# Binomial Approximation to a Poisson Random Variable

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If a coin that comes up heads with probability is tossed times, the number of heads observed follows a binomial probability distribution. The Poisson probability distribution can be regarded as a limiting case of the binomial distribution as the number of tosses grows and the probability of heads on a given toss is adjusted to keep the expected number of heads constant. More precisely, if is a binomial random variable with parameters and , then the probability distribution for approaches a Poisson distribution with parameter λ as approaches infinity.

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Contributed by: Chris Boucher (March 2011)

Open content licensed under CC BY-NC-SA

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"Binomial Approximation to a Poisson Random Variable"

http://demonstrations.wolfram.com/BinomialApproximationToAPoissonRandomVariable/

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Published: March 7 2011