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Long Run Probability Analysis

Long Run Probability Analysis
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2017-07-16 22:37
SequenceCoordinate GeometryProbability & Statistics
This example demonstrates the concept of long-run probability. It simulates multiple trials to show the stability of probability. Core math concepts include probability and statistics. The construction uses commands like Element, If, Length, Intersect, Point, Segment, Sequence, Textfield, Polygon in GeoGebra. Suitable for high school and above students learning probability and statistics.

GeoGebra Commands & Parameters

  1. Element(recordk, 1) → u_1
  2. If(u_1 ≟ n_1 ∨ u_1 ≟ n_2, 1, 0) → w_1
  3. Element(recordk, 2) → u_2
  4. If(u_2 ≟ n_1 ∨ u_2 ≟ n_2, 1, 0) → w_2
  5. Element(recordk, 20) → u_{20}
  6. Element(recordk, 18) → u_{18}
  7. Element(recordk, 16) → u_{16}
  8. Element(recordk, 14) → u_{14}
  9. Element(recordk, 12) → u_{12}
  10. Element(recordk, 10) → u_{10}
  11. Element(recordk, 8) → u_8
  12. Element(recordk, 6) → u_6
  13. Element(recordk, 5) → u_5
  14. Element(recordk, 4) → u_4
  15. Element(recordk, 3) → u_3
  16. Element(recordk, 7) → u_7
  17. Element(recordk, 9) → u_9
  18. Element(recordk, 11) → u_{11}
  19. Element(recordk, 13) → u_{13}
  20. Element(recordk, 15) → u_{15}
  21. Element(recordk, 17) → u_{17}
  22. Element(recordk, 19) → u_{19}
  23. If(u_{20} ≟ n_1 ∨ u_{20} ≟ n_2, 1, 0) → w_{20}
  24. If(u_{18} ≟ n_1 ∨ u_{18} ≟ n_2, 1, 0) → w_{18}
  25. If(u_{16} ≟ n_1 ∨ u_{16} ≟ n_2, 1, 0) → w_{16}
  26. If(u_{14} ≟ n_1 ∨ u_{14} ≟ n_2, 1, 0) → w_{14}
  27. If(u_{12} ≟ n_1 ∨ u_{12} ≟ n_2, 1, 0) → w_{12}
  28. If(u_{10} ≟ n_1 ∨ u_{10} ≟ n_2, 1, 0) → w_{10}
  29. If(u_8 ≟ n_1 ∨ u_8 ≟ n_2, 1, 0) → w_8
  30. If(u_6 ≟ n_1 ∨ u_6 ≟ n_2, 1, 0) → w_6
  31. If(u_5 ≟ n_1 ∨ u_5 ≟ n_2, 1, 0) → w_5
  32. If(u_4 ≟ n_1 ∨ u_4 ≟ n_2, 1, 0) → w_4
  33. If(u_3 ≟ n_1 ∨ u_3 ≟ n_2, 1, 0) → w_3
  34. If(u_7 ≟ n_1 ∨ u_7 ≟ n_2, 1, 0) → w_7
  35. If(u_9 ≟ n_1 ∨ u_9 ≟ n_2, 1, 0) → w_9
  36. If(u_{11} ≟ n_1 ∨ u_{11} ≟ n_2, 1, 0) → w_{11}
  37. If(u_{13} ≟ n_1 ∨ u_{13} ≟ n_2, 1, 0) → w_{13}
  38. If(u_{15} ≟ n_1 ∨ u_{15} ≟ n_2, 1, 0) → w_{15}
  39. If(u_{17} ≟ n_1 ∨ u_{17} ≟ n_2, 1, 0) → w_{17}
  40. If(u_{19} ≟ n_1 ∨ u_{19} ≟ n_2, 1, 0) → w_{19}
  41. Length(recordk) → s
  42. Intersect(xAxis, yAxis) → A
  43. Point(xAxis) → B
  44. Point(xAxis) → C
  45. Point(xAxis) → D
  46. Point(xAxis) → E
  47. Point(yAxis) → F
  48. Segment(F, A) → f
  49. Segment(B, G) → g
  50. Segment(H, C) → h
  51. Segment(I, D) → i
  52. Segment(E, J) → j
  53. Segment(A, E) → k
  54. Segment(F, J) → l
  55. Sequence(Segment[A + (0, i), E + (0, i)], i, 0, 10) → list1
  56. Sequence(Segment[K + (0, i), O + (0, i)], i, 0, 10) → list2
  57. Segment(P, K) → m
  58. Segment(L, G_1) → n
  59. Segment(M, H_1) → p
  60. Segment(I_1, N) → q
  61. Segment(O, J_1) → r
  62. Segment(J_1, P) → b
  63. Textfield(n_1) → InputBox11
  64. Textfield(n_2) → InputBox12
  65. Polygon(Q_1, Q_2, R, Q) → poly1, q_1, q_2, s_2, q_3
  66. Polygon(S, T, U, V) → poly2, s_1, t_1, u, v

AI Drawing Prompt Reference

Draw a coordinate system with points A, B, C, D, E on the x-axis and point F on the y-axis. Connect F and A to form line segment f. Simulate multiple trials and record the results u_1 to u_20. If u_i equals n_1 or n_2, mark it as 1; otherwise, mark it as 0, using w_i to represent these marks. Plot the distribution of these marks to observe the stability of long-run probability.
The prompt above was compiled from the original drawing commands and is for reference only.