积极 AI Logo 积极 AI

大数定律演示 by cemccourseware

大数定律演示 by cemccourseware
几何画板及绘图内容加载中，请稍等……
2018-07-21 01:29
函数概率统计函数图像
这个范例演示了大数定律，展示了随着试验次数的增加，事件发生的频率逐渐接近理论概率。核心数学概念包括概率统计中的频率稳定性和概率极限。使用了If, Segment, LaTeX, RotateText, Polygon等GeoGebra命令，构造了多个条形图来直观展示频率变化。适合高中及以上学生或教师使用。

GeoGebra 命令及参数

  1. If(Mod[Max[{freq1, freq2, freq3, freq4, freq5, freq6}], 2] ≟ 0, Max[{freq1, freq2, freq3, freq4, freq5, freq6}] + 2, Max[{freq1, freq2, freq3, freq4, freq5, freq6}] + 3) → maxFreq
  2. If(maxFreq ≟ 0, 1, Min[1, (MaxY - MinY) / maxFreq]) → yheight
  3. Segment((MinX, MinY), (MinX, MaxY)) → yaxis
  4. Segment((MinX, MinY), (MaxX, MinY)) → xaxis
  5. LaTeX((("" * maxFreq) * "")) → Label1
  6. LaTeX((("" * maxFreq / 2) * "")) → Label2
  7. RotateText("Frequency", π / 2) → Freq
  8. LaTeX("Explore\ what\ happens\ to\ the\ frequencies\ of\ the\ rolls\ of\ a\ standard\ die\ and\\ tosses\ of\ a\ coin\ as\ we\ allow\ for\ more\ trials.") → Instructions
  9. LaTeX("\textbf{Instructions\text{:}}\ First\ select\ whether\ you\ are\ running\ trials\ with\ a\ die\ or\ a\ coin.\\ Then\ use\ the\ buttons\ to\ run\ trials\ and\ observe\ how\ the\ frequency\ changes.") → Instructions2
  10. Polygon((MinX + BetweenBars, MinY), (MinX + BarWidth + BetweenBars, MinY), (MinX + BarWidth + BetweenBars, MinY + (freq1 * yheight)), (MinX + BetweenBars, MinY + (freq1 * yheight))) → Bar1, f, g, h, i
  11. Polygon((MinX + (2 * BetweenBars) + BarWidth, MinY), (MinX + (2 * (BarWidth + BetweenBars)), MinY), (MinX + (2 * (BarWidth + BetweenBars)), MinY + (freq2 * yheight)), (MinX + (2 * BetweenBars) + BarWidth, MinY + (freq2 * yheight))) → Bar2, j, k, l, m
  12. Polygon((MinX + (3 * BetweenBars) + (2 * BarWidth), MinY), (MinX + (3 * (BarWidth + BetweenBars)), MinY), (MinX + (3 * (BarWidth + BetweenBars)), MinY + (freq3 * yheight)), (MinX + (3 * BetweenBars) + (2 * BarWidth), MinY + (freq3 * yheight))) → Bar3, n, p, q, r
  13. Polygon((MinX + (4 * BetweenBars) + (3 * BarWidth), MinY), (MinX + (4 * (BarWidth + BetweenBars)), MinY), (MinX + (4 * (BarWidth + BetweenBars)), MinY + (freq4 * yheight)), (MinX + (4 * BetweenBars) + (3 * BarWidth), MinY + (freq4 * yheight))) → Bar4, s, t, a, b
  14. Polygon((MinX + (5 * BetweenBars) + (4 * BarWidth), MinY), (MinX + (5 * (BarWidth + BetweenBars)), MinY), (MinX + (5 * (BarWidth + BetweenBars)), MinY + (freq5 * yheight)), (MinX + (5 * BetweenBars) + (4 * BarWidth), MinY + (freq5 * yheight))) → Bar5, c, d, e, f_1
  15. Polygon((MinX + (6 * BetweenBars) + (5 * BarWidth), MinY), (MinX + (6 * (BarWidth + BetweenBars)), MinY), (MinX + (6 * (BarWidth + BetweenBars)), MinY + (freq6 * yheight)), (MinX + (6 * BetweenBars) + (5 * BarWidth), MinY + (freq6 * yheight))) → Bar6, g_1, h_1, i_1, j_1