=+(ii) Let Yni, 1 i n, be independent and distributed as Poisson(n1n), n 1.

=+(ii) Let Yni, 1 ≤ i ≤ n, be independent and distributed as Poisson(n−1λn), n ≥ 1. Show that n i=1 Yni has the same distribution as Sn. Furthermore, show that Xni = λ−1/2 n (Yni − n−1λn) satisfy Liapounov’s condition (6.37)

with δ = 2. [Hint: You may use the fact that the fourth central moment of Poisson(λ) is λ + 3λ2.]