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