albania, I'd gladly welcome your profs input on this. If you didn't notice, I am an obsessive SOB.
This is my proof that demonstrates the symmetry of the Poisson distribution as the expectancy goes to infinity.
Unfortunately, this only proves that the sum from zero to
n-1 is
1/2, as the initial assumption for the symmetry starts from the fact that
Pi(n-1,n) and
Pi(n,n) are equal. As they are equal, I have a symmetry line at
k=n+1/2. I then have to prove that
Pi(n,n) goes to zero as
n goes to infinity, allowing that the original sum from zero to
n is still
1/2. I could just not be so picky about it, and change the symmetry line to exist at
k=n, but I know it is not there.
This is why I still don't like this proof, as having the answer before hand allowed me to begin this line of inquiry. I would much rather see an actual proof, that does not require me to know the answer previously.