# Cinvergence in distribution

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• June 29th 2011, 10:15 AM
slavert
Cinvergence in distribution
Let $(X_{n}) i (Y_{n})$ be indpendent sequences of iid. $X_{n}~exp(1)$,
$Y_{n}~Poiss(1)$. Find the limit in distribution:
$Z_{n}= \frac{(X_{1}+...+X_{n})^{2}-(Y_{1}+...+Y_{n})^{2}}{n\sqrt{n}}$
I suppose clt and Slutsky theorem should be uses but don't know.
Thanks in advance