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Normal and Poisson Distribution Graphs

Normal and Poisson Distribution Graphs
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2014-04-28 19:28
Probability & Statistics
This example demonstrates the graphical characteristics of normal and Poisson distributions. By adjusting parameters, you can observe how the distribution shapes change. Key mathematical concepts include probability and statistics, specifically the normal and Poisson distributions. GeoGebra commands such as Point, Segment, Intersect, Polygon, and If are used for construction. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 1]) → V
  2. Segment(A, V) → a
  3. Point(xAxis) → W
  4. Intersect(xAxis, yAxis) → Z
  5. Polygon(A, V, W, Z) → poly01, a_1, v, w, z
  6. Point(Circle[B, 1]) → A_1
  7. Segment(B, A_1) → b
  8. Point(xAxis) → B_1
  9. Intersect(w, v) → C_1
  10. Polygon(B, A_1, B_1, C_1) → poly02, b_1, a_2, b_2, c_1
  11. Point(xAxis) → E_1
  12. Point(Circle[C, 1]) → D_1
  13. Segment(C, D_1) → c
  14. Point(Circle[D, 1]) → F_1
  15. Segment(D, F_1) → d
  16. Point(Circle[E, 1]) → G_1
  17. Segment(E, G_1) → e
  18. Point(Circle[G, 1]) → H_1
  19. Segment(G, H_1) → f
  20. Point(Circle[H, 1]) → I_1
  21. Segment(H, I_1) → g
  22. Point(Circle[I, 1]) → J_1
  23. Segment(I, J_1) → h
  24. Point(Circle[J, 1]) → K_1
  25. Segment(J, K_1) → i
  26. Point(Circle[F, 1]) → L_1
  27. Segment(F, L_1) → j
  28. Point(Circle[K, 1]) → M_1
  29. Segment(K, M_1) → k
  30. Point(Circle[L, 1]) → N_1
  31. Segment(L, N_1) → l
  32. Point(Circle[M, 1]) → O_1
  33. Segment(M, O_1) → m
  34. Point(Circle[N, 1]) → P_1
  35. Segment(N, P_1) → q
  36. Point(Circle[O, 1]) → Q_1
  37. Segment(O, Q_1) → r
  38. Point(Circle[P, 1]) → R_1
  39. Segment(P, R_1) → s
  40. Point(Circle[Q, 1]) → S_1
  41. Segment(Q, S_1) → t
  42. Point(Circle[R, 1]) → T_1
  43. Segment(R, T_1) → d_1
  44. Point(Circle[S, 1]) → U_1
  45. Segment(S, U_1) → e_1
  46. Point(Circle[T, 1]) → V_1
  47. Segment(T, V_1) → f_1
  48. Point(Circle[U, 1]) → W_1
  49. Segment(U, W_1) → g_1
  50. Polygon(C, D_1, E_1, B_1) → poly03, c_2, d_2, e_2, b_3
  51. Point(xAxis) → Z_1
  52. Polygon(D, F_1, Z_1, E_1) → poly04, d_3, f_2, z_1, e_3
  53. Point(xAxis) → A_2
  54. Polygon(E, G_1, A_2, Z_1) → poly05, e_4, g_2, a_3, z_2
  55. Point(xAxis) → B_2
  56. Polygon(F, L_1, B_2, A_2) → poly06, f_3, l_1, b_4, a_4
  57. Point(xAxis) → C_2
  58. Polygon(G, H_1, C_2, B_2) → poly07, g_3, h_1, c_3, b_5
  59. Point(xAxis) → D_2
  60. Polygon(H, I_1, D_2, C_2) → poly08, h_2, i_1, d_4, c_4
  61. Point(xAxis) → E_2
  62. Polygon(I, J_1, E_2, D_2) → poly09, i_2, j_1, e_5, d_5
  63. Point(xAxis) → F_2
  64. Polygon(J, K_1, F_2, E_2) → poly10, j_2, k_1, f_4, e_6
  65. Point(xAxis) → G_2
  66. Polygon(K, M_1, G_2, F_2) → poly11, k_2, m_1, g_4, f_5
  67. Point(xAxis) → H_2
  68. Polygon(L, N_1, H_2, G_2) → poly12, l_2, n_1, h_3, g_5
  69. Point(xAxis) → I_2
  70. Polygon(M, O_1, I_2, H_2) → poly13, m_2, o_1, i_3, h_4
  71. Point(xAxis) → J_2
  72. Polygon(N, P_1, J_2, I_2) → poly14, n_2, p_{22}, j_3, i_4
  73. Point(xAxis) → K_2
  74. Polygon(O, Q_1, K_2, J_2) → poly15, o, q_1, k_3, j_4
  75. Point(xAxis) → L_2
  76. Polygon(P, R_1, L_2, K_2) → poly16, p_{24}, r_1, l_3, k_4
  77. Point(xAxis) → M_2
  78. Polygon(Q, S_1, M_2, L_2) → poly17, q_2, s_1, m_3, l_4
  79. Point(xAxis) → N_2
  80. Polygon(R, T_1, N_2, M_2) → poly18, r_2, t_1, n_3, m_4
  81. Point(xAxis) → O_2
  82. Polygon(S, U_1, O_2, N_2) → poly19, s_2, u_1, o_2, n_4
  83. Point(xAxis) → P_2
  84. Polygon(T, V_1, P_2, O_2) → poly20, t_2, v_1, p_{23}, o_3
  85. Point(xAxis) → Q_2
  86. Polygon(U, W_1, Q_2, P_2) → poly21, u, w_1, q_3, p_{21}
  87. Polygon(K, M_1, G_2, F_2) → poly11a, k_5, m_5, g_6, f_6
  88. Polygon(L, N_1, H_2, G_2) → poly12a, l_5, n_5, h_5, g_7
  89. Polygon(M, O_1, I_2, H_2) → poly13a, m_6, o_4, i_5, h_6
  90. Polygon(N, P_1, J_2, I_2) → poly14a, n_6, p_{25}, j_5, i_6
  91. Polygon(O, Q_1, K_2, J_2) → poly15a, o_5, q_4, k_6, j_6
  92. Polygon(P, R_1, L_2, K_2) → poly16a, p_{26}, r_3, l_6, k_7
  93. Polygon(Q, S_1, M_2, L_2) → poly17a, q_5, s_3, m_7, l_7
  94. Polygon(R, T_1, N_2, M_2) → poly18a, r_4, t_3, n_7, m_8
  95. Polygon(S, U_1, O_2, N_2) → poly19a, s_4, u_2, o_6, n_8
  96. Polygon(T, V_1, P_2, O_2) → poly20a, t_4, v_2, p_{27}, o_7
  97. Polygon(U, W_1, Q_2, P_2) → poly21a, u_3, w_2, q_6, p_{28}
  98. Polygon(I, J_1, E_2, D_2) → poly09a, i_7, j_7, e_7, d_6
  99. Polygon(H, I_1, D_2, C_2) → poly08a, h_7, i_8, d_7, c_5
  100. Polygon(J, K_1, F_2, E_2) → poly10a, j_8, k_8, f_7, e_8
  101. Polygon(G, H_1, C_2, B_2) → poly07a, g_8, h_8, c_6, b_6
  102. Polygon(F, L_1, B_2, A_2) → poly06a, f_8, l_8, b_7, a_5
  103. Polygon(E, G_1, A_2, Z_1) → poly05a, e_9, g_9, a_6, z_3
  104. Polygon(D, F_1, Z_1, E_1) → poly04a, d_8, f_9, z_4, e_{10}
  105. Polygon(C, D_1, E_1, B_1) → poly03a, c_7, d_9, e_{11}, b_8
  106. Polygon(B, A_1, B_1, C_1) → poly02a, b_9, a_7, b_{10}, c_8
  107. Polygon(A, V, W, Z) → poly01a, a_8, v_3, w_3, z_5
  108. Segment(mupointhi, mupoint) → muline
  109. If(prob(X) < 0.2, prob(X) + 0.02, 0.2) → ptextheight