\begin{block}{Normal distribution}
The density function of the normal distribution is often denoted with $\phi(x)$ and may be written as
\begin{equation*}
f(x) = \phi(x) = \frac{1}{\sigma \sqrt{2 \pi }}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}
\end{equation*}
The function has two \textbf{parameters}, $\mu$ and $\sigma$.
$\mu$ is the mean of the normal distribution and determines its location.
$\sigma^2$ is the variance of the distribution and determines its spread. If a random variable $X$ follows normal distribution with mean $\mu$ and variance $\sigma^2$ we write that \mbox{$X \sim N(\mu , \sigma^2)$}.
The distribution function of the normal distribution is denoted with $\Phi(x)$.
\end{block}