Poisson Approximation to the Binomial Distribution

Poisson Approximation to the Binomial Distribution
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2016-03-28 05:24
This example demonstrates the graphical phenomenon of how the Poisson distribution approximates the binomial distribution. Core mathematical concepts involved include the binomial distribution, Poisson distribution, and probability & statistics. Construction highlights using GeoGebra commands/objects: Sequence, BarChart, n (trials), p (success probability), xvals (x values), yvalsbin (binomial y values), b (parameter), lambda (Poisson parameter), yvalspoisson (Poisson y values), a, c, d, text1, text2, text3, e. Suitable for high school and above learning probability statistics and distribution approximation.

GeoGebra Commands & Parameters

  1. Sequence(i, i, 0, n) → xvals
  2. Sequence(BinomialDist[n, p, xvals(i), false], i, 1, n + 1) → yvalsbin
  3. BarChart(xvals, yvalsbin, 0.5) → b
  4. Sequence(Poisson[lambda, xvals(i), false], i, 1, n + 1) → yvalspoisson
  5. BarChart(xvals, yvalspoisson, 0) → a