If I have a discrete random variable $Y$, such that $p(y)=\frac{1}{2}$, $y=2, 4$

Question

If I have a discrete random variable $Y$, such that $p(y)=\frac{1}{2}$ and $y=2, 4$. Is $p(y)$ supposed to be the probability mass function for $Y$?

Answer 1

Yes of course ! The definition of Probability Mass function is if $X$ is random variable with discrete masses then $ P ( X = x )$ will be pmf if $\sum_{x \in A} P ( X = x )=1$. Here your A contains 2 and 4 and obviously sum of probabilities at those point add up to 1. So it is a valid PMF.