Slutsky's theorem says that if Xn ->(D) X and Yn ->(P) y0, y0 a
constant, then
Xn + Yn ->(D) X+y0. It is easy to make a counterexample if both Xn and
Yn converges in distribution. Anybody have an counterexample when Yn
converges in probability to a non-constant random variable?
Kjetil Halvorsen
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