Probability and Statistical Inference

By Robert V. Hogg, Elliot A. Tanis and Dale L. Zimmerman · Pearson · 2020

Study guide: Exam P-1

A two-semester course text in probability and statistical inference that needs a good calculus background but no previous study of probability or statistics. Its first five chapters focus on probability — conditional probability, independence, Bayes' theorem, discrete, continuous and bivariate distributions, functions of random variables, the central limit theorem and Chebyshev's inequality — and the remaining four on statistical inference. The tenth edition adds more than 25 examples and 75 exercises, a section on the hypergeometric distribution and one on hypothesis tests for variances.

On the syllabus

• Exam P — a suggested text (the syllabus requires none); Chapter 1; Chapter 2; Chapter 3 (exclude Chi-Square); Chapter 4 (exclude 4.4, 4.5); Chapter 5: 5.3 (discrete only), 5.5, 5.6, 5.7.

Preface

Prologue

1 Probability

• 1.1 Properties of Probability
• 1.2 Methods of Enumeration
• 1.3 Conditional Probability
• 1.4 Independent Events
• 1.5 Bayes’ Theorem

2 Discrete Distributions

• 2.1 Random Variables of the Discrete Type
• 2.2 Mathematical Expectation
• 2.3 Special Mathematical Expectations
• 2.4 The Binomial Distribution
• 2.5 The Hypergeometric Distribution
• 2.6 The Negative Binomial Distribution
• 2.7 The Poisson Distribution

3 Continuous Distributions

• 3.1 Random Variables of the Continuous Type
• 3.2 The Exponential, Gamma, and Chi-Square Distributions
• 3.3 The Normal Distribution
• 3.4 Additional Models

4 Bivariate Distributions

• 4.1 Bivariate Distributions of the Discrete Type
• 4.2 The Correlation Coefficient
• 4.3 Conditional Distributions
• 4.4 Bivariate Distributions of the Continuous Type
• 4.5 The Bivariate Normal Distribution

5 Distributions of Functions of Random Variables

• 5.1 Functions of One Random Variable
• 5.2 Transformations of Two Random Variables
• 5.3 Several Independent Random Variables
• 5.4 The Moment-Generating Function Technique
• 5.5 Random Functions Associated with Normal Distributions
• 5.6 The Central Limit Theorem
• 5.7 Approximations for Discrete Distributions
• 5.8 Chebyshev’s Inequality and Convergence in Probability
• 5.9 Limiting Moment-Generating Functions

6 Point Estimation

• 6.1 Descriptive Statistics
• 6.2 Exploratory Data Analysis
• 6.3 Order Statistics
• 6.4 Maximum Likelihood and Method of Moments Estimation
• 6.5 A Simple Regression Problem
• 6.6 Asymptotic Distributions of Maximum Likelihood Estimators
• 6.7 Sufficient Statistics
• 6.8 Bayesian Estimation

7 Interval Estimation

• 7.1 Confidence Intervals for Means
• 7.2 Confidence Intervals for the Difference of Two Means
• 7.3 Confidence Intervals for Proportions
• 7.4 Sample Size
• 7.5 Distribution-Free Confidence Intervals for Percentiles
• 7.6 More Regression
• 7.7 Resampling Methods

8 Tests of Statistical Hypotheses

• 8.1 Tests About One Mean
• 8.2 Tests of the Equality of Two Means
• 8.3 Tests for Variances
• 8.4 Tests About Proportions
• 8.5 Some Distribution-Free Tests
• 8.6 Power of a Statistical Test
• 8.7 Best Critical Regions
• 8.8 Likelihood Ratio Tests

9 More Tests

• 9.1 Chi-Square Goodness-of-Fit Tests
• 9.2 Contingency Tables
• 9.3 One-Factor Analysis of Variance
• 9.4 Two-Way Analysis of Variance
• 9.5 General Factorial and 2^k Factorial Designs
• 9.6 Tests Concerning Regression and Correlation
• 9.7 Statistical Quality Control

Appendix A References

Appendix B Tables

Appendix C Answers to Odd-Numbered Exercises

Appendix D Review of Selected Mathematical Techniques

• D.1 Algebra of Sets
• D.2 Mathematical Tools for the Hypergeometric Distribution
• D.3 Limits
• D.4 Infinite Series
• D.5 Integration
• D.6 Multivariate Calculus

Index

Sources

• Probability and Statistical Inference, Tenth Edition: front matter (Pearson, 2020) — the publisher's typeset front matter: title page, copyright page (Tenth Edition, © 2020 Pearson Education, ISBN 978-0-13-518939-9), the contents, the preface (the lead) and the prologue
• SOA Exam P Syllabus, November 2026 — the citation (Tenth Edition, 2020, ISBN 978-0135189399) and the assigned chapters and sections
• Probability and Statistical Inference, 10th edition (Pearson) — the publisher's product page: its table of contents agrees with the front matter, chapter for chapter and section for section