Probability

By Lawrence M. Leemis · Lightning Source · 2018

Study guide: Exam P-1

A calculus-based introduction to probability covering the traditional topics, with a secondary emphasis on Monte Carlo simulation. Examples from a wide range of fields apply the theory to real-world problems, and its description says it covers all of the topics of the SOA's Exam P. The second edition adds moment-ratio diagrams at the end of Chapter 5 and a univariate distribution relationship chart at the end of Chapter 8.

On the syllabus

Exam P — a suggested text (the syllabus requires none); Chapter 1 (exclude 1.1); Chapter 2; Chapter 3 (exclude moment generating functions in 3.4, exclude 3.5); Chapter 4 (exclude 4.7); Chapter 5 (include only beta distribution in 5.5); Chapter 6 (exclude continuous, exclude moment generating functions in 6.3, exclude 6.4); Chapter 7 (exclude 7.1, include only order statistics in 7.2, exclude 7.3); Chapter 8 (exclude 8.1, exclude 8.2).

1 Introduction

1.1 Applications
1.2 Counting
1.3 Sets

2 Probability

2.1 Experiments, Sample Spaces, and Events
2.2 Probability Axioms
2.3 Computing Probabilities
2.4 Conditional Probability
2.5 Rule of Bayes
2.6 Independence

3 Random Variables

3.1 Discrete Random Variables
3.2 Continuous Random Variables
3.3 Cumulative Distribution Functions
3.4 Expected Values
3.5 Inequalities (Markov, Chebyshev)
3.6 Exercises

4 Common Discrete Distributions

4.1 Bernoulli Distribution
4.2 Binomial Distribution
4.3 Geometric Distribution
4.4 Negative Binomial Distribution
4.5 Poisson Distribution
4.6 Hypergeometric Distribution
4.7 Other Distributions
4.8 Exercises

5 Common Continuous Distributions

6 Joint Distributions

6.1 Bivariate Distributions
6.2 Independent Random Variables
6.3 Expected Values
6.4 Bivariate Normal Distribution
6.5 Multivariate Distributions

7 Functions of Random Variables

7.1 Cumulative Distribution Function Technique
7.2 Transformation Technique
7.3 Moment Generating Function Technique

8 Limiting Distributions

8.1 Convergence in Probability
8.2 Convergence in Distribution
8.3 Central Limit Theorem

Sources

Probability, Second Edition: contents (Lawrence M. Leemis, 2018) — the author's contents for the second edition: the eight chapters and their sections (Chapter 8 is listed there as "Limit Theorems"); it lists no Exercises sections
Sample pages from Probability, 2nd Edition (Lawrence M. Leemis) — pages of the book itself (pp. 27, 55–56, 129, 170, 206–207, 211, 242, 257–258, 290–291, 344, 393, 489–490, 542–543, 550), whose headings and running heads confirm the section titles they reach — among them the 3.6 and 4.8 Exercises sections (pp. 170 and 242) — and give Chapter 8's title as "Limiting Distributions"
SOA Exam P Syllabus, November 2026 — the citation (Second Edition, 2018, Lightning Source, ISBN 978-0-9829174-7-3) and the assigned chapters and sections
Lawrence Leemis, home page (College of William & Mary) — the author's own citation (Probability, Second Edition, 2018, Lightning Source, ISBN 978-0-9829174-7-3) and the errata, which date the first printing October 2017 and the second July 2018
Introduction to "Probability" (W&M ScholarWorks) — the book's description (the lead's first two sentences), from the record of the 2011 first edition
Review of Probability, second edition (Journal of Quality Technology, 2021) — that the book's selection of topics aligns with all the topics of the SOA's Exam P, and what the second edition adds: moment-ratio diagrams at the end of Chapter 5 and a univariate distribution relationship chart at the end of Chapter 8