Marginal Probability Density Functions

Definition

The marginal probability density functions of $X, Y$ denoted by $f_{X} (x)$ and $f_{Y} (y)$ respectively, are given by:

\begin{array}{r} f_{X} (x) = \int_{- \infty}^{\infty} f (x, y) d y; - \infty < x < \infty \\ f_{Y} (y) = \int_{- \infty}^{\infty} f (x, y) d x; - \infty < y < \infty \end{array}