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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:
Binomial / Poisson: If X is a binomial(n, p) random variable and Y is a Poisson(np) distribution then P(X = n) â P(Y = n) if n is large and np is small. For more information, see Poisson approximation to binomial.