Poisson Distribution Derivation from Binomial: Formulas and Plots
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Welcome to our exploration of how the Poisson distribution emerges from the binomial distribution. The binomial distribution describes the number of successes in n independent trials, each with probability p. When we let n approach infinity while p approaches zero, but keep their product np constant at lambda, something remarkable happens - the binomial distribution transforms into the Poisson distribution. This limiting process reveals one of the most elegant connections in probability theory.