A Guide Book to Mathematics pp 743-753 | Cite as

# Foundations of the Theory of Probability and the Theory of Errors

Chapter

## Abstract

**Random event**. If a certain event, in given circumstances, may occur or may not occur, then it is called a *random event*. The *probability* of a random event is a quantitative estimation of the probability of its occurrence.

## Keywords

Random Event Random Error Mathematical Expectation White Ball Conditional Equation## Preview

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## Notes

- (1).If the value of
*p*is near to 1, Poisson’s formula can also be applied by considering the event “non-*A*” (the complementary event); its probability is*q*= 1 −*p*, hence is small.Google Scholar - (2).Sometimes the function \(\textup{Erf}\;x=\frac{2}{\sqrt{\pi} }\int\limits_{0}^{x}e^{-t^2}dt=\Phi (x\sqrt{2})\). is called the
*probability integral*.Google Scholar - (1).The number ϱ is determined by the equation \(\mathit{\Phi} (\varrho \sqrt{2})=\frac{1}{2}\).Google Scholar
- (1).In the calculus of probability and mathematical statistics the following notation due to Gauss is in use: [εε] for \(\sum \varepsilon _{i}^{2}\) and [
*ab*] for ∑*a*_{i}*b*_{i}and so on.Google Scholar - (1).For Gauss’ notation see footnote on p. 750.Google Scholar

## Copyright information

© Verlag Harri Deutsch, Zürich 1973