Show that if X is a random variable having the Poisson distribution with the parameter and , then the moment generating function of Z X That is, that of a standardized Poisson random variable, approaches the moment generating function of the standard normal distribution

Question: Show that if X is a random variable having the Poisson distribution with the parameter and , then the moment-generating function of

Show that if X is a random variable having the Poisson with the parameter λ and λ → ∞, then the moment-generating function of
Z = X – λ / √λ
That is, that of a standardized Poisson random variable, approaches the moment-generating function of the standard normal

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