Elementary Introduction to the Theory of Probability

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