Let $X$ be an absolutely continuous $n_1$-dimensional random variable which is independent from $Y, Z$ where are $n_1$- and $n_2$-dimensional random variables, respectively. Further, assume $Z$ is an absolutely continuous random variable ($Y$ have singularities and is dependent on $Z$). How do we prove that $(X+Y, Z)$ is also absolutely continuous?
2026-02-24 03:33:35.1771904015
Absolute Continuity of $(X+Y, Z)$ where $X \perp Y, Z$
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