normal random variable is a continuous random variable that allows you to manually specify the expectation and variance
constituents
- \(\mu\) the mean
- \(\sigma\) the variance
requirements
\begin{equation} X \sim \mathcal{N}(\mu, \sigma^{2}) \end{equation}
PDF:
\begin{equation} f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x-\mu)^{2}}{2 \sigma^{2}}} \end{equation}
additional information
normal maximizes entropy
no other random variable uses as little parameters to convey as much information