The memory-less property is followed by which of the following continuous distribution:
Exponential distribution
The memoryless property states \(P(X>s+t \mid X>s)=P(X>t)\) — the future is independent of the elapsed waiting time.
For the exponential distribution with survival function \(P(X>t)=e^{-\lambda t}\):
\[P(X>s+t \mid X>s)=\frac{e^{-\lambda(s+t)}}{e^{-\lambda s}}=e^{-\lambda t}=P(X>t)\]
The exponential distribution is the unique continuous distribution with this property. Normal, uniform, and general gamma (with shape ≠ 1) distributions do not satisfy it.
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