The origin of mathematical statistics, the basic concepts of mathematical statistics

The relationship between origin and physical statistics and probability theory can be compared with the relationship between geodesy and geometry. Geometry arises from the measurement of the land, which is well known. Probability theory is also a gradual result of the observation of a large number of marrow machine phenomena, the collection of a large amount of data, and the inductive analysis.

Therefore, in a sense, the establishment of probability theory is closely related to elementary statistics.

In Western countries, statistics began in 3050 B.C., when Egypt built pyramids and conducted a census and statistics of the entire population in order to collect construction costs. By the time of Aristotle, statistics began to evolve towards rationality. At this time, the application of statistics in health, insurance, domestic and foreign affairs, military and administrative management and other aspects were all detailed and detailed.

The word statistics has evolved from the Italian word statisti (meaning state, politics).

By the 15th century, Italy had entered the Renaissance. Some random games were popular, and some gamblers spent their days meditating and doing a lot of experiments and statistical work in order to win, and found some phenomena that could not be explained, so they consulted the famous mathematician and astronomer Girier (Galico 1564-1642). Gillier, having studied the questions posed by the gamblers, lost some of the brief but valuable theorems of probability theory.

These theorems laid the foundation for the leather exhibition of the makeup tank statistics.

In the 16th and 7th centuries, the methods of entertainment and gambling became more and more complex, and as a result, some people raised new questions that needed to be explained by experts. For example, a famous gambler named Me're (Me're') in France at that time once asked the philosopher and mathematician Bascas (b Fascal 1623-1662) the following question: Is it true that there is a chance of at least one 6 in four times when one is rolled than at least a pair of sixes in four times when two bones are rolled?

This question intrigued Bascar and his friend, another mathematician, Fermat (1601-1665). After several correspondences and careful research, the two proved that Mel's conjecture was correct.

Later, Bascar generalized the problem proposed by Meyer to general random phenomena, obtained generalized solutions, and wrote monographs on the primitive forms and combinatorial analysis of modern probability theory.

The basic concept of early jujube in mathematical statistics

Population, Individual, Simple Random Sample, Statistic, Empirical Distribution Function, Sample Mean, Sample Variance and Sample Moment, Distribution, T-Distribution, F-Distribution, Quantile Distribution, Common Sampling Distribution for Normal Population.

1.Understand the concepts of population, simple random sample, statistic, sample mean, sample variance, and sample moment, where sample variance is defined as.

2.understand the typical patterns that produce variables, t-variables, and f-variables; To understand the upper quantile of the standard normal distribution, distribution, t-distribution and f-distribution, the corresponding numerical table will be checked.

3.Master the sampling distribution of sample mean, sample variance, and sample moment of a normal population.

4.Understand the concept and properties of empirical distribution functions.

See Typical Question Types

1.Calculation of sample capacity of potato;

2.Solving or determining quantiles;

4.solving or determining or proving the distribution function of a population or statistic;

5.Find the numerical characteristics of a population or statistic.

The above is the content of the "2020 Postgraduate Entrance Examination Mathematical Probability Exam Pre-exam Missing Points: Basic Concepts of Mathematical Statistics" compiled by the Zhonggong Postgraduate Entrance Examination for candidates, I hope it will be helpful to everyone, and more mathematical probability theory review knowledge is all in the Mathematical Probability Theory and Mathematical Statistics Channel of the Zhonggong Postgraduate Entrance Examination!

Mathematical statistics is the mathematical foundation of statistics, which studies statistics from a mathematical perspective and provides theoretical support for various applied statistics. It is the study of how to effectively collect, organize, and analyze randomized data to make inferences or recommendations about the problems examined, up to the point where they provide a basis and recommendations for making decisions and actions.

Britain is the birthplace and research center of mathematical statistics, but from the Second World War, the United States also developed rapidly. In recent decades, the widespread application of mathematical statistics has been very noticeable. In the social sciences, electors have contributed to the evaluation of opinion surveys, public opinion polls, economic value evaluation, product sales, and the detection of criminal cases.

In the fields of natural science, military science, industrial and agricultural production, medical and health care, all categories are separated from mathematical statistics.

Mathematical statistics is a branch of mathematics that is a discipline that collects and analyzes data with random influences in an efficient way.

The Encyclopædia Britannica mentions mathematical statistics as "the science and art of collecting and analyzing data." The dual nature of mathematical statistics. One is scientific, mathematical statistics is not a complete art, and there is a lot of rigorous mathematical reasoning, so sometimes we think of it as a branch of mathematics.

But we want to emphasize its artistry, that is to say, mathematical statistics is not pure deductive reasoning, which is the essential difference between it and mathematics, and it also tells us that in the process of learning mathematical statistics, we should not use a dogmatic attitude, thinking that it is wrong to memorize some formulas and apply them. When applying mathematical statistical methods to solve practical problems.

It is necessary to pay attention to both scientific and artistic aspects, and to use different mathematical statistical methods according to actual data and local conditions, and sometimes even inspiration. The data studied by Mathematical Statistics is different from the data we perceive, and it studies data with randomness.

Career Prospects in Mathematical Statistics:

As the demand for data analysis and processing increases, more and more companies need to hire people who specialize in mathematical statistics. Within this field, the salaries of the jobs are also quite good, and the demand for this professional field is constantly growing, so the prospects for majoring in mathematical statistics are very good.

With the rapid development of other related disciplines such as artificial intelligence and machine learning, the mathematical statistics major is constantly collaborating and integrating with these disciplines. With the increase in the technology and skills to be able to process and analyze data, the demand in this field is also increasing. Students majoring in Mathematical Statistics can learn from other disciplines and integrate them into data analysis and processing.

Graduates majoring in mathematical statistics have a variety of career options, such as data analysts, data science state guessers, marketing analysts, risk analysts, and more. These positions offer good salaries and opportunities for career advancement. It is also a very popular field of specialization, and many students want to work in this field.

1.From the perspective of their research purposes, both focus on revealing the quantitative regularity of the overall phenomenon, while statistics claims to be based on the qualitative understanding of the overall phenomenon.

2.From the point of view of its research approach, mathematical statistics.

It is hoped that through the study of the quantitative characteristics of the individuals in the population, the corresponding quantitative characteristics of the population can be understood. Statistics, on the other hand, hopes to achieve an understanding of the corresponding quantitative characteristics of the population through the study of the quantitative characteristics of all the individuals that make up the population (if possible or worthwhile), and at the same time, it hopes to achieve the understanding of the corresponding quantitative characteristics of the population through the study of the quantitative characteristics of some individuals that make up the population.

3.From the perspective of the means of his research, mathematical statistics mainly rely on the eigenvalues of small samples.

the mathematical principles of statistical distributions to infer the corresponding eigenvalues of the population; Statistics, or inferential statistics, mainly relies on the mathematical principle of statistical distribution of eigenvalues of large samples to infer the corresponding eigenvalues of the population.

4.From the perspective of the main scope of its research, the mathematical cavity lead meter focuses on the quantitative analysis of sample data; Statistics not only attaches importance to the quantitative analysis of sample data, but also attaches importance to the quantitative analysis of all the overall data obtained, and at the same time, attaches importance to the research of data collection methods and data collation methods.

5.In terms of its mathematical mechanism of using sample data to infer the population, probability theory.

is their common foundation. In particular, the mathematical basis of the large number of observation methods, which is one of the basic methods of statistics, is the law of large numbers in probability theory.

In statistics, the mathematical basis for inferring the characteristics of a population with a large sample is the central limit theorem in probability theory.

Both the law of large numbers and the central limit theorem are also the foundation of mathematical statistics.

6.Although mathematical statistics emphasizes applicability, it is still a mathematical discipline in itself, focusing on the study of the mathematical basis of applied methods. Statistics focuses more on the research and application of quantitative analysis methods to solve practical problems such as society and economy, while the scientific study of the mathematical basis of the method itself is studied by the corresponding theoretical statistics.

From the above characteristics and comparisons between mathematical statistics and statistics, it can be clearly seen that with the development of modern statistics and the trend of playing an increasingly important role in social, political and economic life, the concept and methods of mathematical statistics research problems have had an important revolutionary impact on the development of statistics

Adolf Kettler.

Adolphe Quetelet (1796-1874), Belgian statistician, mathematician, astronomer, physicist, father of international statistical conferences, father of modern statistics, and founder of the school of mathematical statistics.

He applied probability theory to the study of economic and social phenomena, so that the statistical method for studying social and economic phenomena took a big step forward on the road of accuracy on the basis of "political arithmetic". In 1867, someone named this nascent science, which was both mathematics and statistics, mathematical statistics.

Subsequently, mathematical statistics absorbed the beneficial results of biological research, and the British geneticist and statistician Galton, the British mathematician and philosopher Pearson, the British statistician Gosset, and the American statistician Fisher proposed and developed the theories of regression and correlation, hypothesis testing, x-squared distribution and t-distribution, and mathematical statistics gradually developed into a complete discipline.

(1) The founding period of statistics.

1. The National School.

The main exponents were Herman Conling and Achenwald.

2. The school of political arithmetic.

The founder was William Petty (1623-1687) and the representative figure was John Grant (1620-1674).

2) The period of development of statistics.

1. School of Mathematical Statistics.

The founder was Adolf Kettler (1796-1874) of Belgium.2

Founder Kness (1821-1889).

Mathematical statistics was developed along with the development of probability theory. By the middle of the 19th century, there had been a number of important works, such as Gauss and Legendre's study of error analysis and least squares in observational data. By the end of the 19th century, the passage included K

Through the efforts of a number of scholars, including Pearson, the discipline has begun to take shape. But the development of mathematical statistics as a full-fledged discipline was in the first half of the 20th century, thanks in large part to KThe work of scholars such as Pearson, Fisher, etc.

Fisher's contributions, in particular, were decisive in the establishment of this discipline. 1946 hKramer's Mathematical Methods in Statistics is the first rigorous and systematic work on mathematical statistics, which can be regarded as a sign that mathematical statistics has entered a mature stage.

The development of mathematical statistics can be roughly divided into three periods. The second group of sub-disciplines is a large number of sub-disciplines, all of which are tasked with discussing the principles and methods of statistical inference. The formation of the branches is based on:

Specific forms of statistical inference, such as parameter estimation and hypothesis testing.

Specific statistical perspectives, such as Bayesian statistics and statistical decision theory.

Specific theoretical models or sample structures, such as nonparametric statistics, multivariate statistical analysis, regression analysis, correlation analysis, sequential analysis, time series analysis, and stochastic process statistics. The third category is some sub-disciplines developed for special application problems, such as product sampling inspection, reliability statistics, statistical quality management, etc.