Let be independent random variables such that If the πni are strictly positive and as and (ii) has, asymptotically, a Poisson (λ) distribution. In the above exercise, show that as λ increases,...

Let

be independent random variables such that

If the π_ni
are strictly positive and as

and (ii)

has, asymptotically, a Poisson (λ) distribution.

In the above exercise, show that as λ increases,

converges in law to a normal variate.

In the same setup of show that the divergence of the series

is a necessary and sufficien condition for the asymptotic normality of