2. Random variables and their probability distribution

3. Two-dimensional random variables and their probability distribution

4. Digital characteristics of random variables

5. Law of Large Numbers and Central Limit Theorem

6. Basic concepts of mathematical statistics

7. Parameter estimation

8. Hypothesis test

The focus is on the "basic contents and important conclusions" of each part above (rather than a general understanding); Second, the analysis method of learning topics; Third, complete a certain amount of exercises.

According to everyone's different understanding of the basic concepts, review in a way that ensures the key points and gives consideration to the general. In order to cooperate with candidates' review, we divide the eight assessment points into key assessment points, sub-key assessment points and general assessment points according to the examination situation over the years.

Part I: Random Events and Probability

(1) sample space and random events

(2) Definition and properties of probability (including classical probability, geometric probability and addition formula)

(3) the multiplication formula of conditional probability and probability

(4) the relationship and operation between events (including the independence of events)

(5) Total probability formula and Bayesian formula

(6) Bernoulli probability type

Part II: Random variables and their probability distribution.

The concept and classification of (1) random variables

(2) The probability distribution of discrete random variables and its properties.

(3) Probability density of continuous random variables and its properties.

(4) Distribution function of random variables and its properties.

(5) joint distribution

(6) Distribution of random variable function

Part III: Two-dimensional random variables and their probability distribution.

The Concept and Classification of (1) Multidimensional Random Variable

(2) Joint probability distribution of two-dimensional discrete random variables and its properties.

(3) The joint probability density of two-dimensional continuous random variables and its properties.

(4) Joint distribution function of two-dimensional random variables and its properties.

(5) Edge distribution and conditional distribution of two-dimensional random variables

(6) Independence of random variables

(7) Distribution of Simple Functions of Two Random Variables

Part IV: Numerical characteristics of random variables.

The Concept and Properties of Numerical Expectation of (1) Random Variables

(2) The concept and properties of variance of random variables.

(3) numerical expectation and variance of normal distribution

(4) Moment, covariance and correlation coefficient of random variables.

Part V: Law of Large Numbers and Central Limit Theorem.

(1) Chebyshev inequality

(2) Law of Large Numbers

(3) Central limit theorem

Part VI: Basic concepts of mathematical statistics.

(1) population and sample

(2) Sample function and statistics

(3) sample distribution function and sample moment

Part VII: Parameter estimation.

(1) point estimation

(2) the goodness of the estimator

(3) Interval estimation

Part VIII: Hypothesis test

Basic concepts of (1) hypothesis testing

(2) Hypothetical test of the mean and variance of a single normal population.

(3) Hypothetical test of mean and variance of double normal population.

In recent years, the order of the key contents of the first grade math exam is: ① two-dimensional random variables and their probability distribution; ② Numerical characteristics of random variables; ③ Random events and probability; ④ Mathematical statistics.

In recent years, the order of the key contents of the third mathematics examination is: ① the numerical characteristics of random variables; ② Two-dimensional random variables and their probability distribution; ③ Random events and probability; ④ Mathematical statistics.

In recent years, the order of the key contents of the four tests of mathematics is: ① the numerical characteristics of random variables; ② Two-dimensional random variables and their probability distribution; ③ Random events and probability; ④ Law of large numbers and central limit theorem.