In Section 3 2 it was claimed that the Poisson(A) distribution is the limit of the negative binomial(r, p) distribution as r , p 1, and r(l p) Show that under these conditions the mgf of the negative binomial converges to that of the Poisson

Question: In Section 3.2 it was claimed that the Poisson(A) distribution is the limit of the negative binomial(r, p) distribution as r , p

In Section 3.2 it was claimed that the Poisson(A) is the limit of the negative binomial(r, p) as r → ∞, p → 1, and r(l - p) → λ. Show that under these conditions the mgf of the negative binomial converges to that of the Poisson.

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