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英超每场进球数 - 泊松分布

英超每场进球数 - 泊松分布
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2018-07-01 18:57
函数微积分概率统计最值优化函数图像
①本范例演示英超联赛每场进球数的泊松分布概率模型，通过图表直观展示进球数的概率随平均值λ的变化；②核心数学概念包括泊松分布、概率统计、函数图像、直方图与切线；③作图要点运用了GeoGebra命令Normal（正态分布）、Segment（线段）及对象λ（参数）、f, g（函数）、a-g（坐标点）、B1-A17（辅助点）、C3-C15（轨迹点）；④适合高中及以上数学学习者，用于理解离散概率分布与连续分布的关联及参数对分布形态的影响。

GeoGebra 命令及参数

  1. Normal(λ, sqrt(λ), x, false) → g
  2. Segment((1, 0), (1, f(1))) → a
  3. Segment((2, 0), (2, f(2))) → b
  4. Segment((3, 0), (3, f(3))) → c
  5. Segment((4, 0), (4, f(4))) → d
  6. Segment((5, 0), (5, f(5))) → e
  7. Segment((6, 0), (6, f(6))) → h
  8. Segment((A2, 0), (A2, f(A2))) → C2
  9. Segment((A3, 0), (A3, f(A3))) → C3
  10. Segment((A4, 0), (A4, f(A4))) → C4
  11. Segment((A5, 0), (A5, f(A5))) → C5
  12. Segment((A6, 0), (A6, f(A6))) → C6
  13. Segment((A7, 0), (A7, f(A7))) → C7
  14. Segment((A8, 0), (A8, f(A8))) → C8
  15. Segment((A9, 0), (A9, f(A9))) → C9
  16. Segment((A10, 0), (A10, f(A10))) → C10
  17. Segment((A11, 0), (A11, f(A11))) → C11
  18. Segment((A12, 0), (A12, f(A12))) → C12
  19. Segment((A13, 0), (A13, f(A13))) → C13
  20. Segment((A14, 0), (A14, f(A14))) → C14
  21. Segment((A15, 0), (A15, f(A15))) → C15
  22. Segment((A16, 0), (A16, f(A16))) → C16
  23. Segment((A17, 0), (A17, f(A17))) → C17
  24. Segment((A18, 0), (A18, f(A18))) → C18
  25. Segment((A19, 0), (A19, f(A19))) → C19
  26. Segment((A20, 0), (A20, f(A20))) → C20
  27. Segment((A21, 0), (A21, f(A21))) → C21
  28. Segment((A22, 0), (A22, f(A22))) → C22
  29. Segment((A23, 0), (A23, f(A23))) → C23
  30. Segment((A24, 0), (A24, f(A24))) → C24
  31. Segment((A25, 0), (A25, f(A25))) → C25
  32. Segment((A26, 0), (A26, f(A26))) → C26
  33. Segment((A27, 0), (A27, f(A27))) → C27
  34. Segment((A28, 0), (A28, f(A28))) → C28
  35. Segment((A29, 0), (A29, f(A29))) → C29
  36. Segment((A30, 0), (A30, f(A30))) → C30
  37. Segment((A31, 0), (A31, f(A31))) → C31
  38. Segment((A2 + 0.2, 0), (A2 + 0.2, E2)) → F2
  39. Segment((A3 + 0.2, 0), (A3 + 0.2, E3)) → F3
  40. Segment((A4 + 0.2, 0), (A4 + 0.2, E4)) → F4
  41. Segment((A5 + 0.2, 0), (A5 + 0.2, E5)) → F5
  42. Segment((A6 + 0.2, 0), (A6 + 0.2, E6)) → F6
  43. Segment((A7 + 0.2, 0), (A7 + 0.2, E7)) → F7
  44. Segment((A8 + 0.2, 0), (A8 + 0.2, E8)) → F8
  45. Segment((A9 + 0.2, 0), (A9 + 0.2, E9)) → F9
  46. Segment((A10 + 0.2, 0), (A10 + 0.2, E10)) → F10
  47. Segment((A11 + 0.2, 0), (A11 + 0.2, E11)) → F11
  48. Segment((A12 + 0.2, 0), (A12 + 0.2, E12)) → F12
  49. Segment((A13 + 0.2, 0), (A13 + 0.2, E13)) → F13
  50. Segment((A14 + 0.2, 0), (A14 + 0.2, E14)) → F14
  51. Segment((A15 + 0.2, 0), (A15 + 0.2, E15)) → F15
  52. Segment((A2 + 0.1, 0), (A2 + 0.1, H2)) → I2
  53. Segment((A3 + 0.1, 0), (A3 + 0.1, H3)) → I3
  54. Segment((A4 + 0.1, 0), (A4 + 0.1, H4)) → I4
  55. Segment((A5 + 0.1, 0), (A5 + 0.1, H5)) → I5
  56. Segment((A6 + 0.1, 0), (A6 + 0.1, H6)) → I6
  57. Segment((A7 + 0.1, 0), (A7 + 0.1, H7)) → I7
  58. Segment((A8 + 0.1, 0), (A8 + 0.1, H8)) → I8
  59. Segment((A9 + 0.1, 0), (A9 + 0.1, H9)) → I9
  60. Segment((A10 + 0.1, 0), (A10 + 0.1, H10)) → I10
  61. Segment((A11 + 0.1, 0), (A11 + 0.1, H11)) → I11
  62. Segment((A12 + 0.1, 0), (A12 + 0.1, H12)) → I12
  63. Segment((A13 + 0.1, 0), (A13 + 0.1, H13)) → I13
  64. Segment((A14 + 0.1, 0), (A14 + 0.1, H14)) → I14
  65. Segment((A15 + 0.1, 0), (A15 + 0.1, H15)) → I15
  66. Segment((A2 + 0.3, 0), (A2 + 0.3, E19)) → F19
  67. Segment((A3 + 0.3, 0), (A3 + 0.3, E20)) → F20
  68. Segment((A4 + 0.3, 0), (A4 + 0.3, E21)) → F21
  69. Segment((A5 + 0.3, 0), (A5 + 0.3, E22)) → F22
  70. Segment((A6 + 0.3, 0), (A6 + 0.3, E23)) → F23
  71. Segment((A7 + 0.3, 0), (A7 + 0.3, E24)) → F24
  72. Segment((A8 + 0.3, 0), (A8 + 0.3, E25)) → F25
  73. Segment((A9 + 0.3, 0), (A9 + 0.3, E26)) → F26
  74. Segment((A10 + 0.3, 0), (A10 + 0.3, E27)) → F27
  75. Segment((A11 + 0.3, 0), (A11 + 0.3, E28)) → F28
  76. Segment((A12 + 0.3, 0), (A12 + 0.3, E29)) → F29
  77. Segment((A13 + 0.3, 0), (A13 + 0.3, E30)) → F30
  78. Segment((A14 + 0.3, 0), (A14 + 0.3, E31)) → F31
  79. Segment((A15 + 0.3, 0), (A15 + 0.3, E32)) → F32
  80. Segment((A2 + 0.4, 0), (A2 + 0.4, H19)) → I19
  81. Segment((A3 + 0.4, 0), (A3 + 0.4, H20)) → I20
  82. Segment((A4 + 0.4, 0), (A4 + 0.4, H21)) → I21
  83. Segment((A5 + 0.4, 0), (A5 + 0.4, H22)) → I22
  84. Segment((A6 + 0.4, 0), (A6 + 0.4, H23)) → I23
  85. Segment((A7 + 0.4, 0), (A7 + 0.4, H24)) → I24
  86. Segment((A8 + 0.4, 0), (A8 + 0.4, H25)) → I25
  87. Segment((A9 + 0.4, 0), (A9 + 0.4, H26)) → I26
  88. Segment((A10 + 0.4, 0), (A10 + 0.4, H27)) → I27
  89. Segment((A11 + 0.4, 0), (A11 + 0.4, H28)) → I28
  90. Segment((A12 + 0.4, 0), (A12 + 0.4, H29)) → I29
  91. Segment((A13 + 0.4, 0), (A13 + 0.4, H30)) → I30
  92. Segment((A14 + 0.4, 0), (A14 + 0.4, H31)) → I31
  93. Segment((A15 + 0.4, 0), (A15 + 0.4, H32)) → I32

AI 绘图提示语参考

画一个泊松分布函数图，表示英超联赛每场比赛进球数的概率分布。设置参数λ，绘制函数g表示泊松分布。在x轴上从1到6绘制6条垂直线段，每条线段对应一个整数x值，长度为f(x)。在x轴上从7到31绘制25条垂直线段，每条线段对应一个x值，长度为f(x)。最后，绘制两条平行于x轴的线段，分别位于x=1.2和x=2.2，长度为f(1)和f(2)。
以上提示语为根据原始绘图命令整理而来，仅供参考。