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Poisson Theorem

Poisson's theorem gives the estimate

(n!)/(k!(n-k)!)p^kq^(n-k)∼e^(-np)((np)^k)/(k!)

for the probability of an event occurring k times in n trials with n>>1, p<<1, and np approx 1.

See also

Poisson Distribution

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References

Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, p. 71, 1984.

Referenced on Wolfram|Alpha

Poisson Theorem

Cite this as:

Weisstein, Eric W. "Poisson Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PoissonTheorem.html

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