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Gaussian Limit of Binomial and Poisson Distributions---III
We can do the same trick for the Poisson distribution.
Fix
finite and let
be independent with each
as Poisson random variable with parameter
.
Then from additivity
has Poisson distribution with parameter
.
Meanwhile, from central limit theorem,
y
is Gaussian with mean
and standard deviation
.
Here again
and
are mean and standard deviation of individual distribution.
Here mean is given by
Geoffrey Fox
,
Northeast Parallel Architectures Center
at Syracuse University,
gcf@npac.syr.edu
finite and let 
be independent with each 
as Poisson random variable with parameter 
.
has Poisson distribution
with parameter 
.
and standard deviation 
.
and 
are mean and standard deviation of
individual distribution.
