Standard Gaussian Distribution

probability-theory

Definition

Standard Gaussian Distribution

The standard Gaussian distribution is a Gaussian distribution with a mean $\mu =0$ and a variance ${\sigma }^2=1$.

Cumulative Distribution Function

The cdf is given by:

$$\Phi (x)=P(X\le x)={\int }_{-\infty }^{x}f(z)dz=\frac{1}{\sqrt{2\pi }}{\int }_{-\infty }^x{e}^{-z^2/2}dz$$

which does not have a closed form solution.