Memoryless

Definition

A random variable${\displaystyle X}$ is memoryless if $${\displaystyle \Pr(X>t+s\mid X>s)=\Pr(X>t)}$$where ${\displaystyle \Pr }$ is its probability mass function or probability density function when ${\displaystyle X}$ is discrete or continuous respectively and ${\displaystyle t}$ and ${\displaystyle s}$ are nonnegative numbers. In discrete cases, the definition describes the first success in an infinite sequence of independent and identically distributedBernoulli trials, like the number of coin flips until landing heads. In continuous situations, memorylessness models random phenomena, like the time between two earthquakes. The memorylessness property asserts that the number of previously failed trials or the elapsed time is independent, or has no effect, on the future trials or lead time.