Probability and Statistical Inference (9th Edition)

Main subject categories: • Probability • Statistics • Probability Inference • Statistical InferenceWritten by three veteran statisticians, this applied introduction to probability and statistics emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation.Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts. Cover 1 Title Page 2 Copyright Page 3 Contents 4 Preface 6 ACKNOWLEDGMENTS 7 Prologue 8 1 PROBABILITY 10 1.1 Properties of Probability 10 1.2 Methods of Enumeration 20 1.3 Conditional Probability 29 1.4 Independent Events 38 1.5 Bayes’ Theorem 44 2 DISCRETE DISTRIBUTIONS 50 2.1 Random Variables of the Discrete Type 50 2.2 Mathematical Expectation 58 2.3 Special Mathematical Expectations 65 2.4 The Binomial Distribution 74 2.5 The Negative Binomial Distribution 83 2.6 The Poisson Distribution 88 3 CONTINUOUS DISTRIBUTIONS 96 3.1 Random Variables of the Continuous type 96 3.2 The Exponential, Gamma, and Chi-Square Distributions 104 3.3 The Normal Distribution 114 3.4* Additional Models 123 4 BIVARIATE DISTRIBUTIONS 134 4.1 Bivariate Distributions of the Discrete Type 134 4.2 The Correlation Coefficient 143 4.3 Conditional Distributions 149 4.4 Bivariate Distributions of the Continuous Type 155 4.5 The Bivariate Normal Distribution 164 5 DISTRIBUTIONS OF FUNCTIONS OF RANDOM VARIABLES 172 5.1 Functions of One Random Variable 172 5.2 Transformations of Two Random Variables 180 5.3 Several Random Variables 189 5.4 The Moment-Generating Function Technique 196 5.5 Random Functions Associated with Normal Distributions 201 5.6 The Central Limit Theorem 209 5.7 Approximations for Discrete Distributions 215 5.8 Chebyshev’s Inequality and Convergence in Probability 222 5.9 Limiting Moment-Generating Functions 226 6 POINT ESTIMATION 234 6.1 Descriptive Statistics 234 6.2 Exploratory Data Analysis 247 6.3 Order Statistics 257 6.4 Maximum Likelihood Estimation 265 6.5 A Simple Regression Problem 276 6.6* Asymptotic Distributions of Maximum Likelihood Estimators 284 6.7 Sufficient Statistics 289 6.8 Bayesian Estimation 297 6.9* More Bayesian Concepts 303 7 INTERVAL ESTIMATION 310 7.1 Confidence Intervals for Means 310 7.2 Confidence Intervals for the Difference of Two Means 317 7.3 Confidence Intervals for Proportions 327 7.4 Sample Size 333 7.5 Distribution-Free Confidence Intervals for Percentiles 340 7.6* More Regression 347 7.7* Resampling Methods 356 8 TESTS OF STATISTICAL HYPOTHESES 364 8.1 Tests About One Mean 364 8.2 Tests of the Equality of Two Means 374 8.3 Tests About Proportions 382 8.4 The Wilcoxon Tests 390 8.5 Power of a Statistical Test 401 8.6 Best Critical Regions 408 8.7* Likelihood Ratio Tests 415 9 MORE TESTS 424 9.1 Chi-Square Goodness-of-Fit Tests 424 9.2 Contingency Tables 433 9.3 One-Factor Analysis of Variance 444 9.4 Two-Way Analysis of Variance 454 9.5* General Factorial and 2[Sup(k)] Factorial Designs 464 9.6* Tests Concerning Regression and Correlation 471 9.7* Statistical Quality Control 476 EPILOGUE 488 APPENDICES 490 A: REFERENCES 490 B: TABLES 492 C: ANSWERS TO ODD-NUMBERED EXERCISES 518 D: REVIEW OF SELECTED MATHEMATICAL TECHNIQUES 530 D.1 Algebra of Sets 530 D.2 Mathematical Tools for the Hypergeometric Distribution 534 D.3 Limits 537 D.4 Infinite Series 538 D.5 Integration 542 D.6 Multivariate Calculus 544 Index 550 A 550 B 550 C 550 D 550 E 551 F 551 G 551 H 551 I 551 J 551 K 551 L 551 M 551 N 552 O 552 P 552 Q 552 R 552 S 552 T 553 U 553 V 553 W 553 X 553 Z 553 For a one- or two-semester course; calculus background presumed, no previous study of probability or statistics is required. Written by three veteran statisticians, this applied introduction to probability and statistics emphasises the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts. The full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps. Upon purchase, you'll gain instant access to this eBook. Time limit The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed. For a one- or two-semester course; calculus background presumed, no previous study of probability or statistics is required. Written by three veteran statisticians, this applied introduction to probability and statistics emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts