However, what we can get through a limited number of operations is feeble in a sense, and the results that look very close to 75 and 68 are simply not enough to explain the existence of mathematical expectations-no matter how close they are to the target value.

When the discrete random variable X takes a countable value, its mathematical expectation requires the series ∑| Xi |π to converge, otherwise the mathematical expectation does not exist; If a continuous random variable takes a value in an infinite interval, its mathematical expectation is generalized integral.