Let $X_n,Y_n$ be two sequence of real random variables on the same probability space. Is it true that if $Y_n\to c$ in probability ($c\in\mathbb{R}$), then it exists $\bar{n}$ such that $X_n$ and $Y_n$ are independent $\forall n\ge\bar{n}$?
2026-04-01 03:27:47.1775014067
Independence of sequences of random variables.
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Certainly not. What about if $X_n=Y_n$?