Is the law of large numbers inevitable? What is the popular understanding of the law of large number

No, all physical quantities in the world have imaginary space values. The law of large numbers says that space must be real, so it thinks that the mean is more essential than the variance, and if you go to any physics textbook, you don't talk about the mean, but about energy. A simple derivation will know that there is no uniform motion.

Vibration is the essence. The conservation of the mean pushes out the normal distribution, and the normal distribution is affected by its own 0 expected impact error and accumulates, that is, if a thing is a random variable but has a mean, then its energy will be infinite. Of course, energy cannot be infinite, so the conclusion must be that this thing is not a random variable.

That is, if a data is normally distributed, we should assume that there is some mechanism by which its conclusions can be unique. It should be the sum of a constant and a number with an energy of 0 at infinity. As long as it is randomly distributed, it cannot be normally distributed.

However, for all physical quantities, inaccuracy is the essence, that is to say, all physical quantities should be random variables, so that they cannot satisfy the normal distribution.

**What is it? Financial markets have existed for more than 100 years, so why have they never been normally distributed? Because financial markets are about trading with uncertainty. About the prospective transaction.

The law of large numbers states that the sample mean almost inevitably converges to the population mean. This law can be called the fundamental theorem of statistics. Chapter 0 of Middle School Physics tells us to repeat the measurement several times and then take the average.

The principle behind this is the law of large numbers. So it's familiar to everyone.

For problems, this is either challenging the mathematical proof of the law of large numbers, or doubting the looseness of its premises. Skepticism about mathematical proofs can be very deep, for example, all the way down to the incompleteness of Gödel's axiomatic system. Skepticism about the looseness of preconditions is more subjective.

The reasonable approach is to conform and exploit, not to exploit and abuse.

That is, when the sample size is infinite, the sample mean can be used instead of the overall expectation.

1. The Law of Large Numbers.

It is not an empirical law, but a theorem that has been rigorously proven on some additional conditions, and it is a law of nature.

Therefore, it is usually not called a theorem, but a "law" of large numbers.

2. The law of large numbers is generally speaking, that is, when the sample size is large, the sample mean and the true mean are fully close. This conclusion is consistent with the central limit theorem.

Together, it becomes modern probability theory.

Cornerstones of statistics, theoretical science, and social science.

The law of large numbers is the law of large numbers.

is the law that describes the results of a fairly many replicated experiments. According to this law, we know that the larger the sample size, the closer its average will be to the expected value.

The law of large numbers is important because it "guarantees" the long-term stability of the mean of some random events. It was found that in repeated trials, the frequency of events tended to a stable value as the number of trials increased; At the same time, it is also found that in the physical quantities.

The arithmetic mean of the measured values is also stable.

The above content refers to: Encyclopedia - The Law of Large Numbers.

Markov's law of large numbers is a weak law of large numbers, which is the general form of Chebyshev's law of large numbers.

Markov's law of large numbers can be used not only for independent random variables.

sequences, and can also be applied to dependent sequences of random variables under certain conditions, and Chebyshev's law of large numbers can be regarded as a special case of Markov's law of large numbers.

The Law of Large Numbers. The first limit theorem in the history of probability theory belonged to Bernoulli, which later generations called the "law of large numbers". The arithmetic mean of a sequence of random variables is discussed in probability theory.

Mathematical expectations to random variables.

The law of convergence of the arithmetic mean.

Central Limit Theorem

The central limit theorem refers to the asymptotic asymptotic distribution of the sequence and distribution of random variables in probability theory.

A class of theorems. This set of theorems is the theoretical basis of mathematical statistics and error analysis, and points out the condition that a large number of random variables approximately obey the normally distributed tract. It is the most important class of theorems in the chain grinding of probability theory, and has a wide range of practical application backgrounds.

In nature and production, some phenomena are affected by many random factors that are independent of each other, and if the effects of each factor are small, the total effects can be regarded as obeying a normal distribution.

In Mathematics and Statistics,The Law of Large Numbers(Also called.)The Law of Large Numbers. , the law of large numbers) is a law that describes the result of an experiment that is repeated quite a few times. According to this law, we know that the larger the number of samples, the more itArithmetic meanThe higher the probability of approaching the expected value. The law of large numbers is important because it "illustrates" the long-term stability of the mean of some random events.

As we know, the law of large numbers is a study of a class of theorems about the statistical regularity of random phenomena, and when we repeat a large number of the same experiment, the final experimental result may be stable around a certain value. Just like tossing a coin, when we keep tossing, thousands or even tens of thousands of times, we will find that the number of heads or tails will be close to half.

The meaning of the law of strong numbers

This series of problems is actually the problem to be studied by the law of large numbers. This regular phenomenon has been discovered for a long time, and many mathematicians have studied it, including Bernoulli.

Later, in order to commemorate him, people thought that he was the first person to study this problem, in fact, there were mathematicians who studied it before him.)

Bernoulli proposed a limit theorem in 1713, which at that time did not have a name, and later it was called Bernoulli's law of large numbers. Hence the theory of probability.

The first limit theorem about the law of large numbers in history belongs to Bernoulli, which is the fundamental law of probability theory and mathematical statistics, and belongs to the category of the law of weak large numbers.

When an experiment is repeated in large quantities, the final frequency is infinitely close to the event probability. Bernoulli, on the other hand, succeeded in expressing this phenomenon in real life through the language of mathematics, giving it a precise mathematical meaning. He gave people a new understanding and a deeper understanding of this kind of problem, and pointed out the direction and played a leading role in the later people's research on the law of large numbers.

It laid the foundation for the development of the law of large numbers. In addition to Bernoulli, there are many mathematicians who have made important contributions to the development of the law of large numbers, and some have even spent their whole lives in the work, such as Demo Kitchener-Laplace.

Lyapunov, Lindbergh.

Feller, Chebyshev.

Sinchin and so on. The role of these people in the law of large numbers and even the progress of probability theory is immeasurable.

The law of large numbers should be applied in life, such as the embodiment of population proportions.

The law of large numbers is also known as the "law of large numbers" or the "law of averages". In the repetition of a large number of random events, there are often almost inevitable laws, which are the laws of large numbers. Under the condition that the experiment is constant, the trial is repeated multiple times, and the frequency of random events approximates its probability.

The law of large numbers reflects a basic law of the world: in a large group containing many individuals, the individual differences due to accident are disorganized, irregular, and difficult to look at individual individuals. However, due to the effect of the law of large numbers, the whole group can present a certain stable form.

For example, if we observe the birth of babies in individual or small families, we find that there is no certain regularity in the birth of boys and girls, but through a large number of observations, it will be found that the proportion of male and female babies in the total number of babies will tend to be 50%.

The most common thing in life is the insurance industry that relies on the law of large numbers to make money.

For example, when you buy an electronic product online, you will often sell us an extended warranty.

For example, a 2,000 yuan washing machine, an extra 100 yuan can be extended for one year, if you master the law of large numbers, it is easy to think. The manufacturer's expected cost of this washing machine maintenance service must be less than 100 yuan, otherwise the manufacturer will lose money.

As we all know, insurance companies have very high profits, assuming that the compensation amount of a personal accident insurance is 1 million, and the probability of an accident is 1 in 1 million, then the expected loss is 1 yuan.

If you pay 10 yuan to buy it, the insurance company can make 10 times the profit, which is basically the same as opening a casino.

The Law of Large Numbers. The formula is g=log*vn.

Probability theory. The first limit theorem in history belonged to Bernoulli, which later generations called the "law of large numbers". The arithmetic mean of a sequence of random variables is discussed in probability theory.

Mathematical expectations to random variables.

The law of convergence of the arithmetic mean.

An overview of the law of large numbers.

The law of large numbers is defined when a random event occurs.

When it occurs a sufficient number of times, the frequency of random events tends to be closer to the expected probability. It can be simply understood that the larger the sample size, the closer the parity probability is to the expected value.

The conditions of the law of large numbers are as follows: 1. Independent repetition of events; 2. The number of repetitions is enough.

The counterpart to the "law of large numbers" is the "law of decimals", the content of the law of decimals: if the sample size is relatively small, then any kind of extreme cases can occur. However, when we judge the probability of an uncertain event occurring, we often violate the law of large numbers.

Bernoulli's Law of Large Numbers Formula:

Bernoulli's law of large numbers allows fn to be the second or number of events a in Bernoulli's experiment, and p is the probability of a occurrence in each experiment, then for any given real number >0, then it is true.

Basics. There is a sequence of random variables, and if it has properties like (1), then the random variable is said to obey the law of large numbers. (also translated as "Bey's Law of Large Numbers").

Bernoulli's law of large numbers lets fn be the number of times event a occurs in Bernoulli's experiment, and p is the probability that a will occur in each experiment, then for any given real number >0, there is true. That is, when n tends to infinity, the frequency of event a in the n-heavy Bernoulli event fn n is infinitely close to the probability p that event A occurs in an experiment.

What is the Law of Large Numbers? For example, we've all tossed a coin, and we all know that the probability of throwing heads and tails is the same, both are 50%, let's say we toss a coin 10 times, our expectation is 5 heads and 5 tails, but if you really go to the experiment, and each set tosses 10 times, and then record the number of heads up, you will find that exactly 5 heads are not as stable as we expected, the number of heads upIt fluctuates greatlySometimes it's 7 times, sometimes it's 6 times, sometimes it's 4 times.

But if you are full and have nothing to do, and each set throws 10,000 times, you will find that the number of heads up will stabilize at around 5,000 times, and the error book grind will not be exceeded

If you toss 100,000 times per set, you will find that the number of heads up will stabilize at around 50,000 times, and the error will not exceed that

The law of large numbers means that the more times you toss in each set, the closer the number of heads will be to 50%, just like in the figure below

InRandom eventsA large number of repetitions tend to appear almostCertainlyThis law is the law of large numbers. In layman's terms, this theorem is that the experiment is repeated many times under the condition that the experiment remains the sameThe frequency of a random event approximates its probability。There is a certain necessity in chance.

In the coin toss scenario, there is a scenario where the probability is often miscalculated, suppose you toss a coin 5 times in a row, all face up, then what is the probability that the 6th coin toss is still facing up?

The correct answer is 50%, because nature does not remember the results of the first 5 times. I remember a few years ago with Brother Egg in Macau Sands overnight gambling, we continued to bet big, but the result of shaking the dice or the child is continuous small, after 6 small in a row, we feel that the next one is a big probability is very large, and then... And then we lost all our cash ...

Then I also used Brother Dan's bank card... And then it also attracted usury...

The law of large numbers and the lesson of losing money tells us that the more you gamble, the more inevitable you will lose.