5 Statistical moments

Expected value and Variance

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.

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Risk Assessment Copyright © 2015 by R.A. Borrelli is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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