# Sum of independent and dependent makes it independent?

Assume there are two independent variables $X$ and $Z$. Let $Y=X+Z$. Are $Y$ and $X$ dependent/independent? Thanks!

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If $X$ and $Y$ are independent, $X$ is independent of $X+Z$. Since it's also independent of $-Z$, $X$ is independent of $X$ and $X$ needs to be constant.