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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Elementary Probabilities

Frontmatter

Chapter 1. Basic Probabilities. Discrete Spaces

Without Abstract
T. Cacoullos

Chapter 2. Distributions. Random Variables

Without Abstract
T. Cacoullos

Chapter 3. Expectation. Variance. Moments

Without Abstract
T. Cacoullos

Chapter 4. General Problems

Without Abstract
T. Cacoullos

Advanced Topics

Frontmatter

Chapter 5. Multivariate Distributions

Without Abstract
T. Cacoullos

Chapter 6. Generating Functions. Characteristic Functions

Without Abstract
T. Cacoullos

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.
T. Cacoullos

Chapter 8. Limit Theorems. Laws of Large Numbers. Central Limit Theorems

Without Abstract
T. Cacoullos

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.
T. Cacoullos

Chapter 10. General Exercises

Without Abstract
T. Cacoullos

Backmatter

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