Ebook: Probability Through Problems
- Tags: Probability Theory and Stochastic Processes
- Series: Problem Books in Mathematics
- Year: 2001
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-viii
Terminology and Notation....Pages 1-4
Modeling Random Experiments....Pages 5-13
Classical Probability Spaces....Pages 15-25
Fields....Pages 27-37
Finitely Additive Probability....Pages 39-54
Sigma Fields....Pages 55-67
Countably Additive Probability....Pages 69-86
Conditional Probability and Independence....Pages 87-116
Random Variables and Their Distributions....Pages 117-154
Expectation and Variance....Pages 155-181
Conditional Expectation....Pages 183-212
Characteristic Functions....Pages 213-232
Limit Theorems....Pages 233-252
Back Matter....Pages 253-259
Content:
Front Matter....Pages i-viii
Terminology and Notation....Pages 1-4
Modeling Random Experiments....Pages 5-13
Classical Probability Spaces....Pages 15-25
Fields....Pages 27-37
Finitely Additive Probability....Pages 39-54
Sigma Fields....Pages 55-67
Countably Additive Probability....Pages 69-86
Conditional Probability and Independence....Pages 87-116
Random Variables and Their Distributions....Pages 117-154
Expectation and Variance....Pages 155-181
Conditional Expectation....Pages 183-212
Characteristic Functions....Pages 213-232
Limit Theorems....Pages 233-252
Back Matter....Pages 253-259
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