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.
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