The Poisson distribution is a discrete probability distribution that depends on one parameter, m. If X is a random variable with the Poisson distribution with parameter m, then the probability that X = k is

E⁻m × mk/k!, k = 0, 1, 2, … ,

where E is the base of the natural logarithm and ! is the factorial function. For all other values of k, the probability is zero.

The expected value the Poisson distribution with parameter m is m, and the standard error of the Poisson distribution with parameter m is m^½.