Is a constant (deterministic random variable) Gaussian? Consider a constant $c$. Is this constant a Gaussian random variable (i.e. is $c\sim\mathcal{N}(c,0)$)?
I realize a constant is easily described as a discrete random variable, but I wish to use normal random variable properties on constants when combining them with other continuous random variables.
It makes sense to me that this should be, but it leads to a delta function for the pdf which I assume is bad form. 

The advantages of considering Dirac distributions as normal distributions (with variance zero) outweigh the disadvantages. For example, one wants to define a family of random variables as normal if every linear combination of this family has a one-dimensional normal distribution. This would not be correct if Dirac distributions were not normal.
