Marginal Distribution

Discrete Marginal Distribution §

def. Marginal Distributions are used when you only have the joint distribution available, and you want to get the distribution of one of the variables. They’re called that because you can write them in the margins.

Joint Marginal Distribution §

def. Marginal Distribution of Continuous Joint Distributions. Let $X,Y$ and given $f_{X,Y}$. Then PDF of $X$ is:

$$f_X(\bar{x})={\int }_{y=-\infty }^{\infty }{f}_{X,Y}(\bar{x},y)dy$$

…and vice versa for $f_Y$.

The red area is the marginal probability density at x.