If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution?(adsbygoogle = window.adsbygoogle || []).push({});

I tried to do this with the sum of bernouli variables and exponential variables and didn'treally get anywhere with either.

Does anyone know if this is even possible and where I can find the proof steps?

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# Sum of IID random variables and MGF of normal distribution

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