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Binomial Distribution with Normal and Poisson Approximation by gesges

Binomial Distribution with Normal and Poisson Approximation by gesges
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2014-09-24 14:14
FunctionSequenceProbability & Statistics
This applet visualizes the Binomial Distribution and its Normal and Poisson approximations. By adjusting parameters n and p, you can observe changes in the distribution curves. It uses GeoGebra commands such as Sequence, If, Polygon, Line, Sum, and Integral for construction. Suitable for high school and above students or teachers for probability and statistics education.

GeoGebra Commands & Parameters

  1. Sequence(Polygon[(i - 0.475, 0), (i - 0.475, ((Binomial[n, i] * p^(i)) * (1 - p)^(n - i))), (i + 0.45, ((Binomial[n, i] * p^(i)) * (1 - p)^(n - i))), (i + 0.45, 0)], i, 0, n) → list1
  2. If(b, Max[list1] / 0.925, 1) → a
  3. If(b, 1, 0) → c
  4. Polygon((-2, 1.05), (-2, 1.6), (103, 1.6), (103, 1.05)) → poly1, f, g, h, i
  5. Sequence(Polygon[(i - 0.475, 0), (i - 0.475, ((Binomial[n, i] * p^(i)) * (1 - p)^(n - i))), (i + 0.45, ((Binomial[n, i] * p^(i)) * (1 - p)^(n - i))), (i + 0.45, 0)], i, 0, criticallow) → list2
  6. Sequence(Polygon[(i - 0.475, 0), (i - 0.475, ((Binomial[n, i] * p^(i)) * (1 - p)^(n - i))), (i + 0.45, ((Binomial[n, i] * p^(i)) * (1 - p)^(n - i))), (i + 0.45, 0)], i, criticalhigh, n) → list3
  7. Line(A, B) → k
  8. If(n ≤ 20, 20, n) → xmax
  9. Sequence(Polygon[(i - 0.475, 0), (i - 0.475, (ℯ^(((-n) * p)) * ((n * p))^(i) / i!)), (i + 0.45, (ℯ^(((-n) * p)) * ((n * p))^(i) / i!)), (i + 0.45, 0)], i, 0, n) → list4
  10. Sequence(((Binomial[n, i] * p^(i)) * (1 - p)^(n - i)), i, 0, criticallow) → criticallowsequence
  11. Sum(criticallowsequence) → criticallowvalue
  12. Sequence(((Binomial[n, i] * p^(i)) * (1 - p)^(n - i)), i, criticalhigh, n) → criticalhighsequence
  13. Sum(criticalhighsequence) → criticalhighvalue
  14. If(d, criticallow + 1, 0) → criticalhighslidermin
  15. Polygon((m - 0.475, 0), (m - 0.475, ((Binomial[n, m] * p^(m)) * (1 - p)^(n - m))), (m + 0.45, ((Binomial[n, m] * p^(m)) * (1 - p)^(n - m))), (m + 0.45, 0)) → poly2, r, s, t, a_1
  16. Integral(q, -50, criticallow + 0.5) → criticallownormal
  17. Integral(q, criticalhigh - 0.5, n + 50) → criticalhighnormal

AI Drawing Prompt Reference

Draw the binomial distribution and its normal and Poisson approximations. First, plot the binomial distribution bars based on parameters n and p. Then, adjust n and p to observe changes in the distribution curves. Next, shade the area for the normal approximation and mark its upper and lower bounds. Finally, plot the Poisson approximation bars and adjust n and p to observe changes.
The prompt above was compiled from the original drawing commands and is for reference only.