Probability and Statistical Inference, Global Edition

About our authors Robert V. Hogg was Professor Emeritus of Statistics at the University of Iowa since 2001. He got his B.A. in mathematics at the University of Illinois and M.S. and Ph.D. degrees in mathematics, specializing in actuarial sciences and statistics, from the University of Iowa. Known for his gift of humor and his passion for teaching, Hogg had far-reaching influence in the field of statistics. Throughout his career, he played a major role in defining statistics as a unique academic field, and almost literally "wrote the book" on the subject. He authored more than 70 research articles and co-authored 4 books, including Introduction of Mathematical Statistics, 6th Edition with J. W. McKean and  A.T. Craig; Applied Statistics for Engineers and Physical Scientists, 3rd Edition with J. Ledolter; and A Brief Course in Mathematical Statistics, 1st Edition with E.A. Tanis. His texts have become classroom standards used by hundreds of thousands of students.Among the many awards he received for distinction in teaching, Hogg was honored at the national level (the Mathematical Association of America Award for Distinguished Teaching), the state level (the Governor's Science Medal for Teaching), and the university level (Collegiate Teaching Award). His important contributions to statistical research have been acknowledged by his election to fellowship standing in the ASA and the Institute of Mathematical Statistics.Elliot Tanis, Professor Emeritus of Mathematics at Hope College, received his M.S. and Ph.D. degrees from the University of Iowa. Tanis is the co-author of A Brief Course in Mathematical Statistics with R. Hogg and Probability and Statistics: Explorations with MAPLE, 2nd Edition with Z. Karian. He has authored over 30 publications on statistics and is a past chairman and governor of the Michigan MAA, which presented him with both its Distinguished Teaching and Distinguished Service Awards.  He taught at Hope for 35 years and in 1989 received the HOPE Award (Hope's Outstanding Professor Educator) for his excellence in teaching.  In addition to his academic interests, Dr. Tanis is also an avid tennis player and devoted Hope sports fan.Dale Zimmerman is the Robert V. Hogg Professor in the Department of Statistics and Actuarial Science at the University of Iowa.

• 1. Probability 1.1 Properties of Probability1.2 Methods of Enumeration1.3 Conditional Probability1.4 Independent Events1.5 Bayes' Theorem2. Discrete Distributions 2.1 Random Variables of the Discrete Type2.2 Mathematical Expectation2.3 Special Mathematical Expectations2.4 The Binomial Distribution2.5 The Hypergeometric Distribution2.6 The Negative Binomial Distribution2.7 The Poisson Distribution3. Continuous Distributions 3.1 Random Variables of the Continuous Type3.2 The Exponential, Gamma, and Chi-Square Distributions3.3 The Normal Distribution3.4 Additional Models4. Bivariate Distributions 4.1 Bivariate Distributions of the Discrete Type4.2 The Correlation Coefficient4.3 Conditional Distributions4.4 Bivariate Distributions of the Continuous Type4.5 The Bivariate Normal Distribution5. Distributions of Functions of Random Variables 5.1 Functions of One Random Variable5.2 Transformations of Two Random Variables5.3 Several Independent Random Variables5.4 The Moment-Generating Function Technique5.5 Random Functions Associated with Normal Distributions5.6 The Central Limit Theorem5.7 Approximations for Discrete Distributions5.8 Chebyshev's Inequality and Convergence in Probability5.9 Limiting Moment-Generating Functions6. Point Estimation 6.1 Descriptive Statistics6.2 Exploratory Data Analysis6.3 Order Statistics6.4 Maximum Likelihood and Method of Moments Estimation6.5 A Simple Regression Problem6.6 Asymptotic Distributions of Maximum Likelihood Estimators6.7 Sufficient Statistics6.8 Bayesian Estimation7. Interval Estimation 7.1 Confidence Intervals for Means7.2 Confidence Intervals for the Difference of Two Means7.3 Confidence Intervals for Proportions7.4 Sample Size7.5 Distribution-Free Confidence Intervals for Percentiles7.6 More Regression7.7 Resampling Methods8. Tests of Statistical Hypotheses 8.1 Tests About One Mean8.2 Tests of the Equality of Two Means8.3 Tests for Variances8.4 Tests About Proportions8.5 Some Distribution-Free Tests8.6 Power of a Statistical Test8.7 Best Critical Regions8.8 Likelihood Ratio Tests9. More Tests 9.1 Chi-Square Goodness-of-Fit Tests9.2 Contingency Tables9.3 One-Factor Analysis of Variance9.4 Two-Way Analysis of Variance9.5 General Factorial and 2k Factorial Designs9.6 Tests Concerning Regression and Correlation9.7 Statistical Quality ControlAPPENDICES A. References B. Tables C. Answers to Odd-Numbered Exercises D. Review of Selected Mathematical Techniques D.1 Algebra of SetsD.2 Mathematical Tools for the Hypergeometric DistributionD.3 LimitsD.4 Infinite SeriesD.5 IntegrationD.6 Multivariate CalculusIndex