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Expected Value Experiment: Probability Distribution and Pie Chart in a Rhombus G

Expected Value Experiment: Probability Distribution and Pie Chart in a Rhombus G
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2017-08-16 05:19
Probability & StatisticsSlider Animation
① This GeoGebra example demonstrates an interactive experiment where random selections or operations within a rhombus grid produce outcomes whose expected value is computed and visualized via a pie (circle) chart. ② Core mathematical concepts include expected value, probability distributions, discrete random variables, geometric properties of rhombi, and quadrilateral classification. ③ Construction highlights: using commands such as Element, Point, Vector, Sequence, Zip, Textfield, and TableText, the applet builds multiple points (A–G), vectors (u, v, w), function lists (fnlist), operator lists (ops, bin_op, comb_op), and text objects (text2–text6). Sliders or input fields control parameters, dynamically updating tables and the pie chart. ④ Suitable for high school or college probability and statistics courses, this example helps students intuitively grasp expected value calculations and distribution visualization, and is ideal for math lab activities or inquiry-based learning.

GeoGebra Commands & Parameters

  1. Element(ops, bin_{op}) → op
  2. Point(yAxis) → A
  3. Element(fnlist, comb_{op}) → o
  4. Vector(A, B) → u
  5. Vector(A, C) → v
  6. Vector(B, D) → w
  7. Vector(C, D) → a
  8. Vector(A, B) → b
  9. Vector(B, E) → c
  10. Vector(A, F) → d
  11. Vector(F, E) → e
  12. Vector(B, E) → h
  13. Sequence(-5, 5) → list1
  14. Zip((a1, b), b, list1) → list2
  15. Zip((a2, b), b, list1) → list3
  16. Zip((a3, b), b, list1) → list4
  17. Textfield(f) → InputBox1
  18. Textfield(g) → InputBox2
  19. Zip((s, t), s, lista, t, listo) → list5
  20. Zip((0, s), s, lista) → list6
  21. Zip((a3, s), s, listo) → list7
  22. Zip(Vector[S, T], S, list6, T, list7) → list8
  23. Zip((a2, s), s, listo) → list9
  24. Zip(Vector[S, T], S, list6, T, list9) → list10
  25. TableText({{A1, B1, C1, D1}, {A2, B2, C2, D2}, {A3, B3, C3, D3}, {A4, B4, C4, D4}, {A5, B5, C5, D5}, {A6, B6, C6, D6}, {A7, B7, C7, D7}, {A8, B8, C8, D8}, {A9, B9, C9, D9}, {A10, B10, C10, D10}, {A11, B11, C11, D11}, {A12, B12, C12, D12}, {A13, B13, C13, D13}, {A14, B14, C14, D14}, {A15, B15, C15, D15}, {A16, B16, C16, D16}, {A17, B17, C17, D17}, {A18, B18, C18, D18}}, "|_") → table