PROBABILITIES Course

Marginal Distribution

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This page is about the discrete marginal distribution and the continuous marginal distribution.


Discrete Marginal Distribution

The marginal distribution, loi marginale, or the marginal probability mass function of X and Y is

@ \mathbb{P}(X=x) = \sum_{y_i \in Y(\Omega)} \mathbb{P}(X=x \cap Y=y_i) @

@ \mathbb{P}(Y=y) = \sum_{x_i \in X(\Omega)} \mathbb{P}(X=x_i \cap Y=y) @


Continuous Marginal Distribution

The marginal distribution, loi marginale, or the marginal probability density function of X and Y is

@ f_X(x) = \int_{-\infty}^{+\infty} f_{X,Y}(x, y)\ dy @

@ f_Y(y) = \int_{-\infty}^{+\infty} f_{X,Y}(x, y)\ dx @