Probability theory and mathematical statistics, statistics and applied statistics all study random variables and their probability distribution, numerical characteristics, law of large numbers and central limit theorem, statistics and its probability distribution, parameter estimation and hypothesis testing, regression analysis, variance analysis, Markov chain and so on.

2. Differences:

(1) Probability theory and mathematical statistics belong to a branch of mathematics and pay more attention to theoretical research. Their conclusions are widely used in the study of random phenomena in various fields.

The theories and methods of probability theory and mathematical statistics have been widely used in industry, agriculture, military and science and technology, such as prediction and filtering in space technology and automatic control, time series analysis in oil exploration and economic management, statistical analysis of Markov process and point process in earthquake prediction, etc.

(2) Social statistics describe variables and mathematical statistics describe random variables.

Variable and random variable are two different and related mathematical concepts, which can be transformed into each other under certain conditions. Social statistics is based on variables, while mathematical statistics is based on random variables. What is the difference between probability theory and mathematical statistics, statistics and applied statistics?

3. Statistics pays more attention to application, and many conclusions come from probability theory and mathematical statistics. Mathematical statistics pays more attention to the derivation of formulas, while statistical principles only transform the formulas of mathematical statistics into easier-to-use forms.

Extended data:

1. Probability theory and mathematical statistics are a unique and active branch of mathematics. On the one hand, it has a unique research topic, its own unique concepts and methods, rich content and profound results; On the other hand, it is closely related to other disciplines and is an important part of modern mathematics.

Due to its rapid development and wide application in recent years, it has developed into an independent first-class discipline.

At the same time, he infiltrated into basic disciplines and engineering disciplines, and combined with other disciplines to develop into a marginal discipline, which is a new trend in the development of probability theory and mathematical statistics.

2. Statistics is a comprehensive science that infers the essence of the tested object and even predicts the future of the object by searching, sorting, analyzing and describing the data.

Statistics uses a lot of professional knowledge in mathematics and other disciplines, and its application covers almost all fields of social science and natural science.

3. Introduce the basic knowledge and skills of applied statistics by using statistical system, and integrate them into the practical application of spreadsheets, and introduce applied statistical methods such as parameter estimation and hypothesis testing.

Baidu Encyclopedia-Probability Theory and Mathematical Statistics

Baidu Encyclopedia-Statistics

Baidu Encyclopedia-Applied Statistics