Astrophysics (index)

Poisson Distribution

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

The Poisson Distribution gives the probability of how many events will happen within a given interval for events that are independent but happen with a fixed probability. It is named for French mathematician Siméon Denis Poisson.


= probability(X = k)

= ——————
  • X - random variable which can have any value 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:



Referenced by:
Photon Noise