N is a discrete random variable, and p(X 1), p(X2), p(X3), ... p (xn) are the probability functions of these data. P(X 1), p(X2), p(X3), ... p (Xn) in several random data is understood as the frequency f(Xn), X2, X3, ..., xn of data X 1.

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In probability theory and mathematical statistics, mathematical expectation (or simply mean, or expectation) is the sum of the possible results multiplied by the results in each experiment, which is one of the most basic mathematical characteristics. It reflects the average value of random variables.

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.