Venkatarama Krishnan - Probability and Random Processes

1. Chapter 01
2. Chapter 02
3. Chapter 03
4. Chapter 04
5. Chapter 05
6. Chapter 06
7. Chapter 10
8. Chapter 14
9. Chapter 15
10. Chapter 17
11. Chapter 18
12. Chapter 19
13. Chapter 21
14. Chapter 23

1. Chapter 03
2. Chapter 04
3. Chapter 05
4. Chapter 06
5. Chapter 07
6. Chapter 01
7. Chapter 02
8. Chapter 03
9. Chapter 04
10. Chapter 05
11. Chapter 06
12. Chapter 07
13. Chapter 08
14. Chapter 09
15. Chapter 10
16. Chapter 12
17. Chapter 13
18. Chapter 14
19. Chapter 15
20. Chapter 18
21. Chapter 19
22. Chapter 20
23. Chapter 21
24. Chapter 22
25. Chapter 23
26. Chapter 24

SECOND EDITION

VENKATARAMA KRISHNAN

Professor Emeritus of Electrical and Computer Engineering
Center for Advanced Computation and Telecommunications
University of Massachusetts Lowell

With Contribution from

KAVITHA CHANDRA

Professor of Electrical and Computer Engineering
Center for Advanced Computation and Telecommunications
University of Massachusetts Lowell

Copyright 2016 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Krishnan, Venkatarama, 1929
Probability and random processes / Venkatarama Krishnan. Second edition.
pages cm
Includes bibliographical references and index.

ISBN 978-1-118-92313-9 (cloth : alk. paper) 1. Probabilities. 2. Stochastic processes. 3. EngineeringStatistical methods. 4. ScienceStatistical methods. I. Title.
QA273.K74 2015
519.2dc23
2015023986

Vishnu sahasranamam

Shree rma rma rmti

ram rm manoram

Sahasra nmatathtulyam

rmanma varnan

This book is respectfully dedicated to the memory of my mother

and the memory of my father

Avvaiyar Tamil Poet

If a king and a well-learned person are balanced

A well-learned person weighs more than the king

Whereas the king is revered only in his country

A well-learned person is valued wherever he goes

On a well-learned person

In this second edition, additional sections have been incorporated to make it a more complete tome. In is a new chapter on Probability Modeling of Teletraffic Engineering written by my colleague Kavitha Chandra discussing various probability models in teletraffic engineering.

This new edition now contains 455 carefully detailed figures and 377 representative examples, some with multiple solutions with every step explained clearly enhancing the clarity of presentation to yield a more comprehensive reference tome. It explains in detail the essential topics of applied mathematical functions to problems that engineers and researchers solve daily in the course of their work. The usual topics like set theory, combinatorics, random variables, discrete and continuous probability distribution functions, moments, and convergence of random variables, autocovariance and cross covariance functions, stationarity concepts, Wiener and Kalman filtering, and tomographic imaging of the first edition have all been retained. Graphical Fourier transform tables and a number of probability tables with accuracy up to nine decimal places are given in the seven appendices. A new eighth appendix on finding the roots of the probability generating function has also been added. The index has been carefully prepared to enhance the utility of this reference.

With these added material on theory and applications of probability, the second edition of Probability and Random Processes is a more comprehensive reference tome for practicing scientists and engineers in economics, science, and technology.

As in the first edition, the additional graphs in this edition were also created with Mathcad software. All algebraic calculations were also verified with Mathcad software. Mathcad is a registered trademark of Parametric Technology Corporation Inc., http://www.ptc.com/product/mathcad/

Since the publication of the first edition of this book, many other books on Probability have appeared and they have influenced me to a considerable extent in the choice of additional topics. I once again extend my scientific debt of gratitude to all these authors.