Poisson Approximation to Binomial Distribution Visualization

This GeoGebra example demonstrates how the Poisson distribution approximates the binomial distribution when the number of trials n is large and the success probability p is small. The core mathematical concept is the Poisson theorem, stating that as n→∞ with np=λ held constant, the binomial distribution B(n,p) converges to the Poisson distribution P(λ). The construction uses GeoGebra commands Poisson and BinomialDist to generate probability mass functions, with sliders for parameters n and p, and objects b, c, d, binom to adjust and compare the two distributions' bar charts. It is suitable for high school or college probability and statistics courses to illustrate limit theorems and approximation techniques, helping students visually grasp the conditions and error behavior of the Poisson approximation.