The Gaussian distribution, also known as the normal distribution, is a probability distribution for an independent random variable. It is usually used for modeling the Central Limit theorem [1]. The normal distribution is noted as: \[ \mathcal{N}(\mu, \sigma^2) \] where \(\mu\) is the mean, or average, while \(\sigma^2\) is the standard deviation. More precisely, the former is the peak, or highest point, of the graph and about which the graph is symmetric; the latter determines the amount of dispersion away from the mean. Infact, visually the Gaussian distribution is symmetric about the mean, meaning that data near the mean are more frequent in occurrence than data far from the mean.
The probability density function [2] that produce the normal distribution is the following: \[ f(x) = \frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{1}{2}\left(\frac{x - \mu}{\sigma}\right)^2} \] where \(x\) is value of the variable or data being examined and \(f(x)\) the probability function; \(\mu\) and \(\sigma\) represent, as mentioned previously, the mean and the standard deviation.