Foundations of the Theory of Probability and the Theory of Errors

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


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.


Random Event Random Error Mathematical Expectation White Ball Conditional Equation 
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  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

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