Theory and Problems of Probability, Random Variables, and Random Processes
Hwei P. Hsu, Ph.D. Professor of Electrical Engineering Fairleigh Dickinson University
Start of Citation[PU]McGraw-Hill Professional[/PU][DP]1997[/DP]End of Citation
HWEI P. HSU is Professor of Electrical Engineering at Fairleigh Dickinson University. He received his B.S. from National TaiwanUniversity and M.S. and Ph.D. from Case Institute of Technology. He has published several books which include Schaum's Outline of Analog and Digital Communications and Schaum's Outline of Signals and Systems. Schaum's Outline of Theory and Problems of PROBABILITY, RANDOM VARIABLES, AND RANDOM PROCESSES Copyright © 1997 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the UnitedStates of America. Except as permitted under the Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 PRS PRS 9 0 1 0 9 8 7 ISBN 0-07-030644-3 Sponsoring Editor: Arthur Biderman ProductionSupervisor: Donald F. Schmidt Editing Supervisor: Maureen Walker Library of Congress Cataloging-in-Publication Data Hsu, Hwei P. (Hwei Piao), date Schaum's outline of theory and problems of probability, random variables, and random processes / Hwei P. Hsu. p. cm. — (Schaum's outline series) Includes index. ISBN 0-07-030644-3 1. Probabilities—Problems, exercises, etc. 2. ProbabilitiesOutlines,syllabi, etc. 3. Stochastic processes—Problems, exercises, etc. 4. Stochastic processes—Outlines, syllabi, etc. I. Title. QA273.25.H78 1996 519.2'076—dc20 9618245 CIP
The purpose of this book is to provide an introduction to principles of probability, random variables, and random processes and their applications. The book is designed for students in various disciplines of engineering,science, mathematics, and management. It may be used as a textbook and/or as a supplement to all current comparable texts. It should also be useful to those interested in the field for self-study. The book combines the advantages of both the textbook and the so-called review book. It provides the textual explanations of the textbook, and in the direct way characteristic of the review book, it giveshundreds of completely solved problems that use essential theory and techniques. Moreover, the solved problems are an integral part of the text. The background required to study the book is one year of calculus, elementary differential equations, matrix analysis, and some signal and system theory, including Fourier transforms. I wish to thank Dr. Gordon Silverman for his invaluable suggestions andcritical review of the manuscript. I also wish to express my appreciation to the editorial staff of the McGraw-Hill Schaum Series for their care, cooperation, and attention devoted to the preparation of the book. Finally, I thank my wife, Daisy, for her patience and encouragement. HWEI P. HSU MONTVILLE, NEW JERSEY
Start of Citation[PU]McGraw-Hill Professional[/PU][DP]1997[/DP]End of CitationContents
Chapter 1. Probability 1.1 Introduction 1.2 Sample Space and Events 1.3 Algebra of Sets 1.4 The Notion and Axioms of Probability 1.5 Equally Likely Events 1.6 Conditional Probability 1.7 Total Probability 1.8 Independent Events Solved Problems Chapter 2. Random Variables 2.1 Introduction 2.2 Random Variables 2.3 Distribution Functions 2.4 Discrete Random Variables and Probability MassFunctions 2.5 Continuous Random Variables and Probability Density Functions 2.6 Mean and Variance 2.7 Some Special Distributions 2.8 Conditional Distributions Solved Problems Chapter 3. Multiple Random Variables 3.1 Introduction 3.2 Bivariate Random Variables 3.3 Joint Distribution Functions 3.4 Discrete Random Variables - Joint Probability Mass Functions 3.5 Continuous Random Variables - Joint...