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

被引：2

作者：

Vinogradov, O. P. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Mech & Math, Chair Probabil Theory, Moscow, Russia

来源：

MOSCOW UNIVERSITY MATHEMATICS BULLETIN | 2021年 / 76卷 / 03期

关键词：

Bernoulli's law of large numbers; Chebyshev's inequality; Chebyshev's theorem;

D O I：

10.3103/S0027132221030086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：135 / 138

页数：4

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