1. let x be a random variable and c be a constant, then E(CX)=CE(X).

2. Let x and y be any two random variables, then E(X+Y)=E(X)+E(Y).

3. Let x and y be independent random variables, then E(XY)=E(X)E(Y).

In statistics, when estimating the expected value of a variable, the common method is to measure the value of this variable repeatedly, and then use the average value of the obtained data as the estimation of the expected value of this variable.

In probability distribution, expected value and variance or standard deviation are important characteristics of distribution.