Normal Approximation to a Poisson Random Variable

parameter λ

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If

λ

is a positive integer, then a Poisson random variable with parameter

λ

can be thought of as a sum of

λ

independent Poisson random variables, each with parameter one. It is a consequence of the central limit theorem that for large values of

λ

such a random variable can be well approximated by a normal random variable with the same mean and variance.