this is the PDF of a normal distribution.
${\displaystyle f(x\mid \mu ,\sigma ^{2})={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}}$
where
- $\mu$ is the mean or expectation of the distribution (and also its median and mode)
- $\sigma$ is the standard deviation
Is there a notion like the domain of definition of a function to specify a range where $\mu$ and $\sigma$ take on.
In another word, could $\mu$ and $\sigma$ be any value, such as $10^{-99}, 10^{-100}$, or even $\infty$, $-\infty$?