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中心极限定理与大数定律演示

中心极限定理与大数定律演示
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2016-03-18 12:58
函数概率统计
①本范例通过动态图表演示中心极限定理与大数定律的数学现象；②涉及核心概念包括概率分布、样本均值、正态分布逼近、统计规律；③作图要点：运用了Sequence（数列）、Line（线段）、Textfield（文本框）、Point（点）、Polygon（多边形）、PolyLine（多段线）、Segment（线段）、Histogram（直方图）、Slider（滑块动画）等GeoGebra命令与对象；④适合高中及以上数学、统计学学习者及教师用于教学演示与概念理解。

GeoGebra 命令及参数

  1. Sequence(RandomUniform[0, 1, 50], i, 1, m) → UniformSample
  2. Sequence(Sequence[Sum[Element[UniformSample, i], j] / j, j, 1, 50], i, 1, m) → UniformMeans
  3. Line(A, B) → DragLine
  4. Sequence(Point[{0, Element[UniformSample, 1, i]}], i, 1, floor(x(A))) → UniformPoints
  5. Textfield(m) → inputBox1
  6. Point({0.6, Element[UniformMeans, 1, floor(x(A))]}) → Sample1Mean
  7. Sequence(Sequence[Sum[(Element[Transpose[UniformMeans], i] > (HistogramWidth * k)) ∧ (Element[Transpose[UniformMeans], i] < (HistogramWidth * (k + 1)))], k, 0, floor(1 / HistogramWidth)], i, 1, 50) → HistogramHeights
  8. Sequence(Polygon[{(HistogramxLocation, (HistogramWidth * (k - 1))), (HistogramxLocation + (Element[HistogramHeights, floor(x(A)), k] * HistogramMaxHeight / m), (HistogramWidth * (k - 1))), (HistogramxLocation + (Element[HistogramHeights, floor(x(A)), k] * HistogramMaxHeight / m), (HistogramWidth * k)), (HistogramxLocation, (HistogramWidth * k))}], k, 1, floor(1 / HistogramWidth)) → Histogram
  9. Sequence(Sequence[Segment[(i - 1, Element[UniformMeans, j, i - 1]), (i, Element[UniformMeans, j, i])], j, 1, m], i, Max[2, floor(x(A)) - LengthOfLines], floor(x(A))) → UniformSampleLines
  10. Textfield(LengthOfLines) → inputBox2
  11. Polygon(Corner[4], Corner[3], (0.8 * Corner[3]) + (0.2 * Corner[2]), (0.8 * Corner[4]) + (0.2 * Corner[1])) → poly1, b, c, d, e
  12. PolyLine((-0.2, 1.04), (0, 1.05), (0.2, 1.04)) → Xaxisarrow
  13. PolyLine((HistogramxLocation - 0.2, 0.99), (HistogramxLocation, 1), (HistogramxLocation + 0.2, 0.99)) → histogramaxisarrow
  14. Segment(Sample1Mean, (HistogramxLocation, y(Sample1Mean))) → xbarguideline