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.
Examination requirements
1. Understand the concept of sample space (basic event space), understand the concept of random events, and master the relationship and operation of events.
2. Understand the concepts of probability and conditional probability, master the basic properties of probability, calculate classical probability and geometric probability, and master the addition formula, subtraction formula, multiplication formula, total probability formula and Bayesian formula of probability.
3. Understand the concept of event independence and master the probability calculation with event independence; Understand the concept of independent repeated test and master the calculation method of related event probability.
Second, the numerical characteristics of random variables
Examination content
Mathematical expectation (mean), variance, standard deviation and their properties of random variables Mathematical expectation moment, covariance, correlation coefficient and their properties of random variable functions
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.
Third, the law of large numbers and the central limit theorem
Examination content
Chebyshev Inequality Chebyshev's Law of Large Numbers Bernoulli's Law of Large Numbers Democracy-Laplace Theorem Levi-Lindbergh Theorem
Examination requirements
1. Understanding Chebyshev Inequality.
2. 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).
3. Understand de moivre-Laplace Theorem (binomial distribution takes normal distribution as the limit distribution) and Levi-Lindbergh Theorem (central limit theorem of independent identically distributed random variable sequence).
Fourthly, parameter estimation.
Examination content
Concept estimation of point estimation and estimated value Method of moment estimation Maximum likelihood estimation Method of estimation criterion Interval estimation Concept Interval estimation of mean and variance of a single normal population Interval estimation of mean difference and variance ratio of two normal populations.
Examination requirements
1. Understand the concepts of point estimation, estimator and parameter estimation.
2. Master moment estimation methods (first-order moment, second-order moment) and maximum likelihood estimation methods.
3. Understand the concepts of unbiased estimator, validity (minimum variance) and consistency (consistency), and verify unbiased estimator.
4. In order to understand the concept of interval estimation, we will find the confidence interval of the mean and variance of a single normal population, and the confidence interval of the mean difference and variance ratio of two normal populations.
Hypothesis test of verb (verb abbreviation)
Examination content
Two types of false hypothesis testing in significance testing Hypothesis testing of mean and variance of single and two normal populations.
Examination requirements
1. Understand the basic idea of significance test, master the basic steps of hypothesis test, and understand two possible errors in hypothesis test.
2. Master the hypothesis test of the mean and variance of single and two normal populations.
The above is the specific content of the postgraduate mathematical probability and statistics examination outline. I hope it will help everyone. I would like to remind you that in the final sprint stage, you'd better return to the outline, do targeted topics and conduct more test simulations. Let's do the examination paper order and time allocation of postgraduate mathematics. Come on!