https://obs-web.rs.umbc.edu/ 2026-08-02T08:40:15+00:00 https://obs-web.rs.umbc.edu/ https://obs-web.rs.umbc.edu/lib/tpl/bootstrap3/images/favicon.ico text/html 2024-11-04T20:45:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://obs-web.rs.umbc.edu/doku.php?id=wiki:maths:normal&rev=1730771135&do=diff Normal Distribution a.k.a. Gaussian Distribution, Bell Curve, whatever. $$\mathcal{Norm}(\mathbf{X}=x; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\exp{\biggl(-\frac{(x-\mu)^2}{2\sigma^2}\biggr)}$$ Sum of Normals Normal Distributions have the favorable quality that their parameters add in quadrature: Given $\mathcal{Norm_A}(\mu_A, \sigma_A)$ & $\mathcal{Norm_B}(\mu_B, \sigma_B)$ Then, $\mathcal{Norm_A}+\mathcal{Norm_B} = \mathcal{Norm}\biggl(\mu_A+ \mu_B, \sqrt{\sigma_A^2 + \sigma_B^2}\biggr… text/html 2024-11-04T20:14:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://obs-web.rs.umbc.edu/doku.php?id=wiki:maths:poisson&rev=1730769240&do=diff Poissonian Processes A Poissonian Process is one governed by Poisson Statistics. Mathematical Formulation $$\mathcal{Pois}(\mathbf{X}=x; \lambda) = \frac{\lambda^{x}e^{-\lambda}}{x!}$$ With the $n$-th sampling from this distribution being noted: $x_n \thicksim \mathcal{Pois}(\lambda)$ Here, $\lambda$ is the average number of occurrences in some period, i.e., the average rate. And $x$$x \thicksim \mathcal{Pois}(\lambda)$$\lambda$$x$$\lambda$$x$$\lambda$$x$$\lambda$$\mathcal{Pois}(\lambda…