**1. Introduction**

**Probability Theory and Mathematical Statistics** mainly include the basic concepts of probability theory, random variables and their probability distribution, digital feature, large number law and the central limit theorem, statistics and probability distribution, parameter estimation and hypothesis test, regression analysis, variance analysis, Markov chain and other content.

Theory and method of probability theory and mathematical statistics have been widely used in industry, agriculture, military and science and technology, such as prediction and filtering is applied in space technology and automatic control, time series analysis application in oil exploration and economic management, Markov point process with statistical analysis was applied to earthquake prediction, etc., at the same time it to the basic disciplines, engineering disciplines infiltration, and other subjects combined development become marginal subject, which is a new trend in the development of probability theory and mathematical statistics.

**2. Practical Applications**

1) Meteorology, hydrology, earthquake prediction, population control and prediction are closely related to the probability theory;

2) Sampling and acceptance of products, the newly developed drugs whether can be used in clinical applications are required to use the hypothesis test;

3) Find the best production plan to carry out experimental design and data processing;

4) The design of the electronic system, the development and the launch of the rocket cannot be separated from the reliability estimation;

5) Dealing with communication problems need to study information theory;

6) The time series analysis method is very useful to investigate the variation law of sunspot;

7) The study of the time variant rate of chemical reaction needs the Markov process to describe;

8) Random model of birth and death is put forward when studying the growth of the population in biology, and the epidemic of infectious diseases should be used in multi variable nonlinear birth and death process;

9) Many services, such as telephone communication, ship loading and unloading, machine maintenance, patient waiting, inventory control, can use probability model to describe, the knowledge involved is the queuing theory.