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Normal approximation to Poisson Distribution

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Normal approximation to Poisson Distribution

Is the Normal approximation to Poisson Distribution a result of the Central limit theorem


When repeating many times the same request, the probability to get an answer has a Poisson distribution of mean T. On the other hand, the probability to be banned from the forum has also a Poisson distribution of mean S. So, what is the probability to get an answer before being banned, as a function of S and T?

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