Probability and Statistical Inference

by Hogg, Robert V.; Tanis, Elliot

• ISBN13: 9780131464131
• ISBN10: 0131464132
• Edition: 7th
• Format: Hardcover w/CD
• Copyright: 2010-01-01
• Publisher: Prentice Hall

Summary

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.

Table of Contents

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

Table of Contents provided by Publisher. All Rights Reserved.

Excerpts

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