 because formula_14

The following sum is a stochastic variable having a compound distribution

where the formula_16 are mutually independent random variables sharing the same common distribution and formula_17 a random integer variable independent of the formula_18 with its own distribution.The moments of formula_19 are obtained as 

where formula_21 is defined as zero for formula_22.In a symmetric distribution (one that is unaffected by being reflected about its mean), all odd central moments equal zero, because in the formula for the "n"th moment, each term involving a value of "X" less than the mean by a certain amount exactly cancels out the term involving a value of "X" greater than the mean by the same amount.