Definition

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