B. V. Gnedenko

An Elementary Introduction to the Theory of Probability

• Broschiertes Buch

Produktbeschreibung

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, more.

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Produktdetails

• Dover Books on Mathema 1.4tics
• Verlag: Dover Publications Inc.
• 5th Revised edition
• Seitenzahl: 160
• Erscheinungstermin: 12. Dezember 2013
• Englisch
• Abmessung: 215mm x 138mm x 8mm
• Gewicht: 202g
• ISBN-13: 9780486601557
• ISBN-10: 0486601552
• Artikelnr.: 21375523

Inhaltsangabe

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