The purpose of this paper is twofold: first, to provide a closed form expression for the median of the Poisson distribution and, second, to improve the known estimates of the difference between the median and the mean of the Poisson distribution. We use elementary techniques based on the monotonicity of certain sequences involving tail probabilities of the Poisson distribution and the Central ...

Poisson Distribution (values n = 0, 1, 2, . . .) The Poisson distribution is the limiting case of the binomial distribution where p → 0 and n → ∞. The expected value E(X) = λ where np → λ as p → 0 and n → ∞. The standard deviation is l. The pdf is given by This distribution dates back to Poisson's 1837 text regarding civil and ...

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