Solutions Probability

6.41: Prove that if X is a random variable having the Poisson distribution with the paramete

Question: Problem 6.41: Prove that if X is a random variable having the Poisson distribution with the parameter \(\lambda \), and \(\lambda \to \infty \), then the moment generating function of

\[Z=\frac{X-\lambda }{\sqrt{\lambda }}\]

converges to the moment generating function of the standard normal distribution

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