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Determine the distribution of the sum

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Question: A skeptic gives the following argument to show that there must be a flaw in the central limit theorem: "We know that the sum of independent Poisson random variables follows a Poisson distribution with a parameter that is the sum of the parameters of the summands. In particular, if n independent Poisson random variables, each with parameter n-1, are summed, the sum has a Poisson distribution with parameter 1. The central limit theorem says that as n approaches infinity, the distribution of the sum tends to a normal distribution, but the Poisson with parameter 1 is not the normal." What do you think of this argument?

Reference no: EM131731593

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