Exponential distribution

Exponential distribution

If events occur randomly at rate $\lambda$ (a Poisson process), the waiting time $X$ to the next one has pdf $\lambda e^{-\lambda x}$ for $x\ge0$, with $P(X>x)=e^{-\lambda x}$, mean $\frac1\lambda$ and variance $\frac1{\lambda^2}$. It is memoryless: having waited doesn't change how much longer you'll wait.