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The marginal distribution refers to the probability distribution of a subset of variables contained in a joint distribution.

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Do marginal density functions derived from a joint pdf always integrate to 1 (are they valid...

If I have a joint pdf of multiple random variables, say 3 for simplicity, $f_{X,Y,Z}(x,y,z)$, is it true that the marginal density functions derived from that joint probability distribution ( $f_{X}(x …
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Do marginal density functions derived from a joint pdf always integrate to 1 (are they valid...

Using two properties of the joint pdf: $\int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty} \int\limits_{-\infty}^{\infty} f(x, y, z) \, dx \, dy \, dz = 1$, and $f_X(x) = \int\limits_{-\in …
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