An Elementary Introduction to the Theory of Probability
This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself.
After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics.
The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.

1000275461
An Elementary Introduction to the Theory of Probability
This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself.
After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics.
The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.

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An Elementary Introduction to the Theory of Probability

An Elementary Introduction to the Theory of Probability

An Elementary Introduction to the Theory of Probability

An Elementary Introduction to the Theory of Probability

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Overview

This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself.
After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics.
The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.


Product Details

ISBN-13: 9780486601557
Publisher: Dover Publications
Publication date: 12/12/2013
Series: Dover Books on Mathematics
Edition description: 5th Revised ed.
Pages: 160
Product dimensions: 5.50(w) x 8.50(h) x 0.35(d)

Table of Contents

PART I. PROBABILITIES
CHAPTER I. THE PROBABILITY OF AN EVENT
1. The concept of probability
2. Impossible and certain events
3. Problem
CHAPTER 2. RULE FOR THE ADDITION OF PROBABILITIES
4. Derivation of the rule for the addition of probabilities
5. Complete system of events
6. Examples
CHAPTER 3. CONDITIONAL PROBABILITIES AND THE MULTIPLICATION RULE
7. The concept of conditional probability
8. Derivation of the rule for the multiplication of probabilities
9. Independent events
CHAPTER 4. CONSEQUENCES OF THE ADDITION AND MULTIPLICATION RULES
10. Derivation of certain inequalities
11. Formula for total probability
12. Bayes's formula
CHAPTER 5. BERNOULLI'S SCHEME
13. Examples
14. The Bernoulli formulas
15. The most probable number of occurrences of an event
CHAPTER 6 BERNOULLI'S THEOREM
16. Content of Bernoulli's theorem
17. Proof of Bernoulli's theorem
PART II. RANDOM VARIABLES
CHAPTER 7. RANDOM VARIABLES AND DISTRIBUTION LAWS
18. The concept of random variable
19. The concept of law of distribution
CHAPTER 8. MEAN VALUES
20. Determination of the mean value of a random variable
CHAPTER 9. MEAN VALUE OF A SUM AND OF A PRODUCT
21. Theorem on the mean value of a sum
22. Theorem on the mean value of a product
CHAPTER 10. DISPERSION AND MEAN MEAN DEVIATIONS
23. Insufficiency of the mean value for the characterization of a random variable
24. Various methods of measuring the dispersion of a random variable
25. Theorems on the standard deviation
CHAPTER 11. LAW OF LARGE NUMBERS
26. Chebyshev's inequality
27. Law of large numbers
28. Proof of the law of large numbers
CHAPTER 12. NORMAL LAWS
29. Formulation of the problem
30. Concept of a distribution curve
31. Properties of normal distribution curves
32. Solution of problems
CONCLUSION
APPENDIX. Table of values of the function F (a)
BIBLIOGRAPHY
INDEX
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