I wonder if someone could clarify these limits for me. They arise in the derivation of the poisson distribution from the binomial distribution as
and
The first is
as
.
I don't see how this works. If anything I would have thought that
as
.
The second is that
\frac{n!}{(n-k)!(n-\lambda)^k = \frac{n(n-1) \ldots (n-k+1)}{(n - \lambda) (n-\lambda) \ldots (n - \lambda)}
is a "quantity that tends to 1 as
(since
remains constant)."
What precisely is the role of
? Is the critical condition not that the numerator and denominator grow at the same rate, and if so, how can this be demonstrated?
Thanks in advance. MD