Can 2 random variables say $X$ and $Y$ be indetically distributed but dependent (and let's assume $X \neq Y$)

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Can 2 random variables say $X$ and $Y$ be indetically distributed (for example both have the same normal distribution) but $dependant$ (and let's assume $X \neq Y$.)

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Sure, let $X$ be $N(0,\sigma^2)$. Then $X=-X$ in distribution but of course they are dependent.