gaussian variable
A variable that has pdf
\begin{equation}
f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{\frac{1}{2} (\frac{x-\mu}{\sigma})^2}
\end{equation}
So, Gaussian random variable is fully defined by \(\mathcal{N}(\mu, \sigma^2)\)
A variable that has pdf
So, Gaussian random variable is fully defined by \(\mathcal{N}(\mu, \sigma^2)\)