Moment (mathematics) - Cumulants

Cumulants

The first moment and the second and third unnormalized central moments are additive in the sense that if X and Y are independent random variables then

and

and

(These can also hold for variables that satisfy weaker conditions than independence. The first always holds; if the second holds, the variables are called uncorrelated).

In fact, these are the first three cumulants and all cumulants share this additivity property.