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On Chebyshev’s Theorem and Bernoulli’s Law of Large Numbers

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Moscow University Mathematics Bulletin Aims and scope

Abstract

The law of large numbers for the case of tossing the fair coin is proven. The proof is based on the method that Chebyshev used to prove his inequality and does not require concepts such as independence, mathematical expectation, and variance. Only the concepts of equiprobability of events, the formula of classical probability, the simplest concepts of combinatorics, and Newton’s binomial formula are assumed to be known.

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REFERENCES

  1. J. Bernoulli, Ars Conjectandi (Impensis Thurnisiorum, Fratrum, Basileae, 1713).

  2. O. P. Vinogradov, On Probability Theory for School Students, Part 1: Handbook (Spets. Uchebno-Nauch. Tsentr, Mosk. Gos. Univ., Moscow, 2015).

  3. O. P. Vinogradov, ‘‘On large numbers law for school students,’’ Math. Ed., No. 2, 2–6 (2019).

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Authors and Affiliations

  1. Chair of Probability Theory, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    O. P. Vinogradov

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  1. O. P. Vinogradov
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Correspondence to O. P. Vinogradov.

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Translated by I. Obrezanova

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Vinogradov, O.P. On Chebyshev’s Theorem and Bernoulli’s Law of Large Numbers. Moscow Univ. Math. Bull. 76, 135–138 (2021). https://doi.org/10.3103/S0027132221030086

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  • DOI: https://doi.org/10.3103/S0027132221030086

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