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Mathematical Statistics and Data Analysis 3rd
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Mathematical Statistics and Data Analysis 3rd This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings.
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THIRD EDITION
Mathematical
Statistics and
Data Analysis
John A. Rice
University of California, Berkeley
Australia • Brazil • Canada • Mexico • Singapore • Spain
United Kingdom • United States
Mathematical Statistics and Data Analysis, Third Edition
John A. Rice
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Printer: R.R. Donnelley/Crawfordsville
© 2007 Duxbury, an imprint of Thomson Brooks/Cole, a part
of The Thomson Corporation. Thomson, the Star logo, and
Brooks/Cole are trademarks used herein under license.
ALL RIGHTS RESERVED. No part of this work covered by
the copyright hereon may be reproduced or used in any form or
by any means—graphic, electronic, or mechanical, including
photocopying, recording, taping, Web distribution, information
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Printed in the United States of America
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Library of Congress Control Number: 2005938314
Student Edition: ISBN 0-534-39942-8
We must be careful not to confuse data with the
abstractions we use to analyze them.
W
ILLIAM JAMES (1842–1910)
Contents
Preface xi
1 Probability 1
1.1 Introduction 1
1.2 Sample Spaces 2
1.3 Probability Measures 4
1.4 Computing Probabilities: Counting Methods 6
1.4.1 The Multiplication Principle 7
1.4.2 Permutations and Combinations 9
1.5 Conditional Probability 16
1.6 Independence 23
1.7 Concluding Remarks 26
1.8 Problems 26
2 Random Variables 35
2.1 Discrete Random Variables 35
2.1.1 Bernoulli Random Variables 37
2.1.2 The Binomial Distribution 38
2.1.3 The Geometric and Negative Binomial Distributions 40
2.1.4 The Hypergeometric Distribution 42
2.1.5 The Poisson Distribution 42
2.2 Continuous Random Variables 47
2.2.1 The Exponential Density 50
2.2.2 The Gamma Density 53
iv
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