Poisson distribution

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)

   λke-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:

 1.16e-1.1
—————————
   6!