# Probability Through Problems

• Marek Capiński
• Tomasz Zastawniak
Book

Part of the Problem Books in Mathematics book series (PBM)

1. Front Matter
Pages i-viii
2. Marek Capiński, Tomasz Zastawniak
Pages 1-4
3. Marek Capiński, Tomasz Zastawniak
Pages 5-13
4. Marek Capiński, Tomasz Zastawniak
Pages 15-25
5. Marek Capiński, Tomasz Zastawniak
Pages 27-37
6. Marek Capiński, Tomasz Zastawniak
Pages 39-54
7. Marek Capiński, Tomasz Zastawniak
Pages 55-67
8. Marek Capiński, Tomasz Zastawniak
Pages 69-86
9. Marek Capiński, Tomasz Zastawniak
Pages 87-116
10. Marek Capiński, Tomasz Zastawniak
Pages 117-154
11. Marek Capiński, Tomasz Zastawniak
Pages 155-181
12. Marek Capiński, Tomasz Zastawniak
Pages 183-212
13. Marek Capiński, Tomasz Zastawniak
Pages 213-232
14. Marek Capiński, Tomasz Zastawniak
Pages 233-252
15. Back Matter
Pages 253-259

### Introduction

This book of problems has been designed to accompany an undergraduate course in probability. It will also be useful for students with interest in probability who wish to study on their own. The only prerequisite is basic algebra and calculus. This includes some elementary experience in set theory, sequences and series, functions of one variable, and their derivatives. Familiarity with integrals would be a bonus. A brief survey of terminology and notation in set theory and calculus is provided. Each chapter is divided into three parts: Problems, Hints, and Solutions. To make the book reasonably self-contained, all problem sections include expository material. Definitions and statements of important results are interlaced with relevant problems. The latter have been selected to motivate abstract definitions by concrete examples and to lead in manageable steps toward general results, as well as to provide exercises based on the issues and techniques introduced in each chapter. The hint sections are an important part of the book, designed to guide the reader in an informal manner. This makes Probability Through Prob­ lems particularly useful for self-study and can also be of help in tutorials. Those who seek mathematical precision will find it in the worked solutions provided. However, students are strongly advised to consult the hints prior to looking at the solutions, and, first of all, to try to solve each problem on their own.

### Keywords

Conditional probability Probability Probability space Random variable Variance

#### Authors and affiliations

• Marek Capiński
• 1
• Tomasz Zastawniak
• 2
1. 1.Nowy Sacz School of Business-NLUNowy SączPoland
2. 2.Department of MathematicsUniversity of HullKingston upon HullEngland

### Bibliographic information

• DOI https://doi.org/10.1007/978-0-387-21659-1
• Copyright Information Springer-Verlag New York 2001
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4757-6291-4
• Online ISBN 978-0-387-21659-1
• Series Print ISSN 0941-3502