Abstract:  Let Y₁,Y₂,…Y,be mutually independant non-negative random variables having an aboolutely continuous distribution function F₁(y)over its support 10,∞)and the corresponding density function f;(y)>0 for y>0.Let a denote the event that Y:-Y+1>0 for all i=1,2, … n-1.Then we show that,conditional on the event A,Y;-Yi+1and Yi+1are independent for all i=1,2,…k if and only if Y;(i=1,2,…k)are exponentially distributed random variables,  wbere 1≤E≤n.We not that the k exponential distributions can have different scale parameters.

Key words:  , characterization, conditional independence, exponential distribution