The theory of probability is a powerful tool that helps electrical and computer engineers to explain, model, analyze, and design the technology they develop. The text begins at the advanced undergraduate level, assuming only a modest knowledge of probability, and progresses through more complex topics mastered at graduate level. The first five chapters cover the basics of probability and both discrete and continuous random variables. The later chapters have a more specialized coverage, including random vectors, Gaussian random vectors, random processes, Markov Chains, and convergence. Describing tools and results that are used extensively in the field, this is more than a textbook; it is also a reference for researchers working in communications, signal processing, and computer network traffic analysis. With over 300 worked examples, some 800 homework problems, and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Further resources for this title, including solutions (for Instructors only), are available online at www.cambridge.org/9780521864701.

• Each chapter contains a 'Notes' section at the end to discuss the more technical points of theory • There are worked examples throughout the main text, accompanied by homework problems (800 in total) and exam preparation at the end of each chapter: a number of examples and problems use MATLAB • The book is structured so that the level of the text varies as the material progresses, such that instructors can target the level (undergraduate or graduate) of the course to suit the background of the students

### Contents

Preface; 1. Introduction to probability; 2. Introduction to discrete random variables; 3. More about discrete random variables; 4. Continuous random variables; 5. Cumulative distribution functions and their applications; 6. Statistics; 7. Bivariate random variables; 8. Introduction to random vectors; 9. Gaussian random vectors; 10. Introduction to random processes; 11. Advanced concepts in random processes; 12. Introduction to Markov chains; 13. Mean convergence and applications; 14. Other modes of convergence; 15. Self similarity and long-range dependence; Bibliography; Index.

### Review

'… stands alone as a textbook that encourages readers to work through and obtain working knowledge of probability and random processes.' IEEE Software