In mathematics and statistics, the Law of Large Numbers (also known as the Law of Large Numbers and the Law of Large Numbers) is a law that describes the results of an experiment repeated a considerable number of times. According to this law, the larger the sample size, the higher the probability that its arithmetic mean will be close to the expected value. The law of large numbers is important because it "accounts" for the long-term stability of the mean of some random events.

We know that the law of large numbers is a class of theorems about the statistical regularity of random phenomena, and that when we repeat an identical experiment a large number of times, the final result is likely to stabilize around a certain value. Like tossing a coin, when we keep tossing it thousands of times, or even tens of thousands of times, we will find that the number of times heads or tails go up will be close to half.

Meaning of the Law of Strong Numbers

This set of problems is actually what the Law of Large Numbers is meant to study. Very early on, people actually discovered this regular phenomenon, and a number of mathematicians studied it, including Bernoulli (who was later credited with being the first to study it in his honor, but in fact it had been studied by mathematicians long before him).

Bernoulli formulated a limit theorem in 1713, which at the time did not have a name, and which was later called Bernoulli's law of large numbers. Thus the first limit theorem on the law of large numbers in the history of probability theory belongs to Bernoulli, and it is a fundamental law of probability theory and mathematical statistics, which belongs to the category of weak laws of large numbers.

When a certain experiment is repeated in large numbers, the final frequency is infinitely close to the event probability. And Bernoulli succeeded in expressing this phenomenon in real life through the language of mathematics, giving it an exact mathematical meaning. He gave people a new awareness and a deeper understanding of this type of problem, and pointed the way and led the way for later people to study the problem of the law of large numbers.

It laid the foundation for the development of the law of large numbers. In addition to Bernoulli, many other mathematicians made important contributions to the development of the law of large numbers, and some even spent their entire lives working on it, such as Dumervil Laplace, Liapunov, Lindbergh, Ferrer, Chebyshev, and Sinchin. The role of all these people in the advancement of the law of large numbers and even probability theory is immeasurable.