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ASQ Quality Press - Mary McShane-Vaughn

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249 pages

English

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Probability is tough – even those fairly well versed in statistical analysis balk at the prospect of tackling it. Many probability concepts seem counterintuitive at first, and the successful student must in effect train him or herself to think in a totally new way. Mastery of probability takes a lot of time, and only comes from solving many, many problems.
The aim of this text and its companion, The Probability Workbook (coming soon), is to present the subject of probability as a tutor would. Probability concepts are explained in everyday language and worked examples are presented in abundance. In addition to paper-and-pencil solutions, solution strategies using Microsoft Excel functions are given. All mathematical symbols are explained, and the mathematical rigor is kept on an algebra level; calculus is avoided.
This book is written for quality practitioners who are currently performing statistical and probability analyses in their workplaces, and for those seeking to learn probability concepts for the American Society for Quality (ASQ) Certified Quality Engineer, Reliability Engineer, Six Sigma Green Belt, Black Belt, or Master Black Belt exams.

Sujets

Business

Qualité, hygiène, sécurité, environnement

Sciences & Techniques

Statistiques

Probabilités et statistiques

Mathematics

Probability

Statistics

Sciences et techniques

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Publié par	ASQ Quality Press
Date de parution	18 janvier 2016
Nombre de lectures	1
EAN13	9781953079695
Langue	English
Poids de l'ouvrage	9 Mo

Informations légales : prix de location à la page 0,4950€. Cette information est donnée uniquement à titre indicatif conformément à la législation en vigueur.

Extrait

Also available from ASQ Quality Press:
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The ASQ CQE Study Guide
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The Certified Quality Engineer Handbook, Third Edition
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The Certified Six Sigma Green Belt Handbook, Second Edition
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The Certified Manager of Quality/Organizational Excellence Handbook, Fourth Edition
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The Certified Six Sigma Black Belt Handbook, Second Edition
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The ASQ Auditing Handbook, Fourth Edition
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The ASQ Quality Improvement Pocket Guide: Basic History, Concepts, Tools, and Relationships
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To request a complimentary catalog of ASQ Quality Press publications, call
800-248-1946, or visit our website at http://www.asq.org/quality-press.
H1499_McShane_pi-000.indd 2 1/12/16 10:45 AMThe Probability
Handbook
Mary McShane-Vaughn
ASQ Quality Press
Milwaukee, Wisconsin
H1499_McShane_pi-000.indd 3 1/12/16 10:45 AMAmerican Society for Quality, Quality Press, Milwaukee 53203
© 2016 by ASQ
All rights reserved.
Printed in the United States of America
21 20 19 18 17 16 5 4 3 2 1
Library of Congress Cataloging-in-Publication Data
Names: McShane-Vaughn, Mary, 1963– | American Society for Quality.
Title: The probability handbook / Mary McShane-Vaughn.
Description: Milwaukee, Wisconsin : ASQ Quality Press, 2015. | "American
Society for Quality." | Includes bibliographical references and index.
Identifiers: LCCN 2015045483 | ISBN 9780873899222 (hardcover : alk. paper)
Subjects: LCSH: Probabilities—Popular works.
Classification: LCC QA273.15 .M44 2015 | DDC 519.2—dc23
LC record available at http://lccn.loc.gov/2015045483
No part of this book may be reproduced in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise, without the prior written permission of the publisher.
Acquisitions Editor: Matt Meinholz
Managing Editor: Paul Daniel O’Mara
Production Administrator: Randall Benson
ASQ Mission: The American Society for Quality advances individual, organizational, and
community excellence worldwide through learning, quality improvement, and knowledge
exchange.
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Printed on acid-free paper
H1499_McShane_pi-000.indd 4 1/12/16 10:45 AMFor my husband, Jim, who walked into graduate orientation at Georgia Tech
at exactly the same time that I did. What are the chances?
H1499_McShane_pi-000.indd 5 1/12/16 10:45 AMH1499_McShane_pi-000.indd 6 1/12/16 10:45 AMTable of Contents
List of Figures and Tables ................................................. ix
List of Formulas ........................................................ xiii
Preface ................................................................ xvii
Acknowledgments ....................................................... xxi
Chapter 1 Introduction ............................................... 1
Chapter 2 Learning to Count .......................................... 3
2.1 Enumeration .................................................. 4
2.2 Factorials ..................................................... 5
2.3 Permutations 8
2.4 Combinations 9
2.5 Microsoft Excel Functions for Counting ........................... 12
Chapter 3 Rules of the Game 15
3.1 Types of Data ................................................... 15
3.2 Sampling 16
3.3 Graphical Displays of Data ...................................... 17
3.4 Events, Trials, and Outcomes .................................... 20
3.5 Classical versus Empirical Probability ............................ 20
3.6 Unions and Intersections ........................................ 21
3.7 Complement Rule .............................................. 22
3.8 Independence ................................................. 22
3.9 Mutually Exclusive Events 24
3.10 Calculating Odds 25
3.11 Conditional Probability ......................................... 26
3.12 Multiplication Rule ............................................ 28
3.13 Addition Rule 29
3.14 Law of Total Probability and Bayes’ Theorem ...................... 29
3.15 Counting Examples 31
3.16 Conditional Probability Examples ................................ 36
Chapter 4 Discrete Probability Distributions ............................ 45
4.1 Probability Concepts for Discrete Random Variables ................ 45
4.2 The Discrete Uniform Distribution ............................... 53
4.3 The Binomial Distribution ...................................... 54
4.4 The Multinomial Distribution ................................... 61
4.5 The Hypergeometric Distribution 63
vii
H1499_McShane_pi-000.indd 7 1/12/16 10:45 AMviii Table of Contents
4.6 The Geometric and Negative Binomial Distributions ................ 69
4.7 The Poisson Distribution ........................................ 74
4.8 Summary of Discrete Probability Distributions ..................... 79
Chapter 5 Continuous Probability Distributions ......................... 81
5.1 Probability Concepts for Continuous Random Variables ............. 81
5.2 Useful Probability Theorems .................................... 85
5.3 The Uniform Distribution ....................................... 87
5.4 The Triangular Distribution ..................................... 88
5.5 The Normal Distribution 90
5.6 The Standard Normal Distribution ............................... 101
5.7 Student’s t Distribution ......................................... 112
5.8 The Gamma Distribution 118
5.9 Chi- square Distribution 121
5.10 The Exponential Distribution .................................... 125
5.11 The Weibull Distribution ........................................ 130
5.12 The F Distribution ............................................. 134
5.13 The Beta Distribution ........................................... 141
5.14 The Lognormal Distribution ..................................... 144
5.15 The Cauchy Distribution 147
5.16 Summary of Continuous Distributions ............................ 148
Appendix A Distribution Road Map ................................... 153
Appendix B Binomial Table ............................................ 155
Appendix C Cumulative Binomial Table ............................... 159
Appendix D Poisson Distribution Table ................................ 163
Appendix E Cumulative Poisson Table ................................. 171
Appendix F Control Chart Table Values 179
Appendix G Cumulative Standard Normal Table ........................ 181
Appendix H Student’s t Table ......................................... 183
Appendix I Chi-square Table 185
Appendix J Cumulative F Table ....................................... 187
Bibliography ........................................................... 205
Index ................................................................. 209
About the Author ....................................................... 219
H1499_McShane_pi-000.indd 8 1/12/16 10:45 AMList of Figures and Tables
Table 2.1 Four friends arranged in a movie theater line ......................... 4
Table 2.2 Enumeration of possible outcomes when tossing a fair coin three times ... 5
Table 2.3 Enumeration of possible outcomes when throwing two dice ............ 5
Figure 2.1 Number of ways to order four friends in a movie theater line ........... 6
Figure 2.2 Number of ways for four friends to place in a race ..................... 8
Figure 2.3 Number of ways for five friends to place in a race 8
Table 2.4 Number of ways for five friends to be chosen for a committee of three .... 9
Table 2.5 Mirror symmetry for combinations, n = 5 ............................ 10
Figure 2.4 Combinations for n = 5 ............................................ 11
Figure 2.5 Tree diagram for different configurations of pizzas .................... 12
Figure 2.6 Microsoft Excel function =fact() ..................................... 13
Figure 2.7 Microsoft Excel function =permut() .................................. 13
Figure 2.8 Micr=combin() 13
Figure 3.1 Example dot plot ................................................. 17
Figure 3.2 Example histogram ............................................... 18
Figure 3.3 Example stem and leaf plot ......................................... 18
Figure 3.4 Example box and whisker plot ...................................... 19
Figure 3.5 Venn diagram with intersection ..................................... 22
Figure 3.6 Tree diagram for socks in a drawer .................................. 24
Figure 3.7 Venn diagram of mutually exclusive events .......................... 24
Figure 3.8 Universe with events A and B ....................................... 26
Figure 3.9 Universe with A given B ........................................... 26
Table 3.1 Defects found per production line ................................... 27
Table 3.2 Reduced table, conditional on defectives ............................. 27
Figure 3.10 Schematic for law of total probability, k = 3 ........................... 30
Table 3.3 Lottery winning combinations and odds 33
Figure 3.11 Monty Hall problem step 1