1. In probability theory and mathematical statistics, mathematical expectation (or simply mean, or expectation) is the sum of the probabilities of every possible result multiplied by its result in the experiment, and it is one of the most basic mathematical characteristics. It reflects the average value of random variables.

2. It should be noted that the expected value is not necessarily equal to the common sense "expectation"-"expected value" is not necessarily equal to every result. The expected value is the average of the output values of variables. The expected value is not necessarily contained in the set of output values of variables.

3. 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.