Definition

Let $X$ and $Y$ be two random variables. The marginal distributions can be computed from their joint pmf $p(x,y)$, as a result the marginal pmf of $X$ is $$p_X(x)=\sum_{y\in\mathscr{Y}}p(x,y), \ x\in\mathscr{X}$$ and the marginal pmf of $Y$ is $$p_Y(y)=\sum_{x\in\mathscr{X}}p(x,y), \ y\in\mathscr{Y}$$