Probability Through Problems

1. Front Matter

   Pages i-viii

   PDF

2. Terminology and Notation

   • Marek Capiński, Tomasz Zastawniak

   Pages 1-4

3. Modeling Random Experiments

   • Marek Capiński, Tomasz Zastawniak

   Pages 5-13

4. Classical Probability Spaces

   • Marek Capiński, Tomasz Zastawniak

   Pages 15-25

5. Fields

   • Marek Capiński, Tomasz Zastawniak

   Pages 27-37

6. Finitely Additive Probability

   • Marek Capiński, Tomasz Zastawniak

   Pages 39-54

7. Sigma Fields

   • Marek Capiński, Tomasz Zastawniak

   Pages 55-67

8. Countably Additive Probability

   • Marek Capiński, Tomasz Zastawniak

   Pages 69-86

9. Conditional Probability and Independence

   • Marek Capiński, Tomasz Zastawniak

   Pages 87-116

10. Random Variables and Their Distributions

    • Marek Capiński, Tomasz Zastawniak

    Pages 117-154

11. Expectation and Variance

    • Marek Capiński, Tomasz Zastawniak

    Pages 155-181

12. Conditional Expectation

    • Marek Capiński, Tomasz Zastawniak

    Pages 183-212

13. Characteristic Functions

    • Marek Capiński, Tomasz Zastawniak

    Pages 213-232

14. Limit Theorems

    • Marek Capiński, Tomasz Zastawniak

    Pages 233-252

15. Back Matter

    Pages 253-259

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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.

• Conditional probability
• Probability
• Probability space
• Random variable
• Variance

M. Capinski and T. Zastawniak

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."—ZENTRALBLATT MATH

• Nowy Sacz School of Business-NLU, Nowy Sącz, Poland

  Marek Capiński

• Department of Mathematics, University of Hull, Kingston upon Hull, England

  Tomasz Zastawniak