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Foundations of the Theory of Probability and the Theory of Errors

  • I. N. Bronshtein
  • K. A. Semendyayev

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. (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. (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
  3. (1).
    The number ϱ is determined by the equation \(\mathit{\Phi} (\varrho \sqrt{2})=\frac{1}{2}\).Google Scholar
  4. (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 ∑aibi and so on.Google Scholar
  5. (1).
    For Gauss’ notation see footnote on p. 750.Google Scholar

Copyright information

© Verlag Harri Deutsch, Zürich 1973

Authors and Affiliations

  • I. N. Bronshtein
  • K. A. Semendyayev

There are no affiliations available

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