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1989 | Book

Exercises in Probability

Author: T. Cacoullos

Publisher: Springer New York

Book Series : Problem Books in Mathematics

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About this book

The author, the founder of the Greek Statistical Institute, has based this book on the two volumes of his Greek edition which has been used by over ten thousand students during the past fifteen years. It can serve as a companion text for an introductory or intermediate level probability course. Those will benefit most who have a good grasp of calculus, yet, many others, with less formal mathematical background can also benefit from the large variety of solved problems ranging from classical combinatorial problems to limit theorems and the law of iterated logarithms. It contains 329 problems with solutions as well as an addendum of over 160 exercises and certain complements of theory and problems.

Table of Contents

Frontmatter

Elementary Probabilities

Frontmatter
Chapter 1. Basic Probabilities. Discrete Spaces
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Chapter 2. Distributions. Random Variables
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Chapter 3. Expectation. Variance. Moments
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Chapter 4. General Problems
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Advanced Topics

Frontmatter
Chapter 5. Multivariate Distributions
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Chapter 6. Generating Functions. Characteristic Functions
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Chapter 7. Distribution of Functions of Random Variables
Abstract
In finding the distribution of a function of a scalar or vector random variable the following formulas turn out to be very useful.
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Chapter 8. Limit Theorems. Laws of Large Numbers. Central Limit Theorems
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Chapter 9. Special Topics: Inequalities, Geometrical Probabilities, Difference Equations
Abstract
In Chapter 8 several inequalities such as the Chebyshev, Markov, and Kolmogorov inequalities were given. Here we give some inequalities concerning expectations.
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Chapter 10. General Exercises
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Backmatter
Metadata
Title
Exercises in Probability
Author
T. Cacoullos
Copyright Year
1989
Publisher
Springer New York
Electronic ISBN
978-1-4612-4526-1
Print ISBN
978-1-4612-8863-3
DOI
https://doi.org/10.1007/978-1-4612-4526-1