\begin{definition}[Definition:Marginal Probability Mass Function]
Let $\left({\Omega, \Sigma, \Pr}\right)$ be a probability space.
Let $X: \Pr \to \R$ and $Y: \Pr \to \R$ both be discrete random variables on $\left({\Omega, \Sigma, \Pr}\right)$.
Let $p_{X, Y}$ be the joint probability mass function of $X$ and $Y$.
Then the probability mass functions $p_X$ and $p_Y$ are called the '''marginal (probability) mass functions''' of $X$ and $Y$ respectively.
The marginal mass function can be obtained from the joint mass function:
{{begin-eqn}}
{{eqn | l=p_X \left({x}\right)
      | r=\Pr \left({X = x}\right)
      | c=
}}
{{eqn | r=\sum_{y \mathop \in \operatorname{Im} \left({Y}\right)} \Pr \left({X = x, Y = y}\right)
      | c=
}}
{{eqn | r=\sum_y p_{X, Y} \left({x, y}\right)
      | c=
}}
{{end-eqn}}
\end{definition}