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Poisson Probability Simulation

Poisson Probability Simulation
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2013-02-21 11:22
FunctionCoordinate GeometryProbability & Statistics
In collections Probability & Statistics
This example demonstrates two-dimensional uniform random distributions and generates Poisson probability distribution examples. Key math concepts include probability & statistics, Poisson distribution, and uniform distribution. It utilizes GeoGebra commands like Sequence, Max, CountIf, Element, Textfield, and If. Suitable for high school students and probability statistics education.

GeoGebra Commands & Parameters

  1. Sequence((RandomUniform[0, n], RandomUniform[0, n]), i, 1, m) → list3
  2. Sequence(Sequence[CountIf[(x(A) > i - 1) ∧ (x(A) < i) ∧ (y(A) > j - 1) ∧ (y(A) < j), A, list3], i, 1, n], j, 1, n) → matrix1
  3. Sequence(Max[Sequence[Element[matrix1, i, j], j, 1, n]], i, 1, n) → list4
  4. Max(list4) → a
  5. Sequence(Element[matrix1, 1, j], j, 1, n) → list5
  6. CountIf(12 ≤ x ≤ 12, list5) → b
  7. Sequence(Sequence[CountIf[k ≤ x ≤ k, Sequence[Element[matrix1, i, j], j, 1, n]], i, 1, n], k, 0, a) → c
  8. Element(c, 10, 9) → d
  9. Element(c, 6, 3) → e
  10. Sequence(Sum[Sequence[Element[c, i, j], j, 1, n]], i, 1, a + 1) → list6
  11. Sequence(Segment[(0, i), (n, i)], i, 0, n) → list1
  12. Sequence(Segment[(i, 0), (i, n)], i, 0, n) → list2
  13. Textfield(n) → inputBox1
  14. Textfield(m) → inputBox2
  15. Element(list6, A3 + 1) → j
  16. If(A3 ≤ a, Element[list6, A3 + 1], 0) → B3
  17. If(A4 ≤ a, Element[list6, A4 + 1], 0) → B4
  18. If(A5 ≤ a, Element[list6, A5 + 1], 0) → B5
  19. If(A6 ≤ a, Element[list6, A6 + 1], 0) → B6
  20. If(A7 ≤ a, Element[list6, A7 + 1], 0) → B7
  21. If(A8 ≤ a, Element[list6, A8 + 1], 0) → B8
  22. If(A9 ≤ a, Element[list6, A9 + 1], 0) → B9
  23. If(A10 ≤ a, Element[list6, A10 + 1], 0) → B10
  24. If(A11 ≤ a, Element[list6, A11 + 1], 0) → B11
  25. If(A12 ≤ a, Element[list6, A12 + 1], 0) → B12
  26. If(A13 ≤ a, Element[list6, A13 + 1], 0) → B13
  27. If(A14 ≤ a, Element[list6, A14 + 1], 0) → B14
  28. If(A15 ≤ a, Element[list6, A15 + 1], 0) → B15
  29. If(A16 ≤ a, Element[list6, A16 + 1], 0) → B16
  30. If(A17 ≤ a, Element[list6, A17 + 1], 0) → B17
  31. If(A18 ≤ a, Element[list6, A18 + 1], 0) → B18
  32. If(A19 ≤ a, Element[list6, A19 + 1], 0) → B19
  33. If(A20 ≤ a, Element[list6, A20 + 1], 0) → B20
  34. If(A21 ≤ a, Element[list6, A21 + 1], 0) → B21
  35. If(A22 ≤ a, Element[list6, A22 + 1], 0) → B22
  36. If(A23 ≤ a, Element[list6, A23 + 1], 0) → B23
  37. If(A24 ≤ a, Element[list6, A24 + 1], 0) → B24
  38. If(A25 ≤ a, Element[list6, A25 + 1], 0) → B25
  39. If(A26 ≤ a, Element[list6, A26 + 1], 0) → B26
  40. If(A27 ≤ a, Element[list6, A27 + 1], 0) → B27
  41. If(A28 ≤ a, Element[list6, A28 + 1], 0) → B28
  42. If(A29 ≤ a, Element[list6, A29 + 1], 0) → B29
  43. If(A30 ≤ a, Element[list6, A30 + 1], 0) → B30
  44. If(A31 ≤ a, Element[list6, A31 + 1], 0) → B31
  45. If(A32 ≤ a, Element[list6, A32 + 1], 0) → B32
  46. If(A33 ≤ a, Element[list6, A33 + 1], 0) → B33
  47. If(A34 ≤ a, Element[list6, A34 + 1], 0) → B34
  48. If(A35 ≤ a, Element[list6, A35 + 1], 0) → B35
  49. If(A36 ≤ a, Element[list6, A36 + 1], 0) → B36
  50. If(A37 ≤ a, Element[list6, A37 + 1], 0) → B37
  51. If(A38 ≤ a, Element[list6, A38 + 1], 0) → B38
  52. If(A39 ≤ a, Element[list6, A39 + 1], 0) → B39
  53. If(A40 ≤ a, Element[list6, A40 + 1], 0) → B40
  54. If(A41 ≤ a, Element[list6, A41 + 1], 0) → B41
  55. If(A42 ≤ a, Element[list6, A42 + 1], 0) → B42
  56. If(A43 ≤ a, Element[list6, A43 + 1], 0) → B43
  57. If(A44 ≤ a, Element[list6, A44 + 1], 0) → B44
  58. If(A45 ≤ a, Element[list6, A45 + 1], 0) → B45
  59. If(A46 ≤ a, Element[list6, A46 + 1], 0) → B46
  60. If(A47 ≤ a, Element[list6, A47 + 1], 0) → B47
  61. If(A48 ≤ a, Element[list6, A48 + 1], 0) → B48
  62. If(A49 ≤ a, Element[list6, A49 + 1], 0) → B49
  63. If(A50 ≤ a, Element[list6, A50 + 1], 0) → B50
  64. If(A51 ≤ a, Element[list6, A51 + 1], 0) → B51
  65. If(A52 ≤ a, Element[list6, A52 + 1], 0) → B52
  66. If(A53 ≤ a, Element[list6, A53 + 1], 0) → B53
  67. If(A54 ≤ a, Element[list6, A54 + 1], 0) → B54
  68. If(A55 ≤ a, Element[list6, A55 + 1], 0) → B55
  69. If(A56 ≤ a, Element[list6, A56 + 1], 0) → B56
  70. If(A57 ≤ a, Element[list6, A57 + 1], 0) → B57
  71. If(A58 ≤ a, Element[list6, A58 + 1], 0) → B58
  72. If(A59 ≤ a, Element[list6, A59 + 1], 0) → B59
  73. If(A60 ≤ a, Element[list6, A60 + 1], 0) → B60
  74. If(A61 ≤ a, Element[list6, A61 + 1], 0) → B61
  75. If(A62 ≤ a, Element[list6, A62 + 1], 0) → B62
  76. If(A63 ≤ a, Element[list6, A63 + 1], 0) → B63
  77. If(A64 ≤ a, Element[list6, A64 + 1], 0) → B64
  78. If(A65 ≤ a, Element[list6, A65 + 1], 0) → B65
  79. If(A66 ≤ a, Element[list6, A66 + 1], 0) → B66
  80. If(A67 ≤ a, Element[list6, A67 + 1], 0) → B67
  81. If(A68 ≤ a, Element[list6, A68 + 1], 0) → B68
  82. If(A69 ≤ a, Element[list6, A69 + 1], 0) → B69
  83. If(A70 ≤ a, Element[list6, A70 + 1], 0) → B70
  84. If(A71 ≤ a, Element[list6, A71 + 1], 0) → B71
  85. If(A72 ≤ a, Element[list6, A72 + 1], 0) → B72
  86. If(A73 ≤ a, Element[list6, A73 + 1], 0) → B73
  87. If(A74 ≤ a, Element[list6, A74 + 1], 0) → B74
  88. If(A75 ≤ a, Element[list6, A75 + 1], 0) → B75
  89. If(A76 ≤ a, Element[list6, A76 + 1], 0) → B76
  90. If(A77 ≤ a, Element[list6, A77 + 1], 0) → B77
  91. If(A78 ≤ a, Element[list6, A78 + 1], 0) → B78
  92. If(A79 ≤ a, Element[list6, A79 + 1], 0) → B79
  93. If(A80 ≤ a, Element[list6, A80 + 1], 0) → B80
  94. If(A81 ≤ a, Element[list6, A81 + 1], 0) → B81
  95. If(A82 ≤ a, Element[list6, A82 + 1], 0) → B82
  96. If(A83 ≤ a, Element[list6, A83 + 1], 0) → B83
  97. If(A84 ≤ a, Element[list6, A84 + 1], 0) → B84
  98. If(A85 ≤ a, Element[list6, A85 + 1], 0) → B85
  99. If(A86 ≤ a, Element[list6, A86 + 1], 0) → B86
  100. If(A87 ≤ a, Element[list6, A87 + 1], 0) → B87
  101. If(A88 ≤ a, Element[list6, A88 + 1], 0) → B88
  102. If(A89 ≤ a, Element[list6, A89 + 1], 0) → B89
  103. If(A90 ≤ a, Element[list6, A90 + 1], 0) → B90
  104. If(A91 ≤ a, Element[list6, A91 + 1], 0) → B91
  105. If(A92 ≤ a, Element[list6, A92 + 1], 0) → B92
  106. If(A93 ≤ a, Element[list6, A93 + 1], 0) → B93
  107. If(A94 ≤ a, Element[list6, A94 + 1], 0) → B94
  108. If(A95 ≤ a, Element[list6, A95 + 1], 0) → B95
  109. If(A96 ≤ a, Element[list6, A96 + 1], 0) → B96
  110. If(A97 ≤ a, Element[list6, A97 + 1], 0) → B97
  111. If(A98 ≤ a, Element[list6, A98 + 1], 0) → B98
  112. If(A99 ≤ a, Element[list6, A99 + 1], 0) → B99
  113. If(A100 ≤ a, Element[list6, A100 + 1], 0) → B100
  114. If(A101 ≤ a, Element[list6, A101 + 1], 0) → B101
  115. If(A102 ≤ a, Element[list6, A102 + 1], 0) → B102
  116. If(A103 ≤ a, Element[list6, A103 + 1], 0) → B103

AI Drawing Prompt Reference

Generate a scatter plot of two-dimensional uniform random distributions within a square of side length n. Count the number of points in each small square to form a matrix. Identify the maximum value a and draw a bar chart to represent the probability distribution of points in each square. Highlight bars with probability value a and color-code bars based on their probability values.
The prompt above was compiled from the original drawing commands and is for reference only.