Cramér-Rao-type Bound and Stam's Inequality for Discrete Random Variables

The variance and the entropy power of a continuous random variable are bounded from below by the reciprocal of its Fisher information through the Cram\'{e}r-Rao bound and the Stam's inequality respectively. In this note, we introduce the Fisher information for discrete random variables and derive the discrete Cram\'{e}r-Rao-type bound and the discrete Stam's inequality.