$$ \frac{\int_{t+h}^{\infty} \lambda e^{-\lambda x} dx}{\int_{t}^{\infty} \lambda e^{-\lambda x} dx} = \frac{\int_{h}^{\infty} \lambda e^{-\lambda x} dx}{\int_{0}^{\infty} \lambda e^{-\lambda x} dx} $$ This is known as the memoryless property of the exponential distribution. From the plots we can see the shape of the curve looks the same wherever you start plotting. Is there a concept describing this?

