I. Random events and probabilities

Examination content

The relationship between random events and events in sample space and the basic properties of complete operation concept probability Basic formula of classical probability of event group probability Geometric probability Conditional independent repetition test of probability events.

Second, random variables and their distribution

Examination content

Concept and Properties of Random Variables Distribution Function Probability Distribution of Discrete Random Variables Probability Density of Continuous Random Variables Distribution of Common Random Variables Distribution of Random Variable Functions

Examination requirements

1, understand the concept and properties of distribution function, and calculate the probability of events related to random variables.

2. Understand the concept and probability distribution of discrete random variables, and master 0- 1 distribution, binomial distribution, geometric distribution, hypergeometric distribution, Poisson distribution and their applications.

3. Grasp the conclusion and application conditions of Poisson theorem, and use Poisson distribution to approximately represent binomial distribution.

4. Understand the concept of continuous random variables and their probability density, and master uniform distribution, normal distribution, exponential distribution and their applications.

5. Find the distribution of random variable functions.

Thirdly, the distribution of multidimensional random variables.

Examination content

Probability distribution, edge distribution and conditional distribution of multidimensional random variables and their distribution functions Probability density, marginal probability density and conditional density of two-dimensional continuous random variables The distribution of two or more simple functions of two-dimensional independent and irrelevant random variables.

Examination requirements

1. Understand the concept and basic properties of the distribution function of multidimensional random variables.

2. Understand the probability distribution of two-dimensional discrete random variables and the probability density of two-dimensional continuous random variables, and master the edge distribution and conditional distribution of two-dimensional random variables.

3. Understand the concepts of independence and irrelevance of random variables, master the conditions of mutual independence of random variables, and understand the relationship between irrelevance and independence of random variables.

4. Grasp the two-dimensional uniform distribution and two-dimensional normal distribution, and understand the probability meaning of parameters.

5. The distribution of its function will be found according to the joint distribution of two random variables, and the distribution of its simple function will be found according to the joint distribution of several independent random variables.

Fourth, the numerical characteristics of random variables

Examination content

Mathematical expectation (mean), variance and standard deviation of random variables and their properties; Mathematical expectation of random variable function; Moment, covariance, correlation coefficient and their properties of Chebyshev inequality.

Examination requirements

1. Understand the concept of numerical characteristics of random variables (mathematical expectation, variance, standard deviation, moment, covariance, correlation coefficient), and use the basic properties of numerical characteristics to master the numerical characteristics of common distributions.

2. Know the mathematical expectation of random variable function.

3. Understanding Chebyshev Inequality

Law of Large Numbers and Central Limit Theorem

Examination content

Chebyshev's Law of Large Numbers Bernoulli's Law of Large Numbers Qinqin's Law of Large Numbers Democratic Laplace's Theorem Liverindberg's Theorem

Examination requirements

1, understand Chebyshev's law of large numbers, Bernoulli's law of large numbers and Sinchin's law of large numbers (the law of large numbers of independent and identically distributed random variable sequences).

2. Understand de moivre-Laplacian central limit theorem (binomial distribution takes normal distribution as the limit distribution) and Levi-Lindbergh central limit theorem (central limit theorem of independent identically distributed random variable sequence), and use relevant theorems to approximately calculate the probability of random events.

Basic concepts of mathematical statistics of intransitive verbs

Examination content

Simple Random Sample Statistical Empirical Distribution Function Sample Mean Sample Variance and Sample Moment Distribution Quantile Normal General Sampling Distribution

Examination requirements

1. Understand the concepts of population, simple random sample, statistics, sample mean, sample variance and sample moment.

2. Understand variables, variables and typical patterns of variables; Understand the standard normal distribution, distribution, distribution and upper quantile of distribution, and look up the corresponding numerical table.

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

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

Seven. parameter estimation

Examination content

Concept estimator and moment estimator of point estimation maximum likelihood estimation method

Examination requirements

1. Understand the concepts of point estimation, estimator and parameter estimation.

2. Master moment estimation methods (first-order moment and second-order moment) and maximum likelihood estimation methods.