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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 random variable that takes values in a countable set \(S\) is said to have a discrete distribution. Typically, \(S \subseteq \R^n\) for some \(n \in \N_+\), so in particular, if \(n \gt 1\), \(X\) is vector-valued. In the picture below, the blue dots are intended to represent points of positive probability.