The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data.
Probability & Statistics, Fourth Edition, was written for a one- or two-semester probability and statistics course. This course is offered primarily at four-year institutions and taken mostly by sophomore and junior level students majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.
- Brief introductions in each technical section give readers a hint about what they are going to encounter, while summaries list the most important ideas.
- In addition to examples using current data, some elementary concepts of probability are illustrated by famous examples such as the birthday problem, the tennis tournament problem, the matching problem, and the collector's problem.
- Special features include sections on Markov chains, the gambler's ruin problem, and utility and preferences among gamblers. These topics are presented in an elementary fashion and can be omitted without loss of continuity.
- Optional sections of the book are indicated by an asterisk in the Table of Contents.
- Chapters 1—5 are devoted to probability and can serve as the text for a one-semester course on probability. Independence is now introduced after conditional probability.
- Chapters 6—10 are devoted to statistical inference. Both classical and Bayesian statistical methods are developed in an integrated presentation which will be useful to students when applying the concepts to the real world.
New to this Edition
- Main results are now labeled as theorems for easy reference.
- Important definitions and assumptions are set off from the main text and are labeled for easy reference.
- Examples help introduce new topics, setting up a scenario and illustrating how the mathematics is applied.
- Chapter 6 now covers the law of large numbers and the central limit theorem.
- Chapter 3 now covers Markov chains.
- Lengthy proofs of several theorems now appear at the end of the appropriate sections to improve the flow of presentation of ideas.
- Section 7.1 has been rewritten to make the introduction to inference more accessible.
- Section 9.1 has been rewritten as a more complete introduction to hypothesis testing.
Table of Contents
1. Introduction to Probability
2. Conditional Probability
3. Random Variables and Distributions
5. Special Distributions
6. Large Random Samples
8. Sampling Distributions of Estimators
9. Testing Hypotheses
10. Categorical Data and Nonparametric Methods
11. Linear Statistical Models