book is a fascinating reference and essential resource, for all engineers, computer scientists and mathematicians.
The Theory of Improper and Noncircular Signals
Complex-valued random signals are embedded in the very fabric of science and engineering, yet the usual assumptions made about their statistical behavior are often a poor representation of the underlying physics. This book deals with improper and noncircular complex signals, which do not conform to classical assumptions, and it demonstrates how correct treatment of these signals can have significant payoffs. The book begins with detailed coverage of the fundamental theory and presents a variety of tools and algorithms for dealing with improper and noncircular signals. It provides a comprehensive account of the main applications, covering detection, estimation, and signal analysis of stationary, nonstationary, and cyclostationary processes. Providing ...
2nd Edition
This highly anticipated revision builds upon the strengths of the previous edition. Sipser's candid, crystal-clear style allows students at every level to understand and enjoy this field. His innovative "proof idea" sections explain profound concepts in plain English. The new edition incorporates many improvements students and professors have suggested over the years, and offers updated, classroom-tested problem sets at the end of each chapter....
In Chapter 1, some of the topics in the conventional circuit theory are reviewed, which have particular importance in the theory of microwave circuits. There include the theory of transmission line, bilinear transformations, and power waves. Chapter 2 gives a review of vector analysis and the fundamental properties of electromagnetic fields to facilitate our later study. In Chapter 3, waveguides are discussed for the first time. Here, the eigenvalue problem is studies in detail including the completeness of eigenfunctions. Without the discussion of the completeness, the theory is only partially correct since no answer is given to certain fundamental questions such as why an exponential variation with distance is assumed for each mode and no other pos...
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