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The Essence of the Law of Large Numbers

In: Algorithms, Fractals, and Dynamics

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  • Michael Keane

Abstract

The law of large numbers, not really a law but a mathematical theorem, is at the same time a justification for application of statistics and an essential tool for the mathematical theory of probability. As such, it must be taught to many students. The traditional method for this, using independent and identically distributed random variables, was developed by Kolmogorov in the 1930’s, and explains well what happens, and much more, at this level of generality. However, it has recently come to light that the reason for the validity of this theorem in its general setting, that of stationarity, is much simpler than was first thought. In this short article, I shall try to explain to the general audience towards whom this collection is directed, the essence of the law of large numbers. A complete treatment should certainly include many references and interesting historical comments, and I apologize for their absence here

Suggested Citation

  • Michael Keane, 1995. "The Essence of the Law of Large Numbers," Springer Books, in: Y. Takahashi (ed.), Algorithms, Fractals, and Dynamics, pages 125-129, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0321-3_11
    DOI: 10.1007/978-1-4613-0321-3_11
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