The second one is the Gaussian Distribution $$ \begin{equation*} p(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp{(-\frac{(x-\mu)^2}{2\sigma^2})}, \end{equation*} $$ with mean value \( \mu \) and standard deviation \( \sigma \). If \( \mu=0 \) and \( \sigma=1 \), it is normally called the standard normal distribution $$ \begin{equation*} p(x) = \frac{1}{\sqrt{2\pi}} \exp{(-\frac{x^2}{2})}, \end{equation*} $$

The following simple Python code plots the above distribution for different values of \( \mu \) and \( \sigma \).