Show that the binomial moment generating function converges to the Poisson moment generating function if we let n → ∞ and p → 0 in such a way that np approaches a value μ > 0. There is in fact a theorem saying that convergence of the mgf implies convergence of the probability distribution. In particular, convergence of the binomial mgf to the Poisson mgf implies b(x; n, p) → p(x; μ).