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Probability Theory

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Abstract

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.

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Further Reading

  • Daykin, C.D., Pentikäinen, T., Pesonen, M.: Practical Risk Theory for Actuaries. Chapman and Hall, London (1994)

    MATH  Google Scholar 

  • Feller, W.: An Introduction to Probability Theory and Its Applications. Wiley, New York (1968)

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  • Heilmann, W.-R.: Fundamentals of Risk Theory. Verlag Versicherungswirtschaft, Karlsruhe (1988)

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  • Johnson, N.L., Kotz, S.: Distributions in Statistics. Discrete Distributions. Wiley, New York (1969)

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  • Johnson, N.L., Kotz, S.: Distributions in Statistics. Continuous Univariate Distributions. Wiley, New York (1970)

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  • Johnson, N.L., Kotz, S.: Distributions in Statistics. Multivariate Distributions. Wiley, New York (1972)

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  • Malliaris, A.G., Brock, W.A.: Stochastic Methods in Economics and Finance. North-Holland, Amsterdam (1982)

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  • Panjer, H.H., Willmot, G.E.: Insurance Risk Models. Society of Actuaries, Schaumburg (1992)

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  • Rektorys, K. et al.: Survey of Applicable Mathematics. Kluwer, Dordrecht (1994)

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Authors and Affiliations

  1. Dept. of Statistics, Faculty of Mathematics and Physics, Charles University of Prague, Sokolovska 83, 186 75, Prague, Czech Republic

    Tomas Cipra

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  1. Tomas Cipra
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Correspondence to Tomas Cipra .

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Cipra, T. (2010). Probability Theory. In: Financial and Insurance Formulas. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-2593-0_26

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