PMF is a function that maps possible outcomes of a discrete random variables to the corresponding probability.

For random variable \(Y\), we have:

\begin{equation} f(k) = P(Y=k) \end{equation}

and \(f\) is a function that is the PMF, which is the mapping between a random variable and a value it takes on to the probability that the random variable takes on that value.

## Shorthand

\begin{equation} P(Y=k) = p(y), where\ y=k \end{equation}

its written smaller \(y\) represents a *case* of \(Y\) where \(Y=y\).

## Shorthand

For this to be correct, we have to