information:filtering, structural:expansion
Symmetries and derivatives

The normal distribution with density f (x) {\textstyle f(x)} (mean μ {\textstyle \mu } and variance σ 2 > 0 {\textstyle \sigma ^{2}>0}) has the following properties:

Furthermore, the density φ {\textstyle \varphi } of the standard normal distribution (i.e. μ = 0 {\textstyle \mu =0} and σ = 1 {\textstyle \sigma =1}) also has the following properties: