I've been doing some multivariate pdf problems such as this: we have $f(x,y,z)=xyz$ and we need to find $f(z)$ in which case we "integrate out" $x$ and $y$ over their respective ranges. I concretely understand this concept, however I do not understand how to generalize the following. If we have $f(x,y)=g(x)h(y)$ then the marginal pdf $f(y)=\frac{1}{k}h(y)$ where $k=\int_{-\infty}^\infty h(y) dy$. Is this the same concept as the example above?
proving marginal pdf from joint pdf
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integration
probability-distributions