Think of this as the “continuous” version of “if I flip a coin 100 times and get 50 heads, then the next one must be tails, because we’re due for one.” It is incorrect.

It doesn’t matter how long we’ve “waited.” An additional wait length is just as likely now as it was when we first started.

  • The Exponential distribution is the only continuous, memoryless distribution.
  • Realistic for some processes (radioactive decay), less so for others (human life).
  • Connected to Poisson processes and the “finite” version of the Geometric distribution, which counts the “finite” waiting time until the first success.

Formal definition

Formally, we say a distribution is memoryless if a r.v. from that distribution satisfies

for all . Furthermore, these two distributions are Independent of one another.