Mathematical expectation (or expectation value) is a mathematical term of statistical random variables, which represents the sum of expected results brought by the results of each test in many random experiments.

For the discrete random variable x, its expected value (also called mathematical expectation) can be expressed as:

E(X)=∑xP(X=x)

Where x is the value of the random variable x, and P(X=x) is the probability that the random variable x takes the value of x.

For continuous random variable x, its expected value can be expressed as:

E(X)=∫xf(x)dx

Where f(x) is the probability density function of random variable x.

Expected value is a useful mathematical feature of random variables, which represents the center position of random variables in a statistical sense. It is the average of random variables, but not all random variables have expectations, because expectations only exist when certain conditions are met.