The relationship between mathematical expectation and arithmetic average means that in the calculation of expected value, using classical probability theory, the probability corresponding to each data is 1, and n. N is the number of data. Then the mathematical expectation is equal to the arithmetic mean.

1. In probability theory and mathematical statistics, mathematical expectation is the probability that every possible result in an experiment is multiplied by the sum of its results, which is one of the most basic mathematical characteristics. It reflects the average value of random variables.

2. The law of large numbers stipulates that as the number of repetitions approaches infinity, the arithmetic average of numerical values almost inevitably converges to the expected value.

3. Arithmetic average, also known as average, is the most basic and commonly used average index in statistics, which can be divided into simple arithmetic average and weighted arithmetic average. Mainly suitable for numerical data, not for quality data. According to the different forms of expression, the arithmetic mean has different calculation forms and formulas.

4. Arithmetic average is a special form of weighted average. In practical problems, when the weights are not equal, the average value is calculated by weighted average, and when the weights are equal, the average value is calculated by arithmetic average.