Based on the R language, the article designs two universal random simulation functions for the law of large numbers, LLN-mean and LLN-graph, used to calculate related variables and draw simulation graphs. At the same time, the law of large numbers is applied to children's education. At the same time, through correlation or correlation analysis, we can find the leading internal factors and highly correlated external factors of children's educational activities. This provides technical support for educational decision-making, educational management, and educational research. The study results found that the law of large numbers has a good test effect on the influencing factors of children's educational activities.

#### Keywords

- Statistical law
- law of large numbers
- axioms
- children's education

#### MSC 2010

- 03B48

Big data technology provides data and “evidence” support for education management and decision-making and provides a new research paradigm for education research. However, education research, education management, and education decision-making emphasize both “regularity” and “purposes.” Therefore, the application of big data technology for educational research and educational decision-making still has limitations. For this reason, big data technology cannot be mechanically applied to solve the problems faced by education [1]. We should rationally look at the “empirical science” of educational research and educational decision-making. At the same time, we must rationally realize the scientific nation of educational research and educational decision-making. Research on children's social attention is helpful to grasp the more serious and urgent problems faced by children. This is conducive to solving children's problems and strengthening precise services for the care and protection of children. “Probability theory and mathematical statistics is a mathematical subject that studies the statistical laws of random phenomena.” “Probability theory is to study a large number of random phenomena from a quantitative perspective and obtain the laws that these random phenomena obey.”

For this reason, we apply the law of large numbers to children's education [2]. At the same time, through correlation or correlation analysis, we can find the leading internal factors and highly correlated external factors of children's educational activities. This provides technical support for educational decision-making, educational management, and educational research.

In statistics, the law of large numbers is as follows:

If _{1}, _{2}, … _{n}_{1}, _{2}, … _{n}

Then we believe that the random variable sequence {_{n}

Bernoulli's theorem is one of the famous laws of large numbers. Let _{n}

This law of large numbers does not tell us why the probability of

At the same time, the textbook describes the law of statistics like this: When a certain condition group is realized, there are multiple possible results. People can’t predict what kind of result will appear beforehand, but the result is obtained when many repeated observations show a certain pattern. We call it the statistical regularity of random phenomena [4]. This description does not conform to scientific norms. Below we define statistical laws based on the definition of probability and hypothesis testing. In this way, statistical laws are scientifically standardized and can be tested in practice. To this end, first, discuss the interpretation of hypothesis testing.

Hypothesis testing in mathematical statistics includes two parts: parametric and non-parametric. Only some discussions on parameter testing are given below [5]. The available parameter inspection system can be described as follows:

Suppose that the distribution function

We divide the sample space X into two disjoint parts X and X − X_{0}. ∀

If X_{0} is the negation domain of negating hypothesis _{0} (also called rejection domain), two types of errors may be made in the choice of hypothesis testing. The first type of error: the observation value (_{1}, …, _{n}_{0} of (_{1}, …, _{n}_{0} is. At this time, we believe that it made a mistake of rejecting the truth [6]. The second type of error: when
_{1}, …, _{n}_{0} of (_{1}, …, _{n}

And the probability of making the second type of error is

It is generally believed that the basic idea is the so-called small probability event principle. Small probability events (or events with very low probability) are almost impossible to occur in an experiment or observation [7]. However, suppose you think carefully about the above logical process of determining the negative domain. In that case, you will find that it has nothing to do with the small probability event principle at all. In the significance test, its basic idea is to make the probability of making the second type of error as small as possible under the control of making the first type of error.

It is still questionable when we consider the empirical significance of the logic of determining the negative domain. Because when in fact _{0}, why do we need to consider the probability of making a mistake in _{0}? We cannot make two types of mistakes at the same time. The two types of errors are incompatible independent events. So the questions with practical empirical significance are as follows: What kind of negation domain is the most likely negation domain when _{0} is true? Is it the negation field that minimizes

This kind of inspection is used to check whether a batch of products is qualified, and the other is to check whether the production process technology system is in a normal state. Under the assumption that the population is normally distributed, these two tests must take _{0} as the central value of the acceptance interval, and the critical point of negation of _{0} is usually within the allowable error value. In the

Let's talk about the empirical significance of significance level _{0}, _{1}, …, _{n}_{0}|_{0}} = _{0} is true, the observation value of (_{1}, …, _{n}_{0} and the probability of _{0} being rejected is _{0} is true is 1 − _{0} is indeed true, it will generally not be negated when _{0}. From this we can also find that _{0} smaller when F is true. Once accepted, the probability of making mistakes is smaller, which makes the research results more credible. This obviously cannot be explained by the idea of the principle of small probability.

Suppose _{A}

(2) In the

“

There are two types of statistical laws in practice. For example, if

In the result of an experiment, if there are the number of (exactly) that relationship

When

Suppose that there are variables _{0}:

In the result of an experiment, if there is a statistically valid number _{A}

Such as “the English vocabulary in children's education is 6000”. There are many ways to measure vocabulary first, and the results of each will be slightly different. Secondly, even with the same method, the result of each measurement will be different in the case of random sampling, and the result of one time rarely is exactly 6000. So this proposition about vocabulary can only be the second type of statistical law.

Illustrate:

When _{A}

In the second statistical law, each trial is generally a

In the practice of science and production society, there are many statistical laws of the second type [12]. When the difference between the test result and

The law of large numbers in mathematical statistics is an abstract reflection of statistical laws [13]. The definition of the law of large numbers and Bernoulli's law of large numbers are explained below.

The definition of the law of large numbers refers to such a statistical law:

Assuming
_{n}_{n}

Axiom 1: If the random variable sequence {_{n}_{n}

There is a statistical law “
_{n}_{n}_{n}

An application of Axiom 1 is “mean estimation,” that is, there is the following inference: Suppose Ω is a statistical population, _{n}_{n}

This inference is the theoretical basis for using the sample mean to estimate the population mean, and the estimate's accuracy is not only related to

Construct the variable _{i}_{i}_{i}_{i}

This statistical law can be used as a theoretical basis for estimating the overall distribution with sample distribution [16]. For example, estimate the distribution ratio of each color ball in the bag. Similarly, the accuracy of this estimation is related to

In summary, it can be inferred that the law of large numbers reflects a limit statistical law. This limit can be regarded as a practical limit. As a statistical law, it can be tested directly by increasing the number of trials, or the following proposition (_{n}_{n}

We further analyzed the various statistical laws mentioned above and found that they can all be attributed to the “law of averages.” For each statistical law, an average variable can be designed. And this mean variable has a limit. The meaning of the second type of statistical law “

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