Multiplication Rule For Expected Value

The multiplication rule for expected value states that the expected value of the product of two random variables is equal to the product of their individual expected values if the two random variables are independent. Mathematically, if X and Y are two independent random variables, then:

E(XY) = E(X) E(Y)

where E(X) and E(Y) are the expected values of X and Y, respectively. This rule is useful in many applications, such as calculating the expected value of the product of two stocks in a portfolio or the expected value of the product of two measurements in a scientific experiment.