Poisson Distribution

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Homework Statement


We can approximate a poisson distribution from the normal. Suppose lambda is a large positive value; let X ~ Poisson(lambda) and let X1.....Xn be independant identicly distributed from a Poisson (lambda/n) distribution. Then X and X1+....+Xn have the same distribution. Use the central limit theorem to determine the approximate distribution of X.......


Homework Equations





The Attempt at a Solution



I know that the above statement is true through moment generating functions. If X is distributed with mean of lambda then n random variables with a mean of lambda over n will sum to a distribution with mean of lambda.

It seems from the question that the distribution of X would just be a poisson distribution with mean of lambda but that doesnt really require any work as the problem states that.

Any help on getting started?
 

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