Question: Let Xn be a random variable having the binomial distribution with parameters n and pn. Assume that limn npn = . Prove that the m.g.f.

Let Xn be a random variable having the binomial with parameters n and pn. Assume that limn→∞ npn = λ. Prove that the m.g.f. of Xn converges to the m.g.f. of the Poisson with mean λ.

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