5 Statistical moments
The PDF for the exponential distribution is given as:
[latex]\rho (x) \equiv \lambda e^{-\lambda x}, \; x > 0[/latex]
Then the expected value is derived as:
[latex]E[X] \equiv \int_{0}^{\infty} x \rho (x) dx = \frac{1}{\lambda}[/latex]
And the variance is derived as:
[latex]Var[X] \equiv \int_{0}^{\infty} x^2 \rho (x) dx = \frac{1}{\lambda^2}[/latex]
The mean and variance are clearly important quantities in statistical analysis and risk assessment.