Factorial Moment

E( (X)_n )

where

:

(x)_n=x(x-1)(x-2)\cdots(x-n+1)

is the Falling Factorial (confusingly, this same notation, the Pochhammer Symbol (''x'')_''n'', is used by some mathematicians, especially in the theory of Special Function s, to denote the Rising Factorial ''x''(''x'' + 1)(''x'' + 2) ... (''x'' + ''n'' − 1); the present notation is used by Combinatorialists ).

For example, if ''X'' has a Poisson Distribution with Expected Value λ, then the ''n''th factorial moment of ''X'' is

:

E( (X)_n )=\lambda^n.

	CATEGORIES ABOUT FACTORIAL MOMENT

	probability distributions

	factorial and binomial topics

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