We present and prove two theorems about equalities for the nth moment of nonnegative integer-valued random variables. These equalities generalize the well known equality for the first moment of a nonnegative integer-valued random variable X in terms of its cumulative distribution function, or in terms of its tail distribution.
RIFFI, MOHAMED I. (2004) "Moments Equalities for Nonnegative Integer-Valued Random Variables," Turkish Journal of Mathematics: Vol. 28: No. 2, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol28/iss2/2