Memoryless property

For stochastic processes, lack-of-memory is synonymous with the Markov property. For a positive random variable T that models the duration of some phenomenon, lack-of-memory means that the time remaining is independent of the time already passed, that is, Pr{T > t + s|T > s} = Pr{T > t} for s, t > 0. The exponential distribution is the only continuous distribution with lack-of-memory, while the geometric distribution is the only discrete distribution with lack-of-memory. Exponential arrivals; Markov processes; Markov property.