Memorylessness

If $X$ is an r.v., then it is said to be memoryless if for any (integers) $m$ and $n$, $P(X>m+n|X>m)=P(X>n)$

How can you tell if something is memoryless???

There are only two distributions that are memoryless:

• Geometric Distribution
• Exponential Distribution

MATH213

Definition 1: Memoryless vs Dynamic systems

A system is memoryless, if the instantaneous output value $y(t)$ depends only on the input value $f(t)$ at time $t$.

A system that is not memoryless is dynamic.

We focus on dynamic systems because they are hard to control.