Which property defines the memoryless property of X∼Exp(λ)X \sim \text{Exp}(\lambda)X∼Exp(λ)?
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)
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)
E[X∣X>s]=E[X]E[X|X>s] = E[X]E[X∣X>s]=E[X]
f(x)=f(x+s)f(x) = f(x+s)f(x)=f(x+s)