PlanetMath: Poisson random variable

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Poisson random variable

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The Poisson discrete probability function with parameter $\lambda>0$ is given by

$\displaystyle f_X(x) = \frac{e^{-\lambda} \lambda^x}{x!},\quad\quad x\in \mathbb{N}.$

A random variable with such a density has expectation, variance, moment generating function and characteristic function given by $E[X] = \lambda$ , $Var[X] = \lambda$ , $M_X(t) = e^{\lambda (e^t - 1)}$ , and $\phi_X(t) = e^{\lambda(e^{it}-1)}$ , respectively.

"Poisson random variable" is owned by Koro. [ full author list (3) | owner history (1) ]

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Other names:

Poisson distribution

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Cross-references: characteristic function, moment generating function, variance, expectation, density, random variable, parameter, discrete probability function
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This is version 8 of Poisson random variable, born on 2001-10-26, modified 2006-12-16.
Object id is 519, canonical name is PoissonRandomVariable.
Accessed 19307 times total.

Classification:

62E15 (Statistics :: Distribution theory :: Exact distribution theory)

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