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Visualization of Independent Identically Distributed Random Variables

Visualization of Independent Identically Distributed Random Variables
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2015-12-13 17:09
FunctionSequenceIntegralProbability & StatisticsGraphing
This applet visualizes the concept of independent identically distributed (i.i.d.) random variables. It covers core probability concepts such as probability density functions, sampling distributions, and the law of large numbers. Construction utilizes GeoGebra commands like Sequence for data generation, RandomUniform for simulation, and IntegralBetween for area calculation under curves. Objects include distribution curves and statistical data lists. Suitable for high school or college statistics courses to demonstrate theoretical distributions and empirical data convergence.

GeoGebra Commands & Parameters

  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