Elements of Probability Theory

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 ExercisesChapter II. Random Variables and Probability Distributions § 6. Discrete Random Variables § 7. The Binomial Distribution § 8. Continuous Random Variables § 9. Functions of Random Variables ExercisesChapter III. Numerical Characteristics of Probability Distributions § 10. Mean Value. The Mathematical Expectation of a Random Variable § 11. The Center of the Prooadiiity 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 Méafa 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 the 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 ExercisesChapter VII Linearcorrelation § 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