In Wikipedia (for example) the Probability mass function of for example a the binomial distribution is given by
$ f(k,n,p):=\binom{n}{k}p^k(1-p)^{n-k} $
In some literature I read
$ P_{n,p}:=\sum_{k=0}^n\binom{n}{k}p^k(1-p)^{n-k} \delta_k $
where $\delta_k$ is the Dirac delta function.
I see that the result is the same, because $\delta_k$ nullifies each not needed addend. Why this verbosity? Does it have a sense, that I didn't get so far?
Thanks for any feedback!