泊松概率模拟
几何画板及绘图内容加载中,请稍等……
①本范例用于演示二维均匀随机分布以及泊松概率分布的生成;②涉及的核心数学概念包括概率统计、泊松分布、均匀分布;③作图要点:从下方『构造摘要』提炼用到了 Sequence(数列)、Max(最大值)、CountIf(计数)、Element(元素)、Textfield(文本框)、If(条件判断)等 GeoGebra 命令/对象;④适合高中及以上学生及概率统计教学使用。
GeoGebra 命令及参数
Sequence((RandomUniform[0, n], RandomUniform[0, n]), i, 1, m) → list3Sequence(Sequence[CountIf[(x(A) > i - 1) ∧ (x(A) < i) ∧ (y(A) > j - 1) ∧ (y(A) < j), A, list3], i, 1, n], j, 1, n) → matrix1Sequence(Max[Sequence[Element[matrix1, i, j], j, 1, n]], i, 1, n) → list4Max(list4) → aSequence(Element[matrix1, 1, j], j, 1, n) → list5CountIf(12 ≤ x ≤ 12, list5) → bSequence(Sequence[CountIf[k ≤ x ≤ k, Sequence[Element[matrix1, i, j], j, 1, n]], i, 1, n], k, 0, a) → cElement(c, 10, 9) → dElement(c, 6, 3) → eSequence(Sum[Sequence[Element[c, i, j], j, 1, n]], i, 1, a + 1) → list6Sequence(Segment[(0, i), (n, i)], i, 0, n) → list1Sequence(Segment[(i, 0), (i, n)], i, 0, n) → list2Textfield(n) → inputBox1Textfield(m) → inputBox2Element(list6, A3 + 1) → jIf(A3 ≤ a, Element[list6, A3 + 1], 0) → B3If(A4 ≤ a, Element[list6, A4 + 1], 0) → B4If(A5 ≤ a, Element[list6, A5 + 1], 0) → B5If(A6 ≤ a, Element[list6, A6 + 1], 0) → B6If(A7 ≤ a, Element[list6, A7 + 1], 0) → B7If(A8 ≤ a, Element[list6, A8 + 1], 0) → B8If(A9 ≤ a, Element[list6, A9 + 1], 0) → B9If(A10 ≤ a, Element[list6, A10 + 1], 0) → B10If(A11 ≤ a, Element[list6, A11 + 1], 0) → B11If(A12 ≤ a, Element[list6, A12 + 1], 0) → B12If(A13 ≤ a, Element[list6, A13 + 1], 0) → B13If(A14 ≤ a, Element[list6, A14 + 1], 0) → B14If(A15 ≤ a, Element[list6, A15 + 1], 0) → B15If(A16 ≤ a, Element[list6, A16 + 1], 0) → B16If(A17 ≤ a, Element[list6, A17 + 1], 0) → B17If(A18 ≤ a, Element[list6, A18 + 1], 0) → B18If(A19 ≤ a, Element[list6, A19 + 1], 0) → B19If(A20 ≤ a, Element[list6, A20 + 1], 0) → B20If(A21 ≤ a, Element[list6, A21 + 1], 0) → B21If(A22 ≤ a, Element[list6, A22 + 1], 0) → B22If(A23 ≤ a, Element[list6, A23 + 1], 0) → B23If(A24 ≤ a, Element[list6, A24 + 1], 0) → B24If(A25 ≤ a, Element[list6, A25 + 1], 0) → B25If(A26 ≤ a, Element[list6, A26 + 1], 0) → B26If(A27 ≤ a, Element[list6, A27 + 1], 0) → B27If(A28 ≤ a, Element[list6, A28 + 1], 0) → B28If(A29 ≤ a, Element[list6, A29 + 1], 0) → B29If(A30 ≤ a, Element[list6, A30 + 1], 0) → B30If(A31 ≤ a, Element[list6, A31 + 1], 0) → B31If(A32 ≤ a, Element[list6, A32 + 1], 0) → B32If(A33 ≤ a, Element[list6, A33 + 1], 0) → B33If(A34 ≤ a, Element[list6, A34 + 1], 0) → B34If(A35 ≤ a, Element[list6, A35 + 1], 0) → B35If(A36 ≤ a, Element[list6, A36 + 1], 0) → B36If(A37 ≤ a, Element[list6, A37 + 1], 0) → B37If(A38 ≤ a, Element[list6, A38 + 1], 0) → B38If(A39 ≤ a, Element[list6, A39 + 1], 0) → B39If(A40 ≤ a, Element[list6, A40 + 1], 0) → B40If(A41 ≤ a, Element[list6, A41 + 1], 0) → B41If(A42 ≤ a, Element[list6, A42 + 1], 0) → B42If(A43 ≤ a, Element[list6, A43 + 1], 0) → B43If(A44 ≤ a, Element[list6, A44 + 1], 0) → B44If(A45 ≤ a, Element[list6, A45 + 1], 0) → B45If(A46 ≤ a, Element[list6, A46 + 1], 0) → B46If(A47 ≤ a, Element[list6, A47 + 1], 0) → B47If(A48 ≤ a, Element[list6, A48 + 1], 0) → B48If(A49 ≤ a, Element[list6, A49 + 1], 0) → B49If(A50 ≤ a, Element[list6, A50 + 1], 0) → B50If(A51 ≤ a, Element[list6, A51 + 1], 0) → B51If(A52 ≤ a, Element[list6, A52 + 1], 0) → B52If(A53 ≤ a, Element[list6, A53 + 1], 0) → B53If(A54 ≤ a, Element[list6, A54 + 1], 0) → B54If(A55 ≤ a, Element[list6, A55 + 1], 0) → B55If(A56 ≤ a, Element[list6, A56 + 1], 0) → B56If(A57 ≤ a, Element[list6, A57 + 1], 0) → B57If(A58 ≤ a, Element[list6, A58 + 1], 0) → B58If(A59 ≤ a, Element[list6, A59 + 1], 0) → B59If(A60 ≤ a, Element[list6, A60 + 1], 0) → B60If(A61 ≤ a, Element[list6, A61 + 1], 0) → B61If(A62 ≤ a, Element[list6, A62 + 1], 0) → B62If(A63 ≤ a, Element[list6, A63 + 1], 0) → B63If(A64 ≤ a, Element[list6, A64 + 1], 0) → B64If(A65 ≤ a, Element[list6, A65 + 1], 0) → B65If(A66 ≤ a, Element[list6, A66 + 1], 0) → B66If(A67 ≤ a, Element[list6, A67 + 1], 0) → B67If(A68 ≤ a, Element[list6, A68 + 1], 0) → B68If(A69 ≤ a, Element[list6, A69 + 1], 0) → B69If(A70 ≤ a, Element[list6, A70 + 1], 0) → B70If(A71 ≤ a, Element[list6, A71 + 1], 0) → B71If(A72 ≤ a, Element[list6, A72 + 1], 0) → B72If(A73 ≤ a, Element[list6, A73 + 1], 0) → B73If(A74 ≤ a, Element[list6, A74 + 1], 0) → B74If(A75 ≤ a, Element[list6, A75 + 1], 0) → B75If(A76 ≤ a, Element[list6, A76 + 1], 0) → B76If(A77 ≤ a, Element[list6, A77 + 1], 0) → B77If(A78 ≤ a, Element[list6, A78 + 1], 0) → B78If(A79 ≤ a, Element[list6, A79 + 1], 0) → B79If(A80 ≤ a, Element[list6, A80 + 1], 0) → B80If(A81 ≤ a, Element[list6, A81 + 1], 0) → B81If(A82 ≤ a, Element[list6, A82 + 1], 0) → B82If(A83 ≤ a, Element[list6, A83 + 1], 0) → B83If(A84 ≤ a, Element[list6, A84 + 1], 0) → B84If(A85 ≤ a, Element[list6, A85 + 1], 0) → B85If(A86 ≤ a, Element[list6, A86 + 1], 0) → B86If(A87 ≤ a, Element[list6, A87 + 1], 0) → B87If(A88 ≤ a, Element[list6, A88 + 1], 0) → B88If(A89 ≤ a, Element[list6, A89 + 1], 0) → B89If(A90 ≤ a, Element[list6, A90 + 1], 0) → B90If(A91 ≤ a, Element[list6, A91 + 1], 0) → B91If(A92 ≤ a, Element[list6, A92 + 1], 0) → B92If(A93 ≤ a, Element[list6, A93 + 1], 0) → B93If(A94 ≤ a, Element[list6, A94 + 1], 0) → B94If(A95 ≤ a, Element[list6, A95 + 1], 0) → B95If(A96 ≤ a, Element[list6, A96 + 1], 0) → B96If(A97 ≤ a, Element[list6, A97 + 1], 0) → B97If(A98 ≤ a, Element[list6, A98 + 1], 0) → B98If(A99 ≤ a, Element[list6, A99 + 1], 0) → B99If(A100 ≤ a, Element[list6, A100 + 1], 0) → B100If(A101 ≤ a, Element[list6, A101 + 1], 0) → B101If(A102 ≤ a, Element[list6, A102 + 1], 0) → B102If(A103 ≤ a, Element[list6, A103 + 1], 0) → B103
AI 绘图提示语参考
在坐标平面上生成一个二维均匀随机分布的散点图,散点位于边长为n的正方形内。统计每个小方格内散点的数量,得到一个矩阵。根据矩阵找出最大值a,并绘制条形图表示每个小方格内散点数量的概率分布。在条形图上标记出概率值为a的条形,并用不同颜色表示不同概率值的条形。
以上提示语为根据原始绘图命令整理而来,仅供参考。