This applied introduction to the mathematics of probability and statistics e mphasizes 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:
Table of Contents
Chapter 1: Probability Basic Concepts
Properties of Probability
Methods of Enumeration
Conditional Probability
Independent Events
Bayes' Theorem
Chapter 2: Discrete Distributions Random Variables of the Discrete Type
Mathematical Expectation
Bernoulli Trials and the Binomial Distribution
The Moment-Generating Function
The Poisson Distribution
Chapter 3: Continuous Distributions Continuous-Type Data and EDA
Random Variables of the Continuous Type
The Uniform and Exponential Distributions
The Gamma and Chi-Square Distributions
Distributions of Functions of a Random Variable
Additional Models
Chapter 4: Multivariate Distributions Distributions of Two Random Variables
The Correlation Coefficient
Conditional Distributions
Transformations of Random Variables
Independent Random Variables
Distributions of Sums of Independent Random Variables
Chebyshev's Inequality and Convergence in Probability
Chapter 5: The Normal Distribution A Brief History of Probability
The Normal Distribution
Random Functions Associated with Normal Distributions
The Central Limit Theorem
Approximations for Discrete Distributions
The Bivariate Normal Distribution
Limiting Moment-Generating Functions
Importance of Understanding Variability
Chapter 6: Estimation Sample Characteristics
Point Estimation
Sufficient Statistics
Confidence Intervals for Means
Confidence Intervals for Difference of Two Means
Confidence Intervals for Variances
Confidence Intervals for Proportions
Sample Size
Order Statistics
Distribution-Free Confidence Intervals for Percentiles
A Simple Regression Problem
More Regression
Resampling Methods
Asymptotic Distributions of Maximum Likelihood Estimators
Chapter 7: Bayesian Methods Subjective Probability
Bayesian Estimation
More Bayesian Concepts
Chapter 8: Tests of Statistical Hypotheses Tests About Proportions
Tests About One Mean and One Variance
Tests of the Equality of Two Normal Distributions
The Wilcoxon Tests
Chi-Square Goodness of Fit Tests
Contingency Tables
One-Factor Analysis of Variance
Two-Factor Analysis of Variance
Tests Concerning Regression and Correlation
Kolmogorov-Smirnov Goodness of Fit Test
Run Test and Test for Randomness
Chapter 9: Theory of Statistical Inference Power of a Statistical Test
Best Critical Regions
Likelihood Ratio Tests
Chapter 10: Quality Improvement Through Statistical Methods
Time Sequences
Statistical Quality Control
General Factorial and 2 k Factorial Designs
More on Design of Experiments
Epilogue
A Review of Selected Mathematical Techniques
Algebra of Sets
Mathematical Tools for the Hypergeometric Distribution
Limits
Infinite Series
Integration
Multivariate Calculus
Review :
"Generally, I think the pedagogy is excellent, providing an almost holistic introduction to statistics, both its mathematical and applications sides. Elements of the subject are introduced in increasing layers of complexity, at a rate that is challenging yet measured. Masterfully done. My overall impression of the book is quite favorable and actually I am considering this text for my next cycle of classes. Strengths: excellent use of examples to illustrate concepts; strong exercise selections; the discussions are generally clear, animated, and focused with the main drive of the text in mind. All the necessary topics central to modern statistics are introduced. The level of the text is quite good for an undergraduate introductory course. Many rather difficult ideas are presented simply, but effectively enough to prepare students for later topics and courses. And the text really bares the soul of statistics. The text motivates the theory by keeping it connected to real-world applications." — David F. Snyder, Texas State University
"Probability and Statistical Inference is a great text to use for a one-year course, where the students are just becoming mathematically prepared. The authors write with great care and clearly develop and motivate the subject. This edition also contains a chapter on Bayesian methods. Chapter 7 is an interesting and modern treatment of the subject—a subject that has included some controversy. Although I am a probabilist, I am certainly pleased to see this treatment in an undergraduate text. Bayesian methods have long needed suitable treatment at the undergraduate level. It provides an up-to-date and complete treatment of mathematics of probability and statistics. This edition also includes many new examples, applications, and exercises. Each of these has improved in an already outstanding text." — Randall Swift, California State Polytechnic University, Pomona
"This latest version of Hogg and Tanis contains many more realistic data scenarios that rely much less on coin tossing and dice and card examples. Students will likely better understand the material if they can relate to the examples. The authors strike a good balance between readability and rigor. The material is accurately presented and theorems are accurate. I am glad to see section 6.13 'Resampling Methods' induded. The 'bootstrap' has been around now for 20 years but many mathematical statistics books still neglect it or relegate it to the exercises. This is a good indication that the text is up-to-date." — Paul Joyce, University of Idaho
"This is a good, solid, calculus-based introduction to probability and statistics at the sophomore-junior level. I have used this textbook twice for such a course, and would like to use it again in the future." — Ching-Yuan Chiang, James Madison University
"The examples in the book are very clear and easy to follow. My students would benefit from this book more than our current textbook." — Mark Ghamsary, Loma Linda University
