Probability Through Problems

This book of problems has been designed to accompany an undergraduate course in probability. The only prerequisite is basic algebra and calculus. Each chapter is divided into three parts: Problems, Hints, and Solutions. To make the book self-contained all problem sections include expository material. Definitions and statements of important results are interlaced with relevant problems. The problems have been selected to motivate abstract definitions by concrete examples and to lead in manageable steps towards general results, as well as to provide exercises based on the issues and techniques introduced in each chapter. The book is intended as a challenge to involve students as active participants in the course.

Probability theory evaluates among other things the relative frequency with which an event (like rain or an earth quake) occurs or is likely to occur. This book of problems has been designed to accompany an undergraduate course in probability. The only prerequisite is basic algebra and calculus. Each chapter is divided into three parts: Problems, Hints, and Solutions. The hints, a feature, frequently absent in textbooks, is crucial in teaching mathematics and will make this book particularly useful for self-study.

Includes supplementary material: sn.pub/extras

Contenu
Terminology and Notation.- 1 Modeling Random Experiments.- 2 Classical Probability Spaces.- 3 Fields.- 4 Finitely Additive Probability.- 5 Sigma Fields.- 6 Countably Additive Probability.- 7 Conditional Probability and Independence.- 8 Random Variables and Their Distributions.- 9 Expectation and Variance.- 10 Conditional Expectation.- 11 Characteristic Functions.- 12 Limit Theorems.