Fundamentals of Probability Theory

  • Palle Thoft-Christensen
  • Michael J. Baker


As emphasized in chapter 1, modern structural reliability analysis is based on a probabilistic point of view. It is therefore important to get a profound knowledge of at least some part of probability theory. It is beyond the scope of this book to give a thorough presentation of probability theory on a rigorous axiomatic basis. What is needed to understand the following chapters is some knowledge of the fundamental assumptions of modern probability theory, combined with a number of definitions and theorems. It will be assumed that the reader is familiar with the terminology and the algebra of simple set theory.


Random Vector Sample Space Central Moment Probability Mass Function Discrete Random Variable 
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    Ang, A. H-S. & W. H. Tang: Probability Concepts in Engineering Planning and Design. Vol. 1, Wiley, N.Y., 1975.Google Scholar
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    Benjamin, J. R. & C. A. Cornell: Probability, Statistics and Decision for Civil Engineers. McGraw-Hill, N.Y., 1970.Google Scholar
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    Bolotin, V. V.: Statistical Methods in Structural Mechanics. Holden-Day, San Francisco, 1969.MATHGoogle Scholar
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    Ditlevsen, O.: Uncertainty Modeling. McGraw-Hill, N.Y., 1981.MATHGoogle Scholar
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    Lin, Y. K.: Probabilistic Theory of Structural Dynamics. McGraw-Hill, N.Y., 1967.Google Scholar
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    Feller, W.: An Introduction to Probability Theory and its Applications. Wiley, N.Y., Vol. I, 1950, Vol. II, 1966.MATHGoogle Scholar
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    Larson, H. J. & B. O. Shubert: Probabilistic Models in Engineering Sciences. T. Wiley & Sons, N.Y., Vol. I & I I, 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1982

Authors and Affiliations

  • Palle Thoft-Christensen
    • 1
  • Michael J. Baker
    • 2
  1. 1.Institute of Building Technology and Structural EngineeringAalborg University CentreAalborgDenmark
  2. 2.Department of Civil EngineeringImperial College of Science and TechnologyLondonEngland

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