Probability mass function of a degenerate distribution Wikipedia article "degenerate distribution" states that "The probability mass function does not exist."  Is it really right? Why can't it be set as 
$$
f(x) = 
\begin{cases}
1 & \quad x = x_0, \\
0 & \quad \text{otherwise}
\end{cases}
$$

I'd have to disagree with wikipedia here....a pmf with $P(x_0)=1$ is totally fine. What is more problematic is trying to do this with a continuous r.v., in which case the degenerate density is a dirac delta function, which technically is not a function in the normal sense.
