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