| Abstract: | For two independent nonnegative random variablesX andY we say thatX is ageless relative toY if the conditional probability P[X> Y+x|X>Y] is defined and is equal to P[X>x] for allx>0. Suppose thatX is ageless relative to a nonlatticeY with P[Y=0] Y]. We show that the only suchX is the exponential variable. As a corollary it follows that exponential variable is the only one which possesses the ageless property relative to a continuous variable. Research partially supported by NRC of Canada grants #A8057 and #T0500. Work partially completed while on leave at Division of Math. Stat., C.S.I.R.O., Australia. |
