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Poisson Distribution. A Poisson random variable is the number of successes that result from a Poisson experiment. The probability distribution of a Poisson random variable is called a Poisson distribution. Given the mean number of successes (Î¼) that occur in a specified region, we can compute the Poisson probability based on the following formula:
A discrete random variable X is said to have a Poisson distribution with parameter Î» k = 0, 1, 2, ..., the probability mass function of X is given by: where. 1  e is Euler's number (e = 2.71828...). 2  k ! is the factorial of k.