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条件概率与超几何分布的 GeoGebra 演示

条件概率与超几何分布的 GeoGebra 演示
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2018-07-04 15:47
概率统计矩阵几何作图
所属专题 Pearson Maths A level Statistics and Mechanics 2 Pearson Maths A level Statistics and Mechanics 2 Pearson Maths A level Statistics and Mechanics 2
①本范例通过 GeoGebra 动态演示条件概率的计算与超几何分布的应用；②涉及核心数学概念包括条件概率、超几何分布、矩阵运算及积分计算；③作图要点运用了 Point, Circle, Intersect, Integral, IntegralBetween, Polygon, PolyLine, LaTeX, IndexOf, Defined 等命令与对象，实现图形交互与公式展示；④适合高中及以上数学学习者，用于理解概率统计与几何结合的应用场景。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Circle(A, 2) → c
  3. Intersect(c, xAxis, 2) → B
  4. Circle(B, 2) → d
  5. Intersect(c, d, 2) → C
  6. Circle(C, 2) → e
  7. Intersect(c, d, 1) → D
  8. Intersect(d, e, 1) → E
  9. Intersect(c, e, 2) → F
  10. Intersect(c, xAxis, 1) → G
  11. Intersect(d, xAxis, 2) → H
  12. Integral(h, -3, -1) → a
  13. IntegralBetween(h, g, -1, 0) → b
  14. Integral(hh, -3, -2) → i
  15. Integral(p, -2, -1) → j
  16. IntegralBetween(g, p, -1, 0) → k
  17. IntegralBetween(h, p, 0, 1) → l
  18. IntegralBetween(g, h, 0, 1) → m
  19. Integral(g, 1, 3) → n
  20. Integral(gg, 2, 3) → o
  21. Integral(p, 1, 2) → q
  22. IntegralBetween(hh, pp, -2, 0) → r
  23. IntegralBetween(gg, pp, 0, 2) → s
  24. IntegralBetween(p, hh, -2, -1) → t
  25. IntegralBetween(gg, hh, -1, 0) → u
  26. IntegralBetween(hh, gg, 0, 1) → v
  27. IntegralBetween(p, gg, 1, 2) → w
  28. Integral(p, -1, 1) → a_1
  29. Integral(gg, -1, 0) → b_1
  30. Polygon((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5)) → poly1, f_1, g_1, h_1, i_1
  31. PolyLine((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5), (-4.5, 2.5)) → j_1
  32. Integral(hh, 0, 1) → ccc
  33. LaTeX("A \cap \left( B \cup C \right)' ") → C1
  34. LaTeX("B\cap \left( A \cup C \right)' ") → C2
  35. LaTeX("C \cap \left( A \cup B \right)' ") → C3
  36. LaTeX("A \cap B") → C4
  37. LaTeX("B \cap C") → C5
  38. LaTeX("A \cap C") → C6
  39. LaTeX("A \cap B \cap C") → C7
  40. LaTeX("\left(A \cup B \cup C\right)' ") → C8
  41. LaTeX("A") → C9
  42. LaTeX("B") → C10
  43. LaTeX("C") → C11
  44. LaTeX("C' ") → C13
  45. LaTeX("\left( B \cup C \right)' ") → C15
  46. LaTeX("\left( A \cup C \right)' ") → C16
  47. LaTeX("\left( A \cup B \right)' ") → C17
  48. LaTeX("A \cap C' ") → C19
  49. LaTeX("B \cap C' ") → C20
  50. LaTeX("B\cap A' ") → C21
  51. LaTeX("C \cap A' ") → C22
  52. LaTeX("C \cap B' ") → C23
  53. LaTeX("A \cap B' ") → C24
  54. LaTeX("\left(A\cup B\right) \cap C' ") → C25
  55. LaTeX("\left(B\cup C\right) \cap A' ") → C26
  56. LaTeX("\left(A\cup C\right) \cap B' ") → C27
  57. LaTeX("A' ") → C12
  58. LaTeX("B' ") → C14
  59. LaTeX("\left(A \cap B \right) \cup \left(A \cap C \right) \cup \left(B \cap C \right)") → C28
  60. LaTeX("\text{Try buttons 1 and 2}") → C18
  61. IndexOf(true, L_1) → d_1
  62. Defined(d_1) → e_1

AI 绘图提示语参考

画一个动态演示条件概率和超几何分布的图形，包含两个同心圆和它们的交点，以及多个积分区域，用不同颜色或线条区分，并显示相关的概率公式和集合运算符号，展示条件概率和超几何分布的应用。
以上提示语为根据原始绘图命令整理而来，仅供参考。