In fact, the only continuous probability distributions that are memoryless are the exponential distributions. If a continuous X has the memoryless property (over the set of reals) X is necessarily an exponential.
What distributions have the memoryless property?
There are only two probability distributions that have the memoryless property:
- The exponential distribution with non-negative real numbers.
- The geometric distribution with non-negative integers.
Is Poisson distribution memoryless?
On the other hand, a Poisson process is a memoryless stochastic point process; that an event has just occurred or that an event hasn't occurred in a long time give us no clue about the likelihood that another event will occur soon.
