Consider three random variables $X, Y$ and $Z$. If $X$ and $Y$ are independent, $Y$ and $Z$ are independent, then does that mean that $X$ and $Z$ are independent too?
2026-03-31 15:18:14.1774970294
are all the variables independent of each other
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Community wiki answer so the question can be marked as answered:
As drhab pointed out in a comment, the premises are consistent with $X=Z$, in which case $X$ and $Z$ will generally not be independent.