9780131464131

This applied introduction to the mathematics of probability and statistics emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variability. Designed for students with a background in calculus, it reinforces basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts.

Empirical and Probability Distributions
Basic Concepts
The Mean, Variance, and Standard Deviation
Continuous-Type Data
Exploratory Data Analysis
Graphical Comparisons of Data Sets
Time Sequences
Probability Density and Mass Functions
Probability
Properties of Probability
Methods of Enumeration
Conditional Probability
Independent Events
Bayes' Theorem
Discrete Distributions
Random Variables of the Discrete Type
Mathematical Expectation
Bernoulli Trials and the Binomial Distribution
The Moment-Generating Function
The Poisson Distribution
Continuous Distributions
Random Variables of the Continuous Type
The Uniform and Exponential Distributions
The Gamma and Chi-Square Distributions
The Normal Distribution
Distributions of Functions of a Random Variable
Mixed Distributions and Censoring
Multivariable Distributions
Distributions of Two Random Variables
The Correlation Coefficient
Conditional Distributions
The Bivariate Normal Distribution
Transformations of Random Variables
Order Statistics
Sampling Distribution Theory
Independent Random Variables
Distributions of Sums of Independent Random Variables
Random Functions Associated with Normal Distributions
The Central Limit Theorem
Approximations for Discrete Distributions
The t and F Distributions
Limiting Moment-Generating Functions
Chebyshev's Inequality and Convergence in Probability
Importance of Understanding Variability
Estimation
Point Estimation
Confidence Intervals for Means
Confidence Intervals for Difference of Two Means
Confidence Intervals for Variances
Confidence Intervals for Proportions
Sample Size
Distribution-Free Confidence Intervals for Percentiles
A Simple Regression Problem
More Regression
Tests of Statistical Hypotheses
Tests about Proportions
Tests about One Mean and One Variance
Tests of the Equality of Two Normal Distributions
Chi-Square Goodness of Fit Test
Contingency Tables
Tests of the Equality of Several Means
Two-Factor Analysis of Variance
Tests Concerning Regression and Correlation
The Wilcoxon Tests
Kolmogorov-Smirnov Goodness of Fit Test
Resampling Methods
Run Test and Test for Randomness
Theory of Statistical Inference
Sufficient Statistics
Power of a Statistical Test
Best Critical Regions
Likelihood Ratio Tests
Bayesian Estimation
Asymptotic Distributions of Maximum Likelihood Estimators
Quality Improvement through Statistical Methods
Statistical Quality Control
General Factorial and 2k Factorial Designs
More on Design of Experiments
Epilogue
Review of Selected Mathematical Techniques
Algebra of Sets
Mathematical Tools for the Hypergeometric Distribution
Limits
Infinite Series
Integration
Multivariate Calculus
References
Tables
Answers to Odd-Numbered Exercises
Index
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We are pleased with the reception that was given to the first six editions ofProbability and Statistical Inference.The seventh edition is still designed for use in a course having from three to six semester hours of credit. No previous study of probability or statistics is assumed, and a standard course in calculus provides an adequate mathematical background. Certain sections have been starred and they 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. In particular, the first five chapters provide a substantial one-semester course in probability and probability distributions. While many statisticians are teaching a course at this level by minimizing probability and concentrating on statistics, we have found that those studying statistics, actuarial science, electrical engineering, economics, finance, genetics, and so on need probability as much as statistics. Thus we choose to place about equal emphasis on these two topics. Chapters 6-10 consist of the second semester of a two-semester sequence as they cover topics in statistics and statistical inference. We have discovered that a fairly good four-semester-hour course can be constructed by an instructor by selecting topics from the first five chapters and Chapters 6 and 8. We have tried to make the seventh edition 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 aReview of Selected Mathematical Techniquesin Appendix A. This review includes a method that makes integration by parts easier. Also, we derive the importantRule of 72,which provides an approximation to the number of years necessary for money to double. ENHANCEMENTS IN THIS EDITION There is better and more logical organization, resulting in a major chapter on the normal distribution. A new section gives a brief history of probability, indicating how the normal distribution was discovered. More real examples and exercises concerning probability were added that will appeal to students of actuarial science, finance, economics, and so on. There is a short but excellent Bayesian chapter, including real example and an indication of how Bayesians prove theorems by establishing "Dutch books." In the section on bootstrapping there is an explanation of the origin of this word. There are examples of Simpson's paradox. Some different statistical techniques, including ordered restricted estimates, have been added. There is somewhat more emphasis on the importance of sufficient statistics, noting that such statistics, if they exist, are always used in statistical inferences. Tests of hypotheses and confidence intervals are tied together. An explanation of the Six Sigma program is in the Epilogue. The figures are improved with the use of color. The CD-ROM includes not only all of the data sets in different formats, but also many more new applications of Minitab andMaple. Illustrations ofMapleas a computer algebra system are given in the text and on the CD-ROM. IMPORTANT POINTS IN THIS EDITION Chapter 1 is a basic chapter on probability after considering how discrete data can arise. This is followed by a chapter on discrete probability distributions. Chapter 3 starts with continuous type data, introducing stem-and-leaf diagrams, order statistics, and box plots and includes many standard continuous distribution. Chapter 4 introduces multivariate distributions, which are considered with more emphasis than in past editions, inclu

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Probability and Statistical Inference

Probability and Statistical Inference

0131464132

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