Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate discrete distributions ▷ Poisson distribution ▷ Probability mass function

Theorem: Let $X$ be a random variable following a Poisson distribution:

\[\label{eq:Poiss} X \sim \mathrm{Poiss}(\lambda) \; .\]

Then, the probability mass function of $X$ is

\[\label{eq:Poiss-pmf} f_X(x) = \frac{\lambda^x \, e^{-\lambda}}{x!}, \; x \in \mathbb{N}_0 \; .\]

Proof: This follows directly from the definition of the Poisson distribution.


Metadata: ID: P102 | shortcut: poiss-pmf | author: JoramSoch | date: 2020-05-14, 20:39.