Gaussian Probability Density Function

Any non-negative function which integrates to 1 (unit total area) is suitable for use as a probability density function (PDF) (§C.1.3). The most general Gaussian PDF is given by shifts of the normalized Gaussian:

$$f(t) \isdef \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{(t-\mu)^2}{2\sigma^2}}$$ (D.28)

The parameter $\mu$ is the mean, and $\sigma^2$ is the variance of the distribution (we'll show this in §D.12 below).