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Goals per game in the Premier League - Poisson Distribution

Goals per game in the Premier League - Poisson Distribution
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2018-07-01 18:57
FunctionCalculusProbability & StatisticsOptimizationGraphing
This example demonstrates the Poisson distribution model for goals per game in the Premier League, visually showing how the probability of goals changes with the mean λ. Key math concepts include Poisson distribution, probability & statistics, function graphing, bar chart, and tangent line. GeoGebra commands used are Normal and Segment, with objects like λ (parameter), f, g (functions), and points a-g, B1-A17 (auxiliary), C3-C15 (locus). Suitable for high school and above, helping learners understand the connection between discrete and continuous distributions and the impact of parameters on distribution shape.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a Poisson distribution function graph showing the probability distribution of goals per game in the Premier League. Set parameter λ and draw function g to represent the Poisson distribution. Draw 6 vertical segments on the x-axis from 1 to 6, each corresponding to an integer x value, with lengths equal to f(x). Then, draw 25 vertical segments on the x-axis from 7 to 31, each corresponding to an x value, with lengths equal to f(x). Finally, draw two horizontal segments parallel to the x-axis at x=1.2 and x=2.2, with lengths equal to f(1) and f(2).
The prompt above was compiled from the original drawing commands and is for reference only.