PropertiesTableNormal.tex

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\begin{table*}[t!]
\caption[Normal distribution -- Properties]{Properties of the normal distribution}

\begin{align*}
\text{\hyperref[PropertiesSec]{Properties}}  \quad& \\
\text{notation} \quad & \op{Normal}(x\given \mu,\sigma)	\checked
\\
\text{PDF}\quad &   \frac{1}{\sqrt{2 \pi \sigma^2}}  \exp\Left\{ - \frac{( x-\mu)^2}{2\sigma^2} \Right\} \checked
\\
\text{CDF} \quad  &   \frac{1}{2}\Left[  1 + \text{erf}\Left(\frac{x-\mu}{\sqrt{2 \sigma^2}} \Right) \Right]	\checked
\\
\text{parameters}\quad &   \mu,\ \sigma \text{ in } \mathbb{R}						\checked
\\
\text{support} \quad &   x \in [-\infty, + \infty]									\checked
\\
\text{median} \quad  &  \mu												\checked
\\
\text{mode} \quad  & \mu													\checked
\\
\text{mean} \quad  &  \mu													\checked
\\
\text{variance} \quad  & \sigma^2											\checked
\\
\text{skew} \quad  &  0													\checked
\\
\text{ex. kurtosis} \quad  &  0													\checked
\\	
\text{entropy} \quad  & \tfrac{1}{2} \ln(2\pi e \sigma^2)							\checked
\\
\text{MGF} \quad  &  \exp\Left({\mu t + \tfrac{1}{2} \sigma^2 t^2 }\Right)				\checked
\\
\text{CF} \quad  &  \exp\Left({i \mu t - \tfrac{1}{2} \sigma^2 t^2}\Right)					\checked
\end{align*}

\end{table*}