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For random variables $\{X_n\}$, $\{Y_n\}$ that converge in distribution to X and Y, what would it mean if $\{(X_n,Y_n)\}$ converges in distribution to (X,Y)?

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    What is the question? If $(X_n,Y_n)\to(X,Y)$ in distribution, then, for any continuous function $u$, $u(X_n,Y_n)\to u(X,Y)$. For example $u$ can be the projection on some coordinates. So yes, this implies that $X_n\to X$ and that $Y_n\to Y$.2011-10-26

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