Preface

This online text was developed specifically for students enrolled in MATH350- Probability Theory and Simulation Methods at the University of Delaware. It is designed to accompany our lectures, assignments, and discussions, providing a structured and focused introduction to key concepts in probability.

The book covers topics including fundamentals of probability, counting techniques, conditional probability, independence, random variables, expectations, common univariate distributions, joint distributions, and limit theorems. It is not intended as a comprehensive reference, but rather as a concise, course‑aligned guide to help you develop intuition and problem‑solving skills in probability.

In addition to serving our course, this text is also an excellent resource for MATH367-Actuarial Seminar: Exam P Preparation course. Key concepts and problem types map directly to the Exam P syllabus, and you will find targeted examples and practice questions throughout to reinforce your understanding.

You are encouraged to read actively; work through examples, pause to answer questions, and revisit tricky sections. Probability takes time to absorb, and deeper understanding often comes through repeated engagement with core ideas.

This resource is freely available online and can also be downloaded as a PDF for offline use. The online format allows for updates, so check periodically for revised versions, new examples, or additional exam‑style questions.

We welcome student feedback, which can help improve the book for future readers. We hope you find this a helpful and accessible resource as you build your understanding of probability and prepare for Exam P.