# Question

Show that if X is a random variable having the Poisson distribution 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 distribution.

Z = X – λ / √λ

That is, that of a standardized Poisson random variable, approaches the moment-generating function of the standard normal distribution.

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