AThe probability distribution of random variable is often characterised by a small number of quantitiesparameters, which also have a practical interpretation. For example, it is often enough to know what its "average value" is. This is captured by the mathematical concept of [[expected value]] of a random variable, denoted E[''X'']. Note that in general, E[''f''(''X'')] is '''not''' the same as ''f''(E[''X'']). Once the "average value" is known, one could then ask how far from this average value the values of ''X'' typically are, a question that is answered by the [[variance]] and [[standard deviation]] of a random variable.
Mathematically, this is known as the (generalised) [[problem of moments]]: for a given class of random variables ''X'', find a collection {''f<sub>i</sub>''} of functions such that the expectation values E[''f<sub>i</sub>''(''X'')] fully characterize the distribution of the random variable ''X''.
