Marek Capinski, Tomasz Jerzy Zastawniak

Probability Through Problems

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Problem Books in Mathematics
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4757-6291-4
• Softcover reprint of the original 1st ed. 2001
• Seitenzahl: 272
• Erscheinungstermin: 8. Juni 2013
• Englisch
• Abmessung: 235mm x 155mm x 15mm
• Gewicht: 439g
• ISBN-13: 9781475762914
• ISBN-10: 1475762917
• Artikelnr.: 39947035

Autorenporträt

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.

Inhaltsangabe

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.

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From the contents:
Modelling Random Experiments
- Classical Probability Spaces
- Fields
- Finitely Additive Probability
- Sigma Fields
- Countably Additive Probability
- Conditional Probability and Independence
- Random Variables and Their Distributions
- Expectation and Variance
- Conditional Expectation
- Characteristic Functions
- Limit Theorems
- Bibliography

Rezensionen

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