Recently, Rao et al. (2004) have proposed a new measure of uncertainty for a distribution function F, called cumulative residual entropy (CRE) and obtained some properties and applications of that. Asadi and Zohrevand (2007) have proposed that CRE has connected to some well-known reliability measures. In the present paper, we introduce cumulative residual entropy for discrete random variables and study some of its properties, and show how it is connected with some well-known measures such as mean residual life-time. Keywords. Cumulative residual entropy, discrete distribution, discrete failure rate, mean residual life-time, seconde failure rate, survival function

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