# Normal Approximation to a Poisson Random Variable

Normal Approximation to a Poisson Random Variable

If is a positive integer, then a Poisson random variable with parameter can be thought of as a sum of independent Poisson random variables, each with parameter one. It is a consequence of the central limit theorem that for large values of such a random variable can be well approximated by a normal random variable with the same mean and variance.

λ

λ

λ

λ