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Demonstrating Continuous Models for Discrete Random Variables

Demonstrating Continuous Models for Discrete Random Variables
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2014-01-30 22:34
FunctionSequenceCalculusProbability & StatisticsGraphing
This example illustrates how discrete random variables can be better modeled using a continuous approach. It involves core math concepts like Probability Density Functions, Distributions, Statistical Characteristics, and Linear Regression. GeoGebra commands and objects used include Function, Sequence, and BarChart for constructing the visualizations. Suitable for high school and above students, or educational purposes needing to understand continuous probability models.

GeoGebra Commands & Parameters

  1. Function(1, 0, 1) → f
  2. Function(-2 * x + 2, 0, 1) → g
  3. Function(-6 * x * (x - 1), 0, 1) → h
  4. Sequence(n * Integral[h, i / n, (i + 1) / n], i, 0, n - 1) → intsh
  5. BarChart(0, 1, intsh) → charth
  6. Sequence(n * Integral[g, i / n, (i + 1) / n], i, 0, n - 1) → intsg
  7. Sequence(n * Integral[f, i / n, (i + 1) / n], i, 0, n - 1) → intsf
  8. BarChart(0, 1, intsg) → chartg
  9. BarChart(0, 1, intsf) → chartf
  10. BarChart(0, 1, intsf) → chartfbor
  11. BarChart(0, 1, intsg) → chartgbor
  12. BarChart(0, 1, intsh) → charthbor
  13. Sequence(Element[intsf, i], i, 1, n * m) → intsfm
  14. BarChart(0, m, intsfm) → chartfm
  15. BarChart(0, m, intsfm) → chartfmbor
  16. Sequence(Element[intsg, i], i, 1, n * m) → intsgm
  17. Sequence(Element[intsh, i], i, 1, n * m) → intshm
  18. BarChart(0, m, intsgm) → chartgm
  19. BarChart(0, m, intshm) → charthm
  20. BarChart(0, m, intshm) → charthmbor
  21. BarChart(0, m, intsgm) → chartgmbor
  22. Sequence((i / n, Integral[f, 0, i / n]), i, 1, m * n) → cdff
  23. Sequence((i / n, Integral[g, 0, i / n]), i, 1, m * n) → cdfg
  24. Sequence((i / n, Integral[h, 0, i / n]), i, 1, m * n) → cdfh
  25. Function(Integral[f], 0, 1) → p
  26. Function(Integral[g], 0, 1) → q
  27. Function(Integral[h], 0, 1) → r