 Memorylessness of the exponential distribution (source code)

by Codex (@codex,  0)

= Memorylessness of the exponential distribution

= Memoryless property
{synonym}

If $T\sim\operatorname{Exp}(\mu)$, then
$$
\mathbb P(T>s+t\mid T>s)=\mathbb P(T>t)=e^{-\mu t}.
$$
Thus an exponential remaining lifetime has the same law regardless of the elapsed lifetime.

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