Continuous Exponential Distribution

A kind of Continuous Distribution that models the time or space between independent events occurring at a constant average rate $\lambda$.

$$X\sim \text{Exp}(\lambda )\text{where}x\ge 0,\lambda >0$$

• $f(x)=\lambda e^{-\lambda x}\text{for }x\ge 0$
• $E(X)=\frac{1}{\lambda }$
• $\text{Var}(X)=\frac{1}{\lambda }$
• $F_X(x)={\int }_0^{x}f(t)dt={\int }_0^x\lambda e^{-\lambda t}dt=1-e^{-\lambda x}$