# Elements of Probability Theory

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Elements of Probability Theory focuses on the basic ideas and methods of the theory of probability. The book first discusses events and probabilities, including the classical meaning of probability, fundamental properties of probabilities, and the primary rule for the multiplication of probabilities. The text also touches on random variables and probability distributions. Topics include discrete and random variables; functions of random variables; and binomial distributions. The selection also discusses the numerical characteristics of probability distributions; limit theorems and estimates of the mean; and the law of large numbers. The text also describes linear correlation, including conditional expectations and their properties, coefficient of correlation, and best linear approximation to the regression function. The book presents tables that show the values of the normal probability integral, Poisson distribution, and values of the normal probability density. The text is a good source of data for readers and students interested in probability theory.

## Table of Contents

Contents

Foreword

Translator's Preface

Introduction

Chapter I. Events and Probabilities

§ 1. Events. Relative Frequency and Probability

§ 2. The Classical Definition of Probability

§ 3. Fundamental Properties of Probabilities. Rule For the Addition of Probabilities

§ 4. The Intersection of Events. Independent Events

§ 5. Conditional Probabilities. The General Rule For the Multiplication of Probabilities. The Formula of Total Probability

Exercises

Chapter II. Random Variables and Probability Distributions

§ 6. Discrete Random Variables

§ 7. The Binomial Distribution

§ 8. Continuous Random Variables

§ 9. Functions of Random Variables

Exercises

Chapter III. Numerical Characteristics of Probability Distributions

§ 10. Mean Value. The Mathematical Expectation of A Random Variable

§ 11. The Centre of the Probability Distribution of A Random Variable

§ 12. The Measure of The Dispersion of A Random Variable. The Moments of A Distribution

Exercises

Chapter IV. The Law of Large Numbers

§ 13. On Events With Very Small Probability

§ 14. Bernoulli's Theorem and The Stability of Relative Frequencies

§ 15. Chebyshev's Theorem

§ 16. The Stability of The Sample Mean and The Method of Moments

Exercises

Chapter V. Limit Theorems and Estimates of the Mean

§ 17. The Characteristic Function

§ 18. The Limit Theorem of De Moivre-Laplace. Estimation of t Relative Frequency

§ 19. Reliability Intervals For Means. The Central Limit Theorem of Lyapunov

Exercises

Chapter Vi. Applications of Probability to the Theory of Observations

§ 20. Random Errors of Measurement and Their Distribution

§ 21 . The Solution of Two Fundamental Problems in the Theory of Errors. Estimation of The True Value of The Quantity Being Measured, and Estimation of The Accuracy of The Apparatus

Exercises

Chapter VII. Linear Correlation

§ 22. On Different Types of Dependence

§ 23. Conditional Expectations and Their Properties

§ 24. Linear Correlation

§ 25. The Coefficient of Correlation

§ 26. The Best Linear Approximation To The Regression Function

§ 27. The Analysis of Linear Correlation In A Given Random Sample. The Significance of The Value of The Coefficient of Correlation

Exercises

Answers to Exercises

Appendix. Tables

I. Values of The Normal Probability Integral

II. Values of The Normal Probability Integral

III. Values of The Normal Probability Density

Iv. The Poisson Distribution

Index

## Product details

- No. of pages: 172
- Language: English
- Copyright: © Pergamon 1965
- Published: January 1, 1965
- Imprint: Pergamon
- eBook ISBN: 9781483136004

## About the Author

### L. Z. Rumshiskii

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