If X∼Exponential(λ)X \sim \text{Exponential}(\lambda)X∼Exponential(λ), what is the memoryless property represented by?
P(X>s+t)=P(X>s)P(X>t)P(X > s+t) = P(X > s)P(X > t)P(X>s+t)=P(X>s)P(X>t)
P(X>s+t∣X>s)=P(X>t)P(X > s+t | X > s) = P(X > t)P(X>s+t∣X>s)=P(X>t)
E[X∣X>s]=E[X]+sE[X|X>s] = E[X] + sE[X∣X>s]=E[X]+s
Var(X∣X>s)=Var(X)Var(X|X>s) = Var(X)Var(X∣X>s)=Var(X)