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二项分布及其正态近似与泊松近似

二项分布及其正态近似与泊松近似
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2017-12-12 01:29
数列概率统计参数方程
这个范例用于演示二项分布，用户可以控制n和p的值。它展示了正态近似曲线（对于某些情况会失效）。该范例涉及二项分布、概率统计和参数方程。使用了Sequence, If, Polygon, Line, Sum, Integral等GeoGebra命令。适合高中数学教学和学习。

GeoGebra 命令及参数

  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