Normal Distribution

a.k.a. Gaussian Distribution, Bell Curve, whatever.

$$\mathcal{Norm}(\mathbf{X}=x; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\exp{\biggl(-\frac{(x-\mu)^2}{2\sigma^2}\biggr)}$$

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, $\mathcal{Norm_A}+\mathcal{Norm_B} = \mathcal{Norm}(\mu_A+ \mu_B, \sqrt{\sigma_A^2 + \sigma_B^2})$