The Exponential Distribution is a continuous probability distribution used to model the time between independent events that occur at a constant average rate. It is widely applied in survival analysis, reliability engineering, and queuing systems.
\[
\mu = \frac{1}{\lambda}, \quad \sigma^2 = \frac{1}{\lambda^2}
\]
\[
f(x) = \lambda e^{-\lambda x}, \quad (\lambda > 0,\ x \geq 0)
\]
\[
F(x) = 1 - e^{-\lambda x}
\]