wiki:maths:normal

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wiki:maths:normal [2024/11/04 20:40] – Roy Proutywiki:maths:normal [2024/11/04 20:45] (current) – Roy Prouty
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 $$\mathcal{Norm}(\mathbf{X}=x; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\exp{\biggl(-\frac{(x-\mu)^2}{2\sigma^2}\biggr)}$$ $$\mathcal{Norm}(\mathbf{X}=x; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\exp{\biggl(-\frac{(x-\mu)^2}{2\sigma^2}\biggr)}$$
 +
 +=== 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, $\mathcal{Norm_A}+\mathcal{Norm_B} = \mathcal{Norm}\biggl(\mu_A+ \mu_B, \sqrt{\sigma_A^2 + \sigma_B^2}\biggr)$
 +