Define mathematical expectation: 1) The sum of the products of all possible values xi of a discrete random variable and the corresponding probability Pi(=xi) is called the mathematical expectation of the discrete random variable [1] (let the series converge absolutely), and it is recorded as E(x). Mathematical expectation is one of the most basic mathematical characteristics. It reflects the average value of random variables. Also called expected value or average value. If a random variable only gets a limited number of values, it is called the mathematical expectation of discrete random variables. It is a generalization of simple arithmetic average, similar to weighted average. 2) Let the probability density function of continuous random variable x be f(x). If the integral is absolutely convergent, the value of the integral is called the mathematical expectation of a random variable, and it is recorded as E(X). 2. The arithmetic mean of the relationship comes from the sample. Is approximate. Mathematical expectation is maternal. Is accurate. If classical probability theory is used in the calculation of expected value, then the corresponding probability of each data is 1/n, where n is the number of data. Then the expected value is equal to the arithmetic mean.