Probability Theory



Chapter 26 deals with formulas and laws of probability theory: 26.1. Random Events and Probability, 26.2. Conditional Probability and Independent Events, 26.3. Random Variables and Their Basic Characteristics, 26.4. Important Discrete Distributions, 26.5. Important Continuous Distributions, 26.6. Random Vectors and Their Basic Characteristics, 26.7. Transformation of Random Variables, 26.8. Conditional Mean Value, 26.9. Martingales, 26.10. Generating Function, 26.11. Convolutions and Sums of Random Variables, 26.12. Random Sums of Random Variables, 26.13. Some Inequalities, 26.14. Limit Theorems of Probability Theory.


Independent Random Variable Wiener Process Negative Binomial Distribution Moment Generate Function Discrete Random Variable 

Further Reading

  1. Daykin, C.D., Pentikäinen, T., Pesonen, M.: Practical Risk Theory for Actuaries. Chapman and Hall, London (1994)MATHGoogle Scholar
  2. Feller, W.: An Introduction to Probability Theory and Its Applications. Wiley, New York (1968)MATHGoogle Scholar
  3. Heilmann, W.-R.: Fundamentals of Risk Theory. Verlag Versicherungswirtschaft, Karlsruhe (1988)MATHGoogle Scholar
  4. Johnson, N.L., Kotz, S.: Distributions in Statistics. Discrete Distributions. Wiley, New York (1969)MATHGoogle Scholar
  5. Johnson, N.L., Kotz, S.: Distributions in Statistics. Continuous Univariate Distributions. Wiley, New York (1970)MATHGoogle Scholar
  6. Johnson, N.L., Kotz, S.: Distributions in Statistics. Multivariate Distributions. Wiley, New York (1972)Google Scholar
  7. Malliaris, A.G., Brock, W.A.: Stochastic Methods in Economics and Finance. North-Holland, Amsterdam (1982)Google Scholar
  8. Panjer, H.H., Willmot, G.E.: Insurance Risk Models. Society of Actuaries, Schaumburg (1992)Google Scholar
  9. Rektorys, K. et al.: Survey of Applicable Mathematics. Kluwer, Dordrecht (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dept. of Statistics, Faculty of Mathematics and PhysicsCharles University of PraguePragueCzech Republic

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