Assume $X \sim \mathcal N(\mu_1, \sigma_1^2)$ and $Y \sim \mathcal N(\mu_2, \sigma_2^2)$. If $\rho_{X,Y} = 0$ then $X \bot Y$.
Can someone give a hint why this is true ?
2026-04-01 17:26:29.1775064389
Does $0$ correlation imply independence for marginally normal distributions?
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