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Introduction to Probability Theory

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Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 202)

Abstract

We have already mentioned in the introduction that the axioms of mathematical probability1 are to be so chosen that they reflect empirical situations when given an appropriate interpretation. We have seen that a characterization of mass phenomena can be given in a certain sense by the empirical probabilities of the events occuring. It is thus desirable to choose the notion of mathematical probability in such a way that the theorems of the mathematical theory yield empirically verifiable facts if the mathematical probability is replaced by the empirical. We then speak briefly of the frequency interpretation of the mathematical theory. The simplest calculation rules of empirical probability are expressed by 1. and 2. (p. 23). These serve as model for the axioms of mathematical probability. In this chapter, we will discuss the most important facts of probability theory. However, we should point out at once that our program is not a complete construction of the theory. Since the main emphasis in this book is on the application of probability in mathematical statistics, many of the important theorems in this chapter will be given without proof.

Keywords

Characteristic Function Probability Theory Conditional Probability Pairwise Disjoint Independent Random Variable 
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References

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1974

Authors and Affiliations

  1. 1.University of ViennaAustria

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