Example 4.8: The Poisson distribution Show that with the help of the Stirling approximation (and n  N, p  1) the binomial distribution W(n) of Example 4.6 with q = 1 − p reduces to the following expression known as the Poisson distribution, i.e.

W(n)

λn n!

e−λ, λ = Np. (4.64)

Show that the result can also be obtained with the help of the formula e−λ = lim n→∞



1 −

λ

n

n

.