### Poisson distribution

(statistics on count of events happening within a given interval)

The **Poisson distribution** gives the probability of each possible number
of occurrences of an event happening within a given interval,
specifically for events that are independent but happen with a
fixed probability per unit time.
It is named for French mathematician Siméon Denis Poisson.

f(k;λ)
= probability(X = k)
λ^{k}e^{-λ}
= ——————
k!

- X - random variable which can have any of 0,1,2,...
- k - a specific value that X can take.
- λ - the expected value of X.
- e - Euler's number, 2.718...
- f(k;λ) - function describing the distribution for a given value of λ.

For example, if something occurs on average
1.1 times per second (i.e., λ=1.1),
then the probability of 6 occurrences within some specific second (i.e., k=6)
is:

1.1^{6}e^{-1.1}
—————————
6!

(*mathematics,statistics,probability*)
**Further reading:**

https://en.wikipedia.org/wiki/Poisson_distribution

**Referenced by page:**

photon noise

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