Question: Suppose thatXBinomial(n, p). First write down the MGF ofX,MX(t). Prove that whenn andp0 butnp=, whereis a positive constant, we haveMX(t) converges to the MGF ofPoisson().

Suppose thatXBinomial(n, p). First write down the MGF ofX,MX(t). Prove that whenn andp0 butnp=, whereis a positive constant, we haveMX(t) converges to the MGF ofPoisson().

(a) (6 points) Suppose that X ~ Binomial (n, 13). First write down the MGF (Moment Generating Function) of X, M X (t). Prove that when n > 00 and p > 0 but up = A, where A is a positive constant, we have M X (t) converges to the MGF of Poisson(A). (Hint: 11mm\

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