An Elementary Introduction to the Theory of Probability
by Gnedenko, B. V.; Khinchin, A. Ya.Edition: 5th
Format: Paperback
Pub. Date: 2013-12-12
Publisher(s): Dover Publications
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Summary
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.
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
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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