The theoretical root is Hinchin's law of large numbers, and the samples are independent and identically distributed. When the data sample size is large, the average value of sample observation is within a small error range from the overall mathematical expectation.

Moment estimation method, also known as moment estimation method, estimates the corresponding parameters in the population by using sample moments. Firstly, the equation containing the global moment of the parameter of interest (that is, the expected value of the power of the random variable under consideration) is derived. Then take a sample and estimate the total torque of this sample. Then the sample moment is used to replace the (unknown) population moment to solve the parameters of interest. So as to obtain an estimate of these parameters.

A method of obtaining estimators by using sample moments as corresponding estimates of total moments. If there are k unknown parameters in the population, the corresponding total moments of the first k order can be estimated by using the sample moments of the first k order, and then the parameter estimators can be obtained by using the functional relationship between the unknown parameters and the total moments.

Extended data:

Precautions:

Distribution list is equivalent to listing each situation, then calculating the probability of each situation separately, and then tabulating.

The distribution table can be divided into two-point distribution (two cases), hypergeometric distribution, n independent repeated experiments (n possible cases) and so on. Different models solve problems in different ways, so we should pay attention to the distinction.

Expectation &; Variance: The calculation methods of expectation and variance are given. Expectation is the probability multiplied by the corresponding x value, and variance is the floating degree, which is related to expectation. Pay attention to two distribution tables A and B at the same time, although expectation and variance are independent variables.

Baidu Encyclopedia-Mathematical Statistics

Baidu Encyclopedia-Normal Distribution

Baidu encyclopedia-moment estimation

Baidu encyclopedia-maximum likelihood estimation

People's Daily Online-20/200914 Analysis on Probability Test Sites of Mathematics Zhenti for Postgraduate Entrance Examination