If I have two random variables that are uncorrelated with each other,does sampling from their individual distributions separately and combining them to form a vector give a sample from their joint distribution?
2026-04-02 08:15:13.1775117713
Uncorrelated random variables and their joint distribution.
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Take $X \sim N(0,1)$ and $Y=X^2$. Then $\mathbb{E}(XY)=\mathbb{E}(X^3)=0$. And hence $X$ and $Y$ are uncorrelated. But they are not independent. So, sampling from $X$ automatically implies sampling from $Y$ and thus the joint density does not factor into the densities of the separate variables.
So, the answer is no.