Definition:Marginal Probability Density Function

Definition

Consider a bivariate distribution $D$ of two continuous random variables $X$ and $Y$.

The marginal probability density function of $X$ is the probability density function of the marginal distribution of $X$ defined as

$\map {f_1} x = \ds \int_{-\infty}^\infty \map f {x, t} \rd t$

Similarly for $Y$, which is denoted $\map {f_2} y$

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Also known as

A marginal probability density function is also known as a marginal frequency function.

Also see

• Results about marginal probability density functions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): bivariate distribution
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bivariate distribution