For the binomial distribution,
Now let
then
now let n go to infinity
which is the MGF of the Poisson distribution
Let Yn be a binomial random variable with n trials and with success probability p. Consider that n tends to infinity and p tends to zero in a way that np remains fixed at np=ƛ. Prove that the distribution of Yn converges to a Poisson distribtution with mean ƛ.
I am supposed to use mgfs but am unsure of how to do so.