An Elementary Introduction to the Theory of Probability

Explores concept of probability, surveys rules for addition and multiplication of probabilities, conditional probability, total probability, Bayes formula, Bernoulli's scheme, random variables, the Chebychev inequality, distribution curves, and the means by which an event is declared to be in practice impossible.

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