Probability and Statistical Inference

by Hogg, Robert V.; Tanis, Elliot A.

• ISBN13: 9780130272942
• ISBN10: 0130272949
• Edition: 6th
• Format: Hardcover w/CD
• Copyright: 2001-01-01
• Publisher: PRENTICE HALL

Summary

This user-friendly introduction to the mathematics of probability and statistics (for readers with a background in calculus) uses numerous applications--drawn from biology, education, economics, engineering, environmental studies, exercise science, health science, manufacturing, opinion polls, psychology, sociology, and sports--to help explain and motivate the concepts. A review of selected mathematical techniques is included, and an accompanying CD-ROM contains many of the figures (many animated), and the data included in the examples and exercises (stored in both Minitab compatible format and ASCII). Empirical and Probability Distributions. Probability. Discrete Distributions. Continuous Distributions. Multivariable Distributions. Sampling Distribution Theory. Importance of Understanding Variability. Estimation. Tests of Statistical Hypotheses. Theory of Statistical Inference. Quality Improvement Through Statistical Methods. For anyone interested in the Mathematics of Probability and Statistics.

Table of Contents

Preface	vii
Prologue	xi
Empirical and Probability Distributions	1	(65)
Basic Concepts	1	(9)
The Mean, Variance, and Standard Deviation	10	(6)
Continuous-Type Data	16	(14)
Exploratory Data Analysis	30	(11)
Graphical Comparisons of Data Sets	41	(8)
Time Sequences	49	(9)
Probability Density and Mass Functions	58	(8)
Probability	66	(42)
Properties of Probability	66	(9)
Methods of Enumeration	75	(11)
Conditional Probability	86	(10)
Independent Events	96	(7)
Bayes' Theorem	103	(5)
Discrete Distributions	108	(57)
Random Variables of the Discrete Type	108	(10)
Mathematical Expectation	118	(13)
Bernoulli Trials and the Binomial Distribution	131	(11)
The Moment-Generating Function	142	(11)
The Poisson Distribution	153	(12)
Continuous Distributions	165	(57)
Random Variables of the Continuous Type	165	(11)
The Uniform and Exponential Distributions	176	(10)
The Gamma and Chi-Square Distributions	186	(7)
The Normal Distribution	193	(12)
Distributions of Functions of a Random Variable	205	(11)
Mixed Distributions and Censoring	216	(6)
Multivariable Distributions	222	(61)
Distributions of Two Random Variables	222	(13)
The Correlation Coefficient	235	(9)
Conditional Distributions	244	(10)
The Bivariate Normal Distribution	254	(7)
Transformations of Random Variables	261	(12)
Order Statistics	273	(10)
Sampling Distribution Theory	283	(58)
Independent Random Variables	283	(7)
Distributions of Sums of Independent Random Variables	290	(9)
Random Functions Associated with Normal Distributions	299	(8)
The Central Limit Theorem	307	(8)
Approximations for Discrete Distributions	315	(5)
The t and F Distributions	320	(5)
Limiting Moment-Generating Functions	325	(6)
Chebyshev's Inequality and Convergence in Probability	331	(10)
Centerpiece: Importance of Understanding Variability	336	(5)
Estimation	341	(85)
Point Estimation	341	(13)
Confidence Intervals for Means	354	(10)
Confidence Intervals for Difference of Two Means	364	(9)
Confidence Intervals for Variances	373	(6)
Confidence Intervals for Proportions	379	(7)
Sample Size	386	(8)
Distribution-Free Confidence Intervals for Percentiles	394	(8)
A Simple Regression Problem	402	(14)
More Regression	416	(10)
Tests of Statistical Hypotheses	426	(130)
Tests About Proportions	426	(10)
Tests About One Mean and One Variance	436	(17)
Tests of the Equality of Two Normal Distributions	453	(14)
Chi-Square Goodness of Fit Tests	467	(11)
Contingency Tables	478	(13)
Tests of the Equality of Several Means	491	(11)
Two-Factor Analysis of Variance	502	(13)
Tests Concerning Regression and Correlation	515	(7)
The Wilcoxon Tests	522	(12)
Kolmogorov-Smirnov Goodness of Fit Test	534	(7)
Resampling Methods	541	(6)
Run Test and Test for Randomness	547	(9)
Theory of Statistical Inference	556	(39)
Sufficient Statistics	556	(5)
Power of a Statistical Test	561	(9)
Best Critical Regions	570	(7)
Likelihood Ratio Tests	577	(6)
Bayesian Estimation	583	(6)
Asymptotic Distributions of Maximum Likelihood Estimators	589	(6)
Quality Improvement Through Statistical Methods	595	(28)
Statistical Quality Control	595	(13)
General Factorial and 2k Factorial Designs	608	(7)
More on Design of Experiments	615	(8)
Epilogue	621	(2)
A REVIEW OF SELECTED MATHEMATICAL TECHNIQUES	623	(20)
A.1 Algebra of Sets	623	(4)
A.2 Mathematical Tools for the Hypergeometric Distribution	627	(3)
A.3 Limits	630	(2)
A.4 Infinite Series	632	(4)
A.5 Integration	636	(2)
A.6 Multivariate Calculus	638	(5)
B REFERENCES	643	(2)
C TABLES	645	(28)
D ANSWERS TO ODD-NUMBERED EXERCISES	673	(26)
Index	699

Excerpts

Preface We are pleased with the reception that was given to the first five editions of Probability and Statistical Inference.The sixth edition is still designed for use in a course having from three to six semester hours of credit. No previous study of statistics is assumed, and a standard course in calculus provides an adequate mathematical background. Certain sections have been starred and are not needed in subsequent sections. This, however, does not mean that these starred sections are unimportant, and we hope many of you will study them. We still view this book as the basis of a junior or senior level course in the mathematics of probability and statistics that is taught by many departments of mathematics and/or statistics. We have tried to make it more "user friendly"; yet we do want to reinforce certain basic concepts of mathematics, particularly calculus. To help the student with methods of algebra of sets and calculus, we include a Review of Selected Mathematical Techniquesin Appendix A. This review includes a method that makes integration by parts easier. Also we derive the important Rule of 72that provides an approximation to the number of years necessary for money to double. MAJOR CHANGES IN THIS EDITION Chapter 1 still provides an excellent introduction to good descriptive statistics and exploratory data analysis and the corresponding empirical distributions. However, probability models are also introduced in Chapter 1 so that the student recognizes from the beginning that the characteristics of the empirical distributions are estimates of those of probability distributions. Hopefully, this creates some interest among students in checking to see if a probability model is appropriate for the situation under consideration throughout the text. Chapters 2-4 provide concepts in probability and basic distributions. These have been simplified somewhat from the previous edition by introducing a few of the easiest distributions through examples. Also the probability generating function has been dropped in this edition, although we note that the moment-generating function can serve in that capacity. Of course, the latter can also be used to compute the moments of a distribution. By request of many statisticians, we have introduced multivariate distributions much earlier, but in such a way that only the first section of that chapter is needed for the chapters that follow on techniques used in statistical inference. Hence, if an instructor so desires, he or she can start statistical methods sooner without conditional distributions. While this book is written primarily as a mathematical introduction to probability and statistics, there are a great many examples and exercises concerned with applications. For illustrations, the reader will find applications in the areas of biology, education, economics, engineering, environmental studies, exercise science, health science, manufacturing, opinion polls, psychology, sociology, and sports. That is, there are many exercises in the text, some illustrating the mathematics of probability and statistics but a great number are concerned with applications. We are certainly more concerned with model checking in this edition than in the previous editions. In addition, there is major effort to emphasize confidence intervals more than previously, and we clearly spell out the relationship between confidence intervals and tests of hypotheses. In that regard, we have increased the emphasis on one-sided confidence intervals somewhat because often a practitioner wants a lower or upper bound for the parameter in question, and these have a natural relationship with one-sided tests of hypotheses. The chapter on confidence intervals is so organized that the instructor can introduce early basic concepts of regression and distribution-free techniques, if he or she chooses to do so. That is