Well, this is my sandbox. What for? I don't know.
Mr. Santana, this is the density, not the distribution!
1 σ 2 π e − ( x − μ ) 2 2 σ 2 {\displaystyle {1 \over \sigma {\sqrt {2\pi }}}e^{-}{(x-\mu )^{2} \over 2\sigma ^{2}}}
