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

Show that if X is a random variable having the Poisson distribution with the parameter lambda and lambda is approaching infinity, then the moment-generating function of Z = (X - lambda)/sqrt(lambda), that is, that of a standardized Poisson random variable, approaches the moment-generating function of the standard normal distribution.

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