Probability, Random Variables and Random Signal Principles,Peebles

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The fourth edition of "Probability, Random Variables and Random Signal Principles" continues the success of previous editions with its concise introduction to probability theory for the junior-senior level course in electrical engineering. The book offers a careful, logical organization which stresses fundamentals and includes almost 900 student exercises and abundant practical applications for engineers to understand probability concepts. The most important new material in this edition relates to discrete-time random processes and sequences, and other topics in the general area of digital signal processing, such as the DT linear system. Key Features: Digital Topics: The new discrete-time material includes coverage of sampling theorems (baseband and bandpass) for random processes as a foundation for the DT material. This material is placed in Chapter 8 for clear exposure. Correlation functions and power spectrums for these processes, which are developed and connected through the sampling theorems and the DT Fourier transforms, are covered in Chapters 7 and 8, with some introduction in sections 6.1-6.3. The structure of linear DT digital systems is developed in both the sequence and transform domains. Other additions: Other additions include more examples within the text, NEW chapter-end summaries, expanded discussions of probability as a relative frequency, material on permutations and combinations, more details on random variable transformations, ergodicity, important inequalities and the weak and strong laws of large numbers. Problems: Unlike the previous editions, chapter-ending problems have now been combined into a single list with numbering that corresponds to the chapter's section to which the problems mainly apply. Additional problems have been added to the new edition. Starred sections: The level of the material is intended for a typical undergraduate program. However a small amount of more advanced material has been scattered throughout the book to serve as stimulation for the more advanced student or for schools using the book at a higher level. These sections are indicated by a star (*). MATLAB-based examples and problems have been integrated into the text in key places (indicated by a computer icon). Appendixes: Important new material has been added to Appendix A, useful properties of impulse functions, while an entire new appendix has been added, Appendix G, covering various mathematical topics of interest, including Leibniz's rule and Schwarz's Inequality. As in previous editions, the appendixes also include important review material for the students. The book has an expanded web site that includes a downloadable version of the solutions manual, as well as JPEG files of the book's figures. 1. Is having a lot of homework problems important to you?2. How important is MATLAB in your course?3. Do you cover discrete-time material in your course?4. What level course do you teach (undergraduate or graduate)? Table of Content: Chapter 1 Probability Chapter 2 The Random Variable Chapter 3 Operations on one Random Variable--Expectation Chapter 4 Multiple Random Variables Chapter 5 Operations of Multiple Random Variables Chapter 6 Random Processes-Temporal Characteristics Chapter 7 Random Processes-Spectral Characteristics Chapter 8 Linear Systems with Random Inputs Chapter 9 Optimum Linear Systems Chapter 10 Some Practical Applications of the Theory Appendix A Review of the Impulse Function Appendix B Gaussian Distribution Function Appendix C Useful Mathematical Quantities Appendix D Review of Fourier Transforms Appendix E Table of Useful Fourier Transforms Appendix F Some Probability Densities and Distributions Appendix G Some Mathematical Topics of Interest Bibliography Index