1, conditional probability: p (b | a) = p (ab)/p (a);

2. Bayesian formula: p (bi | a) = p (a | bi) p (bi)/∑ NJ =1p (a | bj) p (bj);

3. Total probability formula: p (a) = p (a | b1) p (b1)+p (a | b2) p (b2)+...+p (a | bn) p (bn);

4. multiplication theorem: P(AB)=P(B|A)P(A)

The contents of probability theory and mathematical statistics include elementary probability calculation, random variables and their distribution, numerical characteristics, multidimensional random vectors, limit theorems, basic concepts of statistics, point estimation and interval estimation, hypothesis testing, regression correlation analysis and variance analysis. Some materials that are important in theory and application, but generally considered beyond the scope of this course, are selected for teachers and scholars to choose from.

"Probability Theory and Mathematical Statistics" focuses on the explanation of basic concepts, and at the same time strives to have a rigorous discussion within the set mathematical level. More than 100 exercises are selected in the book, with tips and answers at the end. Probability Theory and Mathematical Statistics can be used as a teaching material of probability statistics for non-mathematics majors of science and engineering in colleges and universities, and can also be used by readers who have considerable mathematical preparation (elementary calculus and a little matrix knowledge) for self-study.