Poisson Distribution Derivation from Binomial Distribution

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The Poisson distribution is derived as a limiting case of the binomial distribution. When we have a large number of trials n, a small probability p, but keep the product lambda equals n times p constant, the binomial distribution converges to the Poisson distribution. This graph shows how closely a binomial distribution with n equals 100 and p equals 0.05 approximates a Poisson distribution with lambda equals 5.