积极 AI Logo 积极 AI

独立同分布随机变量可视化演示 by University of Melbourne School of Mathematics and Statistics

独立同分布随机变量可视化演示 by University of Melbourne School of Mathematics and Statistics
几何画板及绘图内容加载中，请稍等……
2015-12-13 17:09
函数数列积分概率统计函数图像
本范例旨在直观演示独立同分布随机变量的统计规律与分布特性。核心数学概念涵盖概率论中的独立同分布假设、样本均值收敛及概率密度函数。作图要点在于使用 GeoGebra 的 Sequence 命令生成序列数据，结合 RandomUniform 模拟随机采样，并通过 IntegralBetween 计算积分区域以展示分布曲线。此外，利用 Translate 和 Segment 对象辅助可视化数据点与统计量。该工具适合高中或大学阶段概率统计课程的教学演示及学生自主探究学习，帮助理解大数定律与中心极限定理的基础。

GeoGebra 命令及参数

  1. Sequence(If[distribution ≟ 1, RandomNormal[0.5, 0.13], InverseGamma[α, β, RandomUniform[0, 1]]], i, 1, 1000) → datalist3raw
  2. Sequence(If[distribution ≟ 1, RandomNormal[0.5, 0.13], InverseGamma[α, β, RandomUniform[0, 1]]], i, 1, 1000) → datalist2raw
  3. Sequence(If[distribution ≟ 1, RandomNormal[0.5, 0.13], InverseGamma[α, β, RandomUniform[0, 1]]], i, 1, 1000) → datalist1raw
  4. Zip((xx + yy + zz) / 3, xx, datalist1, yy, datalist2, zz, datalist3) → meanlistraw
  5. Element(datalist1, experiment) → x1active
  6. If(distribution ≟ 1, F1, F2) → F
  7. RandomUniform(4.5, F(x1active)) → y1
  8. Element(datalist2, experiment) → x2active
  9. RandomUniform(4.5, F(x2active)) → y2
  10. Element(datalist3, experiment) → x3active
  11. RandomUniform(4.5, F(x3active)) → y3
  12. Element(datalist3, 4) → x43
  13. Element(datalist3, 3) → x33
  14. Element(datalist3, 2) → x23
  15. Element(datalist3, 1) → x13
  16. Element(datalist2, 4) → x42
  17. Element(datalist2, 3) → x32
  18. Element(datalist2, 2) → x22
  19. Element(datalist2, 1) → x12
  20. Element(datalist1, 4) → x41
  21. Element(datalist1, 3) → x31
  22. Element(datalist1, 2) → x21
  23. Element(datalist1, 1) → x11
  24. Element(meanlist, 1) → m1
  25. Element(meanlist, 2) → m2
  26. If(distribution ≟ 1, ((x - 0.5) / 0.13 * 8) + 168, (x * 100)) → scalefunc
  27. If(distribution ≟ 1, "cm", "k") → units
  28. Element({x11dp, x21dp, x31dp, x41dp}, experiment) → x1dpactive
  29. Element({x12dp, x22dp, x32dp, x42dp}, experiment) → x2dpactive
  30. Element({x13dp, x23dp, x33dp, x43dp}, experiment) → x3dpactive
  31. Element(meanlist, 3) → m3
  32. Element(meanlist, 4) → m4
  33. Element({m1dp, m2dp, m3dp, m4dp}, experiment) → mdpactive
  34. Translate(DotPlot[Take[datalist2, 1, experiment], false, 0.006], (0, 2 + dpscale / 2)) → datalist2_{dp}underlayer
  35. Translate(DotPlot[Take[datalist1, 1, experiment], false, 0.006], (0, 3 + dpscale / 2)) → datalist1_{dp}underlayer
  36. Translate(DotPlot[Take[datalist3, 1, experiment], false, 0.006], (0, 1 + dpscale / 2)) → datalist3_{dp}underlayer
  37. Segment((0, 4.5), (1, 4.5)) → a
  38. IntegralBetween(4.5, F, 0, 1, false) → c
  39. Segment((0, 0), (1, 0)) → maxis
  40. If(distribution ≟ 1, "", "\$") → dollars
  41. Translate(F, (0, (-1.5 * t51))) → x1F
  42. Translate(F, (0, (-2.5 * t51))) → x2F
  43. Translate(F, (0, (-3.5 * t51))) → x3F
  44. If(distribution ≟ 1, M1, M2) → M
  45. Segment((0, 4.5), (0, 4.45)) → tick1
  46. Segment((1, 4.5), (1, 4.45)) → tick3
  47. Segment((0.5, 4.5), (0.5, 4.45)) → tick2
  48. Segment((0, 2.99), (1, 2.99)) → x1axis
  49. Segment((0, 1.99), (1, 1.99)) → x2axis
  50. Segment((0, 0.99), (1, 0.99)) → x3axis
  51. Translate(DotPlot[Take[meanlist, 1, experiment], false, 0.006], (0, dpscale / 2)) → Mean_{dp}
  52. Segment((0, 4.5), (0, 0)) → guideline1
  53. Segment((1, 4.5), (1, 0)) → guideline2
  54. Segment((0.5, 4.5), (0.5, 0)) → guideline3