Abstract:  Let Y₁,Y₂,…,Y be mutually independent taking random yariables of positive integer value.A denote the  event that Y,-Y,i>0 for all z=1,2,…,n-1.Then we  show that,under  condition A,Y, -Y+i  and     Y..are     independent,for   t=1,2,….K      and     only     if     Y,(z=1,2,…,K)accords     with  geometric  distribution.Here  in  I≤K≤n-1.Note:the  K  geometric   distributions   can  have   diffrent  scale parameters.

Key words:  , characterization, conditional ,  , independence, geometric , distribution