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Laws of Large Numbers

  • Valentin V. Petrov
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 82)

Abstract

We shall consider a sequence of random variables {X n ; n = 1, 2, ...}. By definition, this sequence converges in probability to the random variable X if P(│X n X│ ≧ ε) → 0 for every fixed ε > 0. In this case we use the notation \({X_n}\;\xrightarrow{P}\;X\).

Keywords

Independent Random Variable Common Distribution Finite Variance Arbitrary Positive Constant Common Distribution Function 
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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Copyright information

© Springer-Verlag Berlin · Heidelberg 1975

Authors and Affiliations

  • Valentin V. Petrov
    • 1
  1. 1.Leningard UniversityLeningradUSSR

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