Mathematical expectation is a description of some average values of random variables, and it is a weighted average of random variables. It is an important numerical feature of random variables and represents the average level of random variables.

Probability is the probability that a random variable takes a specific value. This is a stable frequency value. The probability value is between [0, 1].

In particular, knowing the probability distribution of a random variable can uniquely determine its mathematical expectation, and vice versa.