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中心极限定理演示 by Bed Prasad Dhakal

中心极限定理演示 by Bed Prasad Dhakal
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2017-11-18 00:14
函数微积分概率统计几何作图滑块动画
①本范例通过动态演示展示中心极限定理，即大量独立随机样本均值的分布趋于正态分布的现象；②涉及核心数学概念包括概率统计、正态分布、样本均值、标准差；③作图要点运用了 GeoGebra 命令 Mean（均值）、SD（标准差）、Sample（样本）、Histogram（直方图），对象包括C2至C41；④适合高中及以上学生及教师用于概率统计教学和理论学习。

GeoGebra 命令及参数

  1. Mean(list1) → D2
  2. SD(list1) → D3
  3. Sample(list1, n, false) → E1
  4. Sample(list1, n, false) → E2
  5. Sample(list1, n, false) → E3
  6. Sample(list1, n, false) → E4
  7. Sample(list1, n, false) → E5
  8. Sample(list1, n, false) → E6
  9. Sample(list1, n, false) → E7
  10. Sample(list1, n, false) → E8
  11. Sample(list1, n, false) → E9
  12. Sample(list1, n, false) → E10
  13. Sample(list1, n, false) → E11
  14. Sample(list1, n, false) → E12
  15. Sample(list1, n, false) → E13
  16. Sample(list1, n, false) → E14
  17. Sample(list1, n, false) → E15
  18. Sample(list1, n, false) → E16
  19. Sample(list1, n, false) → E17
  20. Sample(list1, n, false) → E18
  21. Sample(list1, n, false) → E19
  22. Sample(list1, n, false) → E20
  23. Sample(list1, n, false) → E21
  24. Sample(list1, n, false) → E22
  25. Sample(list1, n, false) → E23
  26. Sample(list1, n, false) → E24
  27. Sample(list1, n, false) → E25
  28. Sample(list1, n, false) → E26
  29. Sample(list1, n, false) → E27
  30. Sample(list1, n, false) → E28
  31. Sample(list1, n, false) → E29
  32. Sample(list1, n, false) → E30
  33. Sample(list1, n, false) → E31
  34. Sample(list1, n, false) → E32
  35. Sample(list1, n, false) → E33
  36. Sample(list1, n, false) → E34
  37. Sample(list1, n, false) → E35
  38. Sample(list1, n, false) → E36
  39. Sample(list1, n, false) → E37
  40. Sample(list1, n, false) → E38
  41. Sample(list1, n, false) → E39
  42. Sample(list1, n, false) → E40
  43. Sample(list1, n, false) → E41
  44. Sample(list1, n, false) → E42
  45. Sample(list1, n, false) → E43
  46. Sample(list1, n, false) → E44
  47. Sample(list1, n, false) → E45
  48. Sample(list1, n, false) → E46
  49. Sample(list1, n, false) → E47
  50. Sample(list1, n, false) → E48
  51. Sample(list1, n, false) → E49
  52. Sample(list1, n, false) → E50
  53. Sample(list1, n, false) → E51
  54. Sample(list1, n, false) → E52
  55. Sample(list1, n, false) → E53
  56. Sample(list1, n, false) → E54
  57. Sample(list1, n, false) → E55
  58. Sample(list1, n, false) → E56
  59. Sample(list1, n, false) → E57
  60. Sample(list1, n, false) → E58
  61. Sample(list1, n, false) → E59
  62. Sample(list1, n, false) → E60
  63. Sample(list1, n, false) → E61
  64. Sample(list1, n, false) → E62
  65. Sample(list1, n, false) → E63
  66. Sample(list1, n, false) → E64
  67. Sample(list1, n, false) → E65
  68. Sample(list1, n, false) → E66
  69. Sample(list1, n, false) → E67
  70. Sample(list1, n, false) → E68
  71. Sample(list1, n, false) → E69
  72. Sample(list1, n, false) → E70
  73. Sample(list1, n, false) → E71
  74. Sample(list1, n, false) → E72
  75. Sample(list1, n, false) → E73
  76. Sample(list1, n, false) → E74
  77. Sample(list1, n, false) → E75
  78. Sample(list1, n, false) → E76
  79. Sample(list1, n, false) → E77
  80. Sample(list1, n, false) → E78
  81. Sample(list1, n, false) → E79
  82. Sample(list1, n, false) → E80
  83. Sample(list1, n, false) → E81
  84. Sample(list1, n, false) → E82
  85. Sample(list1, n, false) → E83
  86. Sample(list1, n, false) → E84
  87. Sample(list1, n, false) → E85
  88. Sample(list1, n, false) → E86
  89. Sample(list1, n, false) → E87
  90. Sample(list1, n, false) → E88
  91. Sample(list1, n, false) → E89
  92. Sample(list1, n, false) → E90
  93. Sample(list1, n, false) → E91
  94. Sample(list1, n, false) → E92
  95. Sample(list1, n, false) → E93
  96. Sample(list1, n, false) → E94
  97. Sample(list1, n, false) → E95
  98. Sample(list1, n, false) → E96
  99. Sample(list1, n, false) → E97
  100. Sample(list1, n, false) → E98
  101. Sample(list1, n, false) → E99
  102. Sample(list1, n, false) → E100
  103. Mean(E1) → F1
  104. Mean(E2) → F2
  105. Mean(E3) → F3
  106. Mean(E4) → F4
  107. Mean(E5) → F5
  108. Mean(E6) → F6
  109. Mean(E7) → F7
  110. Mean(E8) → F8
  111. Mean(E9) → F9
  112. Mean(E10) → F10
  113. Mean(E11) → F11
  114. Mean(E12) → F12
  115. Mean(E13) → F13
  116. Mean(E14) → F14
  117. Mean(E15) → F15
  118. Mean(E16) → F16
  119. Mean(E17) → F17
  120. Mean(E18) → F18
  121. Mean(E19) → F19
  122. Mean(E20) → F20
  123. Mean(E21) → F21
  124. Mean(E22) → F22
  125. Mean(E23) → F23
  126. Mean(E24) → F24
  127. Mean(E25) → F25
  128. Mean(E26) → F26
  129. Mean(E27) → F27
  130. Mean(E28) → F28
  131. Mean(E29) → F29
  132. Mean(E30) → F30
  133. Mean(E31) → F31
  134. Mean(E32) → F32
  135. Mean(E33) → F33
  136. Mean(E34) → F34
  137. Mean(E35) → F35
  138. Mean(E36) → F36
  139. Mean(E37) → F37
  140. Mean(E38) → F38
  141. Mean(E39) → F39
  142. Mean(E40) → F40
  143. Mean(E41) → F41
  144. Mean(E42) → F42
  145. Mean(E43) → F43
  146. Mean(E44) → F44
  147. Mean(E45) → F45
  148. Mean(E46) → F46
  149. Mean(E47) → F47
  150. Mean(E48) → F48
  151. Mean(E49) → F49
  152. Mean(E50) → F50
  153. Mean(E51) → F51
  154. Mean(E52) → F52
  155. Mean(E53) → F53
  156. Mean(E54) → F54
  157. Mean(E55) → F55
  158. Mean(E56) → F56
  159. Mean(E57) → F57
  160. Mean(E58) → F58
  161. Mean(E59) → F59
  162. Mean(E60) → F60
  163. Mean(E61) → F61
  164. Mean(E62) → F62
  165. Mean(E63) → F63
  166. Mean(E64) → F64
  167. Mean(E65) → F65
  168. Mean(E66) → F66
  169. Mean(E67) → F67
  170. Mean(E68) → F68
  171. Mean(E69) → F69
  172. Mean(E70) → F70
  173. Mean(E71) → F71
  174. Mean(E72) → F72
  175. Mean(E73) → F73
  176. Mean(E74) → F74
  177. Mean(E75) → F75
  178. Mean(E76) → F76
  179. Mean(E77) → F77
  180. Mean(E78) → F78
  181. Mean(E79) → F79
  182. Mean(E80) → F80
  183. Mean(E81) → F81
  184. Mean(E82) → F82
  185. Mean(E83) → F83
  186. Mean(E84) → F84
  187. Mean(E85) → F85
  188. Mean(E86) → F86
  189. Mean(E87) → F87
  190. Mean(E88) → F88
  191. Mean(E89) → F89
  192. Mean(E90) → F90
  193. Mean(E91) → F91
  194. Mean(E92) → F92
  195. Mean(E93) → F93
  196. Mean(E94) → F94
  197. Mean(E95) → F95
  198. Mean(E96) → F96
  199. Mean(E97) → F97
  200. Mean(E98) → F98
  201. Mean(E99) → F99
  202. Mean(E100) → F100
  203. Mean(list3) → H2
  204. SD(list3) → H3
  205. Mean(list3) → mean
  206. SD(list3) → sd
  207. Histogram(list2, list3, false, sd) → b

AI 绘图提示语参考

展示中心极限定理的动态图形，通过增加样本量，观察样本均值的分布如何逐渐接近正态分布。图形包含多个样本集合和它们的均值与标准差，用直方图展示分布变化，滑动条控制样本大小，适合概率统计教学。
以上提示语为根据原始绘图命令整理而来，仅供参考。