The first limit theorem in the history of probability theory belongs to Bernoulli, and later people call it "the law of large numbers". In probability theory, the law that the arithmetic mean of random variable sequence converges to the arithmetic mean of each mathematical expectation of random variable is discussed.

In the repeated occurrence of a large number of random events, there is often an almost inevitable law, that is, the law of large numbers. In layman's terms, this theorem is that when the experiment is repeated many times, the frequency of random events approaches its probability. There is a certain inevitability in accident.

The law of large numbers is divided into weak law of large numbers and strong law of large numbers.

We know that the law of large numbers studies the statistical regularity of random phenomena. When we repeat the same experiment a lot, the final experimental result may be stable near a certain value. Just like tossing a coin, when we keep throwing it thousands or even tens of thousands of times, we will find that the number of heads or tails will be close to half. Besides tossing coins, there are many such examples in reality, such as rolling dice. The most famous experiment is Buffon's throwing needle experiment. These experiments all convey the same message to us, that is, the final result of repeated experiments will be relatively stable. So what is stability? How to express it in mathematical language? Will there be any rules in this? Is it inevitable or accidental?

The law of large numbers is a law that describes the probability properties of multiple experiments. However, it should be noted that the law of large numbers is not an empirical law, but a theorem that has been strictly proved under some additional conditions. It is a natural law, so it is usually not called a theorem, but a "law" of large numbers. The theorem of large numbers we talk about is usually proved by mathematicians and named after them, such as Bernoulli's theorem of large numbers.

And the law of large numbers is also widely used in the insurance industry. The law of large numbers is also called law of large numbers. In the long-term practice, it is found that the almost inevitable law, the law of large numbers, often appears in a large number of repetitions of random phenomena. The significance of this rule is that the more risk units there are, the closer the actual loss results are to the possible expected loss results obtained from infinite units. Based on this, the insurer can predict the danger more accurately, determine the insurance rate reasonably, and balance the insurance premium collected during the insurance period with the loss compensation and other expenses. The law of large numbers is the mathematical basis on which modern insurance industry depends. Insurance companies analyze the relative stability of the loss of the insured subject matter by using the law that the uncertainty will disappear in a large number in individual cases. According to the law of large numbers, the number of each type of subject matter insured by insurance companies must be large enough, otherwise, without a certain quantitative basis, the required law of quantity cannot be produced. However, any insurance company has its limitations, that is, the units with the same risk nature are limited, which requires reinsurance to expand the risk units and spread the risks.