# Fundamentals of Probability Theory

Chapter

## Abstract

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.

## Keywords

Random Vector Sample Space Central Moment Probability Mass Function Discrete Random Variable
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## Bibliography

- [2.1]Ang, A. H-S. & W. H. Tang:
*Probability Concepts in Engineering Planning and Design*. Vol. 1, Wiley, N.Y., 1975.Google Scholar - [2.2]Benjamin, J. R. & C. A. Cornell:
*Probability, Statistics and Decision for Civil Engineers*. McGraw-Hill, N.Y., 1970.Google Scholar - [2.3]Bolotin, V. V.:
*Statistical Methods in Structural Mechanics*. Holden-Day, San Francisco, 1969.MATHGoogle Scholar - [2.4]Ditlevsen, O.:
*Uncertainty Modeling*. McGraw-Hill, N.Y., 1981.MATHGoogle Scholar - [2.5]Lin, Y. K.:
*Probabilistic Theory of Structural Dynamics*. McGraw-Hill, N.Y., 1967.Google Scholar - [2.6]Feller, W.:
*An Introduction to Probability Theory and its Applications*. Wiley, N.Y., Vol. I, 1950, Vol. II, 1966.MATHGoogle Scholar - [2.7]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