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有偏骰子模拟：概率分布与样本均值可视化

有偏骰子模拟：概率分布与样本均值可视化
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2014-01-02 04:04
函数数列概率统计滑块动画函数图像
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① 本范例通过GeoGebra动态模拟一个有偏骰子的多次投掷，直观展示各面出现频率的分布以及样本均值随投掷次数增加的变化趋势。② 核心数学概念包括概率分布、期望值、方差、大数定律以及样本均值与总体均值的差异，涉及离散随机变量的统计特性。③ 作图要点：使用BarChart绘制各面频数柱状图，Random生成随机投掷结果，If条件判断骰子面数，AttachCopyToView固定视图；对象包括a至m等数值、按钮button1和button2控制投掷与重置、变量throw记录投掷次数、one至six统计各面次数、samplemean计算样本均值，以及多个文本对象显示统计结果。④ 适合高中或大学概率统计课程，用于演示有偏随机过程的模拟、频率与概率的关系，以及样本均值收敛于期望值的直观理解，也可作为探究性学习工具。

GeoGebra 命令及参数

  1. BarChart(0.5, 6.5, {a, b, c, d, e, f}) → g
  2. Random(0, (100 * a)) → m
  3. Random(1, 100) → t
  4. If(0 < t ≤ (100 * a), 1, If[(100 * a) < t ≤ (100 * (a + b)), 2, If[(100 * (a + b)) < t ≤ (100 * (a + b + c)), 3, If[(100 * (a + b + c)) < t ≤ (100 * (a + b + c + d)), 4, If[(100 * (a + b + c + d)) < t < (100 * (a + b + c + d + e)), 5, 6]]]]) → throw
  5. BarChart(0.5, 6.5, {one / n, two / n, three / n, four / n, five / n, six / n}) → o
  6. AttachCopyToView(PolyLine[(5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), (5.64467601684467, 0.7762405387700426), (5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7799622570331272), (5.592571961161487, 0.7743796796385004), (5.614902270739995, 0.7706579613754159), (5.629789143792332, 0.7781013979015848), (5.592571961161487, 0.7818231161646694), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), true], 1, (-0.5929237920849864, -0.26025799749899065), (13.616596536371715, 1.2898376590757037), (-571.9999999999993, 638.0000000000001), (1337.0000000000005, -194.99999999999983)) → stroke1
  7. AttachCopyToView(PolyLine[(5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), (5.64467601684467, 0.7762405387700426), (5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7799622570331272), (5.592571961161487, 0.7743796796385004), (5.614902270739995, 0.7706579613754159), (5.629789143792332, 0.7781013979015848), (5.592571961161487, 0.7818231161646694), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), true], 1, (-0.5929237920849864, -0.26025799749899065), (13.616596536371715, 1.2898376590757037), (-569.9999999999997, 677.0000000000002), (1339, -155.9999999999999)) → stroke1_1
  8. AttachCopyToView(PolyLine[(5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), (5.64467601684467, 0.7762405387700426), (5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7799622570331272), (5.592571961161487, 0.7743796796385004), (5.614902270739995, 0.7706579613754159), (5.629789143792332, 0.7781013979015848), (5.592571961161487, 0.7818231161646694), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), true], 1, (-0.5929237920849864, -0.26025799749899065), (13.616596536371715, 1.2898376590757037), (-479.00000000000006, 734.0000000000003), (1430, -98.99999999999993)) → stroke1_2
  9. AttachCopyToView(PolyLine[(5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), (5.64467601684467, 0.7762405387700426), (5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7799622570331272), (5.592571961161487, 0.7743796796385004), (5.614902270739995, 0.7706579613754159), (5.629789143792332, 0.7781013979015848), (5.592571961161487, 0.7818231161646694), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), true], 1, (-0.5929237920849864, -0.26025799749899065), (13.616596536371715, 1.2898376590757037), (-490.99999999999943, 635.0000000000001), (1418, -197.9999999999999)) → stroke1_3
  10. AttachCopyToView(PolyLine[(5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), (5.64467601684467, 0.7762405387700426), (5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7799622570331272), (5.592571961161487, 0.7743796796385004), (5.614902270739995, 0.7706579613754159), (5.629789143792332, 0.7781013979015848), (5.592571961161487, 0.7818231161646694), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), true], 1, (-0.5929237920849864, -0.26025799749899065), (13.616596536371715, 1.2898376590757037), (-527.9999999999993, 681.9999999999999), (1381, -150.99999999999991)) → stroke1_4
  11. AttachCopyToView(PolyLine[(5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), (5.64467601684467, 0.7762405387700426), (5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7799622570331272), (5.592571961161487, 0.7743796796385004), (5.614902270739995, 0.7706579613754159), (5.629789143792332, 0.7781013979015848), (5.592571961161487, 0.7818231161646694), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), true], 1, (-0.5929237920849864, -0.26025799749899065), (13.616596536371715, 1.2898376590757037), (-568.9999999999998, 728.0000000000001), (1340, -105.00000000000003)) → stroke1_5
  12. AttachCopyToView(PolyLine[(5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), (5.64467601684467, 0.7762405387700426), (5.622345707266163, 0.7781013979015848), (5.600015397687656, 0.7799622570331272), (5.592571961161487, 0.7743796796385004), (5.614902270739995, 0.7706579613754159), (5.629789143792332, 0.7781013979015848), (5.592571961161487, 0.7818231161646694), (5.600015397687656, 0.7762405387700426), (5.622345707266163, 0.7743796796385004), true], 1, (-0.5929237920849864, -0.26025799749899065), (13.616596536371715, 1.2898376590757037), (-487.9999999999993, 678.0000000000002), (1421, -154.99999999999994)) → stroke1_6

AI 绘图提示语参考

创建一个模拟掷偏倚骰子的动态图表，展示每个面出现的频率分布和样本均值随投掷次数增加的变化。使用条形图显示每个面的频率直方图，通过随机数生成器模拟掷骰子的结果，并根据概率分布确定每个面的出现。随着投掷次数的增加，绘制样本均值的走势线，并显示统计信息如期望值、方差等。
以上提示语为根据原始绘图命令整理而来，仅供参考。