积极 AI Logo 积极 AI

抛硬币多次试验

抛硬币多次试验
几何画板及绘图内容加载中，请稍等……
2021-11-21 10:14
函数概率统计变换函数图像
①本范例演示了抛硬币多次试验中正面朝上次数的概率分布现象；②涉及的核心数学概念包括概率统计、正态分布、置信区间、相似变换、算术运算、根等；③作图要点——从下方『构造摘要』提炼用到了 Normal（正态分布）、Max（最大值）、Sequence（数列）、Mode（模式）、CountIf（计数）、If（条件判断）、mean（均值）、stdev（标准差）、Min（最小值）、Histogram（直方图）、Textfield（文本框）等 GeoGebra 命令/对象；④适合高中阶段学习概率统计、数据分析的学生使用。

GeoGebra 命令及参数

  1. Normal(coins / 2, h, x, false) → i
  2. Max(i, 0, coins) → A
  3. Sequence(RandomBinomial[coins, 0.5], x, 1, trials) → l1, {48, 42, 56, 56, 53, 51, 53, 56, 56, 59, 49, 49, 52, 52, 51, 41, 45, 60, 49, 48, 46, 47, 56, 44, 55, 51, 38, 52, 48, 54, 42, 48, 50, 50, 50, 53, 55, 51, 52, 53, 43, 43, 48, 55, 48, 36, 54, 56, 52, 54, 56, 51, 51, 56, 44, 47, 47, 39, 46, 52, 52, 51, 43, 56, 43, 51, 55, 53, 48, 58, 42, 55, 51, 52, 52, 53, 54, 46, 49, 52, 45, 55, 50, 57, 49, 58, 57, 50, 50, 52, 42, 46, 45, 48, 54, 50, 46, 49, 48, 36, 48, 50, 42, 46, 39, 53, 44, 48, 47, 50, 57, 58, 52, 44, 49, 51, 42, 45, 44, 48, 55, 46, 50, 50, 52, 51, 44, 43, 54, 49, 58, 62, 47, 48, 45, 48, 49, 57, 46, 46, 48, 50, 57, 49, 47, 52, 37, 48, 51, 49, 44, 49, 43, 54, 56, 49, 55, 50, 56, 34, 56, 48, 55, 48, 63, 46, 51, 43, 48, 43, 52, 49, 48, 51, 48, 49, 61, 49, 51, 42, 51, 52, 49, 41, 49, 57, 37, 56, 52, 46, 51, 42, 49, 50, 60, 46, 53, 47, 58, 51, 44, 55, 48, 53, 49, 54, 49, 53, 58, 54, 53, 50, 55, 49, 54, 45, 44, 53, 45, 57, 46, 46, 55, 55, 45, 51, 55, 46, 57, 48, 44, 49, 51, 52, 48, 41, 50, 54, 39, 53, 48, 49, 55, 52, 53, 51, 53, 54, 52, 44, 50, 43, 48, 59, 50, 53, 46, 51, 52, 47, 49, 50, 53, 50, 50, 53, 53, 41, 45, 46, 51, 44, 53, 47, 47, 49, 51, 47, 44, 52, 53, 46, 55, 53, 53, 50, 50, 53, 46, 50, 52, 41, 48, 60, 50, 55, 58, 54, 54, 57, 48, 50, 55, 49, 49, 46, 54, 52, 44, 59, 46, 52, 53, 39, 51, 51, 49, 50, 55, 57, 53, 51, 51, 48, 51, 43, 49, 47, 56, 47, 51, 43, 46, 47, 52, 50, 47, 47, 55, 55, 54, 38, 58, 53, 46, 54, 52, 56, 47, 48, 51, 50, 52, 55, 52, 51, 57, 54, 48, 48, 43, 50, 52, 52, 55, 45, 51, 50, 53, 56, 57, 50, 48, 51, 51, 47, 54, 45, 45, 51, 45, 52, 51, 58, 47, 49, 43, 48, 48, 52, 50, 47, 56, 44, 47, 60, 53, 50, 48, 56, 51, 47, 55, 55, 55, 44, 46, 49, 51, 58, 48, 53, 52, 50, 43, 41, 50, 51, 47, 48, 43, 48, 44, 56, 51, 51, 49, 50, 51, 49, 37, 52, 64, 50, 54, 40, 54, 51, 48, 45, 53, 56, 50, 51, 54, 49, 41, 51, 55, 42, 40, 44, 51, 48, 51, 54, 55, 57, 49, 50, 54, 49, 48, 47, 53, 50, 54, 46, 49, 46, 49, 41, 59, 42, 52, 52, 55, 45, 46, 57, 52, 45, 48, 46, 56, 49, 43, 51, 61, 58, 56, 42, 55, 46, 34, 47, 58, 54, 42, 55, 51, 54, 50, 52, 44, 52, 53, 44, 47, 49, 46, 53, 46, 46, 46, 48, 46, 48, 51, 50, 61, 39, 47, 43, 50, 47, 53, 46, 46, 52, 47, 54, 47, 51, 47, 60, 57, 51, 48, 46, 40, 58, 51, 54, 54, 44, 50, 48, 52, 41, 54, 43, 47, 52, 51, 42, 56, 45, 50, 49, 48, 53, 51, 50, 43, 56, 45, 57, 48, 56, 52, 48, 51, 52, 53, 49, 49, 53, 52, 57, 47, 54, 45, 54, 58, 53, 50, 44, 43, 46, 52, 44, 53, 45, 43, 52, 53, 53, 44, 49, 51, 50, 50, 51, 44, 55, 51, 48, 47, 52, 46, 46, 50, 46, 52, 51, 45, 55, 40, 50, 46, 43, 52, 49, 51, 47, 51, 50, 54, 45, 46, 48, 50, 47, 41, 54, 47, 46, 65, 54, 50, 57, 40, 50, 52, 48, 58, 49, 47, 54, 57, 44, 48, 54, 46, 47, 55, 44, 50, 49, 52, 50, 47, 58, 48, 45, 50, 44, 43, 50, 44, 53, 53, 58, 56, 46, 36, 55, 49, 59, 57, 55, 55, 49, 55, 56, 50, 52, 47, 47, 59, 46, 47, 51, 50, 44, 42, 49, 58, 60, 54, 51, 53, 48, 51, 48, 60, 46, 48, 53, 58, 52, 40, 52, 45, 42, 52, 40, 48, 50, 41, 57, 63, 46, 51, 47, 49, 47, 56, 58, 61, 49, 43, 52, 40, 49, 52, 58, 46, 47, 56, 55, 54, 52, 56, 45, 61, 48, 51, 43, 51, 47, 50, 54, 50, 43, 62, 52, 43, 49, 59, 54, 59, 45, 43, 47, 43, 51, 51, 56, 56, 50, 42, 47, 54, 53, 41, 54, 49, 46, 49, 49, 46, 51, 51, 48, 58, 56, 49, 46, 45, 51, 47, 48, 49, 57, 44, 53, 59, 44, 48, 50, 45, 55, 47, 51, 46, 50, 52, 55, 47, 53, 57, 50, 49, 41, 50, 38, 43, 46, 57, 55, 46, 60, 56, 59, 49, 48, 47, 50, 54, 48, 58, 60, 46, 52, 48, 56, 44, 55, 50, 54, 49, 56, 62, 55, 53, 47, 53, 42, 41, 50, 52, 49, 41, 56, 47, 49, 49, 52, 47, 44, 43, 47, 43, 47, 58, 48, 48, 54, 43, 53, 56, 52, 48, 40, 38, 52, 50, 51, 48, 52, 40, 50, 49, 46, 46, 50, 49, 44, 50, 50, 52, 42, 46, 43, 46, 45, 59, 52, 43, 56, 35, 49, 48, 49, 48, 50, 52, 41, 50, 48, 51, 51, 42, 44, 60, 56, 45, 50, 48, 51, 55, 46, 44, 49, 51, 60, 48, 46, 51, 54, 47, 56, 59, 55, 50, 53, 55, 49, 54, 47, 58, 52, 53, 56, 55, 52, 53, 43, 47, 46, 48, 46, 47, 55, 43, 54, 61, 53, 60, 62, 55, 60, 55, 56, 42, 47, 59, 44, 44, 51, 50, 52, 48, 59, 54, 44, 49, 46, 50, 57, 43, 49, 55, 55, 47, 43, 62, 55, 51, 52, 59, 51, 59, 50, 62, 49, 49, 44}
  4. Mode(l1) → l4
  5. CountIf(x ≟ Element[l4, 1], l1) → f
  6. Max(l1) → n
  7. CountIf(x ≟ n, l1) → o
  8. If(f > 0, f / trials, o / trials) → l
  9. mean(l1) → a
  10. stdev(l1) → b
  11. Normal(a, b, x, false) → g
  12. Min(l1) → d
  13. Max(l1) → e
  14. Sequence(nCr[coins, i] / 2^(coins), i, 0, coins) → l2, {7.888609052210118E-31, 7.888609052210118E-29, 3.9048614808440084E-27, 1.275588083742376E-25, 3.093301103075262E-24, 5.939138117904503E-23, 9.403635353348797E-22, 1.2627738903068384E-20, 1.4679746474816996E-19, 1.5005963063146263E-18, 1.3655426387463099E-17, 1.1172621589742536E-16, 8.286361012392381E-16, 5.609228993004073E-15, 3.4857351599382454E-14, 1.998488158364594E-13, 1.0616968341311906E-12, 5.246031415707059E-12, 2.4190033750204773E-11, 1.0439909302719954E-10, 4.2281632676015815E-10, 1.6107288638482216E-9, 5.78398092018225E-9, 1.9615239642357197E-8, 6.2932227185896E-8, 1.9131397064512386E-7, 5.518672230147804E-7, 0.0000015125249815960647, 0.0000039433687020183116, 0.000009790432639493739, 0.000023170690580135184, 0.00005232091421320847, 0.00011281697127223077, 0.00023247133474277857, 0.00045810527728724014, 0.0008638556657416528, 0.0015597393964779842, 0.0026979276047186754, 0.00447287997624412, 0.00711073226992655, 0.010843866711637987, 0.015869073236543397, 0.022292269546572867, 0.030068642644214563, 0.03895255978909614, 0.048474296626430755, 0.05795839814029764, 0.06659049999098027, 0.07352701040670738, 0.07802866410507722, 0.07958923738717877, 0.07802866410507722, 0.07352701040670738, 0.06659049999098027, 0.05795839814029764, 0.048474296626430755, 0.03895255978909614, 0.030068642644214563, 0.022292269546572867, 0.015869073236543397, 0.010843866711637987, 0.00711073226992655, 0.00447287997624412, 0.0026979276047186754, 0.0015597393964779842, 0.0008638556657416528, 0.00045810527728724014, 0.00023247133474277857, 0.00011281697127223077, 0.00005232091421320847, 0.000023170690580135184, 0.000009790432639493739, 0.0000039433687020183116, 0.0000015125249815960647, 5.518672230147804E-7, 1.9131397064512386E-7, 6.2932227185896E-8, 1.9615239642357197E-8, 5.78398092018225E-9, 1.6107288638482216E-9, 4.2281632676015815E-10, 1.0439909302719954E-10, 2.4190033750204773E-11, 5.246031415707059E-12, 1.0616968341311906E-12, 1.998488158364594E-13, 3.4857351599382454E-14, 5.609228993004073E-15, 8.286361012392381E-16, 1.1172621589742536E-16, 1.3655426387463099E-17, 1.5005963063146263E-18, 1.4679746474816996E-19, 1.2627738903068384E-20, 9.403635353348797E-22, 5.939138117904503E-23, 3.093301103075262E-24, 1.275588083742376E-25, 3.9048614808440084E-27, 7.888609052210118E-29, 7.888609052210118E-31}
  15. Sequence(Polygon[(-1.5 + i, 0), (-0.5 + i, 0), (-0.5 + i, Element[l2, i]), (-1.5 + i, Element[l2, i])], i, 1, coins + 1) → l3, {7.888609052210118E-31, 7.888609052210118E-29, 3.9048614808440084E-27, 1.275588083742376E-25, 3.093301103075262E-24, 5.939138117904503E-23, 9.403635353348797E-22, 1.2627738903068384E-20, 1.4679746474816996E-19, 1.5005963063146263E-18, 1.3655426387463099E-17, 1.1172621589742536E-16, 8.286361012392381E-16, 5.609228993004073E-15, 3.485735159938249E-14, 1.9984881583645958E-13, 1.061696834131189E-12, 5.246031415707059E-12, 2.419003375020477E-11, 1.0439909302719944E-10, 4.228163267601573E-10, 1.6107288638482251E-9, 5.7839809201822635E-9, 1.9615239642357204E-8, 6.293222718589597E-8, 1.9131397064512384E-7, 5.518672230147798E-7, 0.0000015125249815960658, 0.000003943368702018311, 0.000009790432639493756, 0.00002317069058013516, 0.000052320914213208405, 0.000112816971272231, 0.0002324713347427788, 0.0004581052772872421, 0.0008638556657416547, 0.0015597393964779868, 0.0026979276047186806, 0.004472879976244126, 0.007110732269926534, 0.010843866711638006, 0.015869073236543407, 0.02229226954657293, 0.030068642644214494, 0.038952559789096064, 0.04847429662643066, 0.057958398140297795, 0.06659049999098032, 0.0735270104067074, 0.07802866410507736, 0.07958923738717871, 0.07802866410507714, 0.0735270104067074, 0.06659049999098032, 0.05795839814029735, 0.04847429662643066, 0.038952559789096064, 0.030068642644214494, 0.022292269546572818, 0.015869073236543296, 0.01084386671163795, 0.007110732269926534, 0.004472879976244126, 0.0026979276047186806, 0.0015597393964779938, 0.000863855665741653, 0.0004581052772872421, 0.00023247133474277662, 0.000112816971272231, 0.000052320914213208405, 0.00002317069058013527, 0.000009790432639493756, 0.000003943368702018311, 0.0000015125249815960726, 5.518672230147832E-7, 1.9131397064512384E-7, 6.293222718589575E-8, 1.9615239642357283E-8, 5.7839809201822635E-9, 1.6107288638482119E-9, 4.228163267601556E-10, 1.0439909302719861E-10, 2.41900337502049E-11, 5.246031415707059E-12, 1.0616968341311826E-12, 1.9984881583645998E-13, 3.485735159938219E-14, 5.609228993004048E-15, 8.286361012392286E-16, 1.1172621589742536E-16, 1.3655426387463099E-17, 1.5005963063146263E-18, 1.4679746474816996E-19, 1.2627738903068384E-20, 9.403635353348797E-22, 5.939138117904503E-23, 3.093301103075262E-24, 1.275588083742376E-25, 3.9048614808440084E-27, 7.888609052210118E-29, 7.888609052210118E-31}
  16. Histogram(Sequence[-0.5, coins + 0.5, 1], l1, true, 1 / trials) → c
  17. If(trials > (0.8 * max_{trials}), y(A), Max[l5]) → m
  18. CountIf(x ≟ d, l1) → p
  19. CountIf(x ≟ e, l1) → q
  20. Textfield(max_{trials}) → InputBox1
  21. Textfield(max_{coins}) → InputBox2

AI 绘图提示语参考

绘制多次抛硬币试验的概率分布图，包括直方图和正态分布曲线。首先绘制正态分布曲线，表示硬币正面朝上的概率分布；接着绘制直方图，显示试验结果的频率分布；最后根据试验次数调整直方图的宽度，确保显示效果清晰。
以上提示语为根据原始绘图命令整理而来，仅供参考。