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Definition

The normal (or Gaussian) distribution is a very common continuous probability distribution in probability theory.

Parameters
Notation \mathcal N(\mu, \sigma^2), \mu \in \R, \sigma \gt 0
Mean \mu
Variance \sigma^2
PDF f_X (x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{(x-\mu)^2}{2 \sigma^2}}, x \in \R

Probability Density

f_X (x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{(x-\mu)^2}{2 \sigma^2}}

with the mean \mu, the standard deviation \sigma.

Properties