While studying linear regression, my text book indicates that we account for noise, which is given by the function:
$$ \varepsilon_i \sim \mathcal{N}(0,\beta^{-1}).$$
I know this is a normal distribution and I know through research that noise and error rates usually follow this distribution. However, I am puzzled by how I should interpret this, given that the normal distribution function is represented by:
$$ \mathcal{N}(\mu,\sigma^2).$$
What I do not understand, is what is the significance of the parameters used here? Namely $0$ and $\beta^{-1}$? Should I care about these or is this just standard notation? Does this simply mean that the mean is 0 and the standard deviation is a beta function?