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Q117Section III (Statistics)117 of 180

Slutsky's theorem — convergence in distribution is all that's guaranteed

{Xn,n≥1}\{X_n,n\ge1\}, {Yn,n≥1}\{Y_n,n\ge1\} and Y are random variables defined on the same probability space. Suppose as n→∞n\to\infty, XnX_n converges in probability to 3 and YnY_n converges in distribution to Y. Then which of the following is true as n→∞n\to\infty?

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