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

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