# 全變異數公式基礎 · 脈衝 R04

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261014-advance-20261110-r04-law-of-total-variance-foundations · 2026-10-14 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,10],[2,10],[7,10],[0,1]],"values":[0,1,3,99],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/10], [1, [2, 3], 7/10]], 是, 23/10, 121/100)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/10], [1, [2, 3], 7/10]], 是, 23/10, 121/100)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0001/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 2. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,11],[2,11],[8,11],[0,1]],"values":[1,2,4,100],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/11], [1, [2, 3], 8/11]], 是, 37/11, 138/121)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/11], [1, [2, 3], 8/11]], 是, 37/11, 138/121)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0002/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 3. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,12],[2,12],[9,12],[0,1]],"values":[2,3,5,101],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 1/4], [1, [2, 3], 3/4]], 是, 53/12, 155/144)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/4], [1, [2, 3], 3/4]], 是, 53/12, 155/144)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0003/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 4. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,13],[2,13],[10,13],[0,1]],"values":[3,4,6,102],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/13], [1, [2, 3], 10/13]], 是, 71/13, 172/169)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/13], [1, [2, 3], 10/13]], 是, 71/13, 172/169)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0004/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 5. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,14],[2,14],[11,14],[0,1]],"values":[4,5,7,103],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/14], [1, [2, 3], 11/14]], 是, 13/2, 27/28)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/14], [1, [2, 3], 11/14]], 是, 13/2, 27/28)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0005/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 6. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,15],[2,15],[12,15],[0,1]],"values":[5,6,8,104],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 1/5], [1, [2, 3], 4/5]], 是, 113/15, 206/225)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/5], [1, [2, 3], 4/5]], 是, 113/15, 206/225)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0006/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 7. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,16],[2,16],[13,16],[0,1]],"values":[6,7,9,105],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/16], [1, [2, 3], 13/16]], 是, 137/16, 223/256)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/16], [1, [2, 3], 13/16]], 是, 137/16, 223/256)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0007/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 8. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,17],[2,17],[14,17],[0,1]],"values":[7,8,10,106],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/17], [1, [2, 3], 14/17]], 是, 163/17, 240/289)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/17], [1, [2, 3], 14/17]], 是, 163/17, 240/289)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0008/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 9. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,18],[2,18],[15,18],[0,1]],"values":[8,9,11,107],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 1/6], [1, [2, 3], 5/6]], 是, 191/18, 257/324)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/6], [1, [2, 3], 5/6]], 是, 191/18, 257/324)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0009/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 10. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,19],[2,19],[16,19],[0,1]],"values":[9,10,12,108],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/19], [1, [2, 3], 16/19]], 是, 221/19, 274/361)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/19], [1, [2, 3], 16/19]], 是, 221/19, 274/361)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0010/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 11. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,20],[2,20],[17,20],[0,1]],"values":[10,11,13,109],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/20], [1, [2, 3], 17/20]], 是, 253/20, 291/400)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/20], [1, [2, 3], 17/20]], 是, 253/20, 291/400)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0011/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 12. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,21],[2,21],[18,21],[0,1]],"values":[11,12,14,110],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 1/7], [1, [2, 3], 6/7]], 是, 41/3, 44/63)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/7], [1, [2, 3], 6/7]], 是, 41/3, 44/63)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0012/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 13. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,22],[2,22],[19,22],[0,1]],"values":[12,13,15,111],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/22], [1, [2, 3], 19/22]], 是, 323/22, 325/484)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/22], [1, [2, 3], 19/22]], 是, 323/22, 325/484)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0013/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 14. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,23],[2,23],[20,23],[0,1]],"values":[13,14,16,112],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/23], [1, [2, 3], 20/23]], 是, 361/23, 342/529)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/23], [1, [2, 3], 20/23]], 是, 361/23, 342/529)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0014/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 15. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,24],[2,24],[21,24],[0,1]],"values":[14,15,17,113],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 1/8], [1, [2, 3], 7/8]], 是, 401/24, 359/576)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/8], [1, [2, 3], 7/8]], 是, 401/24, 359/576)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0015/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 16. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,25],[2,25],[22,25],[0,1]],"values":[15,16,18,114],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/25], [1, [2, 3], 22/25]], 是, 443/25, 376/625)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/25], [1, [2, 3], 22/25]], 是, 443/25, 376/625)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0016/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 17. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,26],[2,26],[23,26],[0,1]],"values":[16,17,19,115],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/26], [1, [2, 3], 23/26]], 是, 487/26, 393/676)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/26], [1, [2, 3], 23/26]], 是, 487/26, 393/676)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0017/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 18. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,27],[2,27],[24,27],[0,1]],"values":[17,18,20,116],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 1/9], [1, [2, 3], 8/9]], 是, 533/27, 410/729)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/9], [1, [2, 3], 8/9]], 是, 533/27, 410/729)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0018/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 19. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,28],[2,28],[25,28],[0,1]],"values":[18,19,21,117],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/28], [1, [2, 3], 25/28]], 是, 83/4, 61/112)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/28], [1, [2, 3], 25/28]], 是, 83/4, 61/112)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0019/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 20. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,29],[2,29],[26,29],[0,1]],"values":[19,20,22,118],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/29], [1, [2, 3], 26/29]], 是, 631/29, 444/841)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/29], [1, [2, 3], 26/29]], 是, 631/29, 444/841)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0020/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 21. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,30],[2,30],[27,30],[0,1]],"values":[20,21,23,119],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 1/10], [1, [2, 3], 9/10]], 是, 683/30, 461/900)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/10], [1, [2, 3], 9/10]], 是, 683/30, 461/900)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0021/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 22. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,31],[2,31],[28,31],[0,1]],"values":[21,22,24,120],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/31], [1, [2, 3], 28/31]], 是, 737/31, 478/961)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/31], [1, [2, 3], 28/31]], 是, 737/31, 478/961)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0022/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 23. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,32],[2,32],[29,32],[0,1]],"values":[22,23,25,121],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/32], [1, [2, 3], 29/32]], 是, 793/32, 495/1024)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/32], [1, [2, 3], 29/32]], 是, 793/32, 495/1024)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0023/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 24. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,33],[2,33],[30,33],[0,1]],"values":[23,24,26,122],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 1/11], [1, [2, 3], 10/11]], 是, 851/33, 512/1089)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/11], [1, [2, 3], 10/11]], 是, 851/33, 512/1089)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0024/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 25. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={"masses":[[1,34],[2,34],[31,34],[0,1]],"values":[24,25,27,123],"partition":[[0,1],[2,3]]}。請依 [partition, cell_mass_rows, complete_disjoint_certificate, mean, variance] 欄序回答。

查看答案與解釋([[0, 1], [2, 3]], [[0, [0, 1], 3/34], [1, [2, 3], 31/34]], 是, 911/34, 529/1156)

Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/34], [1, [2, 3], 31/34]], 是, 911/34, 529/1156)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0025/)

全變異數公式 · qf-mod41-totalvar-partition-qualification · candidate





## 26. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,10],[2,10],[7,10],[0,1]],"values":[0,1,3,99],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/10, 2/3, 2/9], [1, [2, 3], 7/10, 3, 0]], 1/15, 343/300, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/10, 2/3, 2/9], [1, [2, 3], 7/10, 3, 0]], 1/15, 343/300, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0026/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 27. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,11],[2,11],[8,11],[0,1]],"values":[1,2,4,100],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/11, 5/3, 2/9], [1, [2, 3], 8/11, 4, 0]], 2/33, 392/363, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/11, 5/3, 2/9], [1, [2, 3], 8/11, 4, 0]], 2/33, 392/363, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0027/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 28. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,12],[2,12],[9,12],[0,1]],"values":[2,3,5,101],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 1/4, 8/3, 2/9], [1, [2, 3], 3/4, 5, 0]], 1/18, 49/48, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 1/4, 8/3, 2/9], [1, [2, 3], 3/4, 5, 0]], 1/18, 49/48, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0028/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 29. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,13],[2,13],[10,13],[0,1]],"values":[3,4,6,102],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/13, 11/3, 2/9], [1, [2, 3], 10/13, 6, 0]], 2/39, 490/507, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/13, 11/3, 2/9], [1, [2, 3], 10/13, 6, 0]], 2/39, 490/507, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0029/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 30. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,14],[2,14],[11,14],[0,1]],"values":[4,5,7,103],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/14, 14/3, 2/9], [1, [2, 3], 11/14, 7, 0]], 1/21, 11/12, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/14, 14/3, 2/9], [1, [2, 3], 11/14, 7, 0]], 1/21, 11/12, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0030/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 31. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,15],[2,15],[12,15],[0,1]],"values":[5,6,8,104],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 1/5, 17/3, 2/9], [1, [2, 3], 4/5, 8, 0]], 2/45, 196/225, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 1/5, 17/3, 2/9], [1, [2, 3], 4/5, 8, 0]], 2/45, 196/225, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0031/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 32. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,16],[2,16],[13,16],[0,1]],"values":[6,7,9,105],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/16, 20/3, 2/9], [1, [2, 3], 13/16, 9, 0]], 1/24, 637/768, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/16, 20/3, 2/9], [1, [2, 3], 13/16, 9, 0]], 1/24, 637/768, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0032/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 33. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,17],[2,17],[14,17],[0,1]],"values":[7,8,10,106],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/17, 23/3, 2/9], [1, [2, 3], 14/17, 10, 0]], 2/51, 686/867, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/17, 23/3, 2/9], [1, [2, 3], 14/17, 10, 0]], 2/51, 686/867, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0033/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 34. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,18],[2,18],[15,18],[0,1]],"values":[8,9,11,107],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 1/6, 26/3, 2/9], [1, [2, 3], 5/6, 11, 0]], 1/27, 245/324, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 1/6, 26/3, 2/9], [1, [2, 3], 5/6, 11, 0]], 1/27, 245/324, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0034/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 35. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,19],[2,19],[16,19],[0,1]],"values":[9,10,12,108],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/19, 29/3, 2/9], [1, [2, 3], 16/19, 12, 0]], 2/57, 784/1083, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/19, 29/3, 2/9], [1, [2, 3], 16/19, 12, 0]], 2/57, 784/1083, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0035/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 36. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,20],[2,20],[17,20],[0,1]],"values":[10,11,13,109],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/20, 32/3, 2/9], [1, [2, 3], 17/20, 13, 0]], 1/30, 833/1200, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/20, 32/3, 2/9], [1, [2, 3], 17/20, 13, 0]], 1/30, 833/1200, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0036/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 37. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,21],[2,21],[18,21],[0,1]],"values":[11,12,14,110],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 1/7, 35/3, 2/9], [1, [2, 3], 6/7, 14, 0]], 2/63, 2/3, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 1/7, 35/3, 2/9], [1, [2, 3], 6/7, 14, 0]], 2/63, 2/3, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0037/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 38. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,22],[2,22],[19,22],[0,1]],"values":[12,13,15,111],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/22, 38/3, 2/9], [1, [2, 3], 19/22, 15, 0]], 1/33, 931/1452, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/22, 38/3, 2/9], [1, [2, 3], 19/22, 15, 0]], 1/33, 931/1452, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0038/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 39. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,23],[2,23],[20,23],[0,1]],"values":[13,14,16,112],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/23, 41/3, 2/9], [1, [2, 3], 20/23, 16, 0]], 2/69, 980/1587, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/23, 41/3, 2/9], [1, [2, 3], 20/23, 16, 0]], 2/69, 980/1587, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0039/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 40. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,24],[2,24],[21,24],[0,1]],"values":[14,15,17,113],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 1/8, 44/3, 2/9], [1, [2, 3], 7/8, 17, 0]], 1/36, 343/576, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 1/8, 44/3, 2/9], [1, [2, 3], 7/8, 17, 0]], 1/36, 343/576, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0040/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 41. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,25],[2,25],[22,25],[0,1]],"values":[15,16,18,114],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/25, 47/3, 2/9], [1, [2, 3], 22/25, 18, 0]], 2/75, 1078/1875, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/25, 47/3, 2/9], [1, [2, 3], 22/25, 18, 0]], 2/75, 1078/1875, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0041/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 42. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,26],[2,26],[23,26],[0,1]],"values":[16,17,19,115],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/26, 50/3, 2/9], [1, [2, 3], 23/26, 19, 0]], 1/39, 1127/2028, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/26, 50/3, 2/9], [1, [2, 3], 23/26, 19, 0]], 1/39, 1127/2028, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0042/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 43. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,27],[2,27],[24,27],[0,1]],"values":[17,18,20,116],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 1/9, 53/3, 2/9], [1, [2, 3], 8/9, 20, 0]], 2/81, 392/729, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 1/9, 53/3, 2/9], [1, [2, 3], 8/9, 20, 0]], 2/81, 392/729, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0043/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 44. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,28],[2,28],[25,28],[0,1]],"values":[18,19,21,117],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/28, 56/3, 2/9], [1, [2, 3], 25/28, 21, 0]], 1/42, 25/48, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/28, 56/3, 2/9], [1, [2, 3], 25/28, 21, 0]], 1/42, 25/48, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0044/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 45. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,29],[2,29],[26,29],[0,1]],"values":[19,20,22,118],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/29, 59/3, 2/9], [1, [2, 3], 26/29, 22, 0]], 2/87, 1274/2523, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/29, 59/3, 2/9], [1, [2, 3], 26/29, 22, 0]], 2/87, 1274/2523, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0045/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 46. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,30],[2,30],[27,30],[0,1]],"values":[20,21,23,119],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 1/10, 62/3, 2/9], [1, [2, 3], 9/10, 23, 0]], 1/45, 49/100, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 1/10, 62/3, 2/9], [1, [2, 3], 9/10, 23, 0]], 1/45, 49/100, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0046/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 47. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,31],[2,31],[28,31],[0,1]],"values":[21,22,24,120],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/31, 65/3, 2/9], [1, [2, 3], 28/31, 24, 0]], 2/93, 1372/2883, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/31, 65/3, 2/9], [1, [2, 3], 28/31, 24, 0]], 2/93, 1372/2883, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0047/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 48. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,32],[2,32],[29,32],[0,1]],"values":[22,23,25,121],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/32, 68/3, 2/9], [1, [2, 3], 29/32, 25, 0]], 1/48, 1421/3072, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/32, 68/3, 2/9], [1, [2, 3], 29/32, 25, 0]], 1/48, 1421/3072, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0048/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 49. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,33],[2,33],[30,33],[0,1]],"values":[23,24,26,122],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 1/11, 71/3, 2/9], [1, [2, 3], 10/11, 26, 0]], 2/99, 490/1089, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 1/11, 71/3, 2/9], [1, [2, 3], 10/11, 26, 0]], 2/99, 490/1089, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0049/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 50. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={"masses":[[1,34],[2,34],[31,34],[0,1]],"values":[24,25,27,123],"partition":[[0,1],[2,3]]}。請依 [cell_rows, within, between, certificate] 欄序回答。

查看答案與解釋([[0, [0, 1], 3/34, 74/3, 2/9], [1, [2, 3], 31/34, 27, 0]], 1/51, 1519/3468, same_law_same_partition_within_and_between_terms)

Wave6第四層核對=([[0, [0, 1], 3/34, 74/3, 2/9], [1, [2, 3], 31/34, 27, 0]], 1/51, 1519/3468, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0050/)

全變異數公式 · qf-mod41-totalvar-within-between-components · candidate





## 51. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,10],[2,10],[7,10],[0,1]],"values":[0,1,3,99],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(121/100, 1/15, 343/300, 121/100, 是)

Wave6第四層核對=(121/100, 1/15, 343/300, 121/100, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0051/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 52. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,11],[2,11],[8,11],[0,1]],"values":[1,2,4,100],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(138/121, 2/33, 392/363, 138/121, 是)

Wave6第四層核對=(138/121, 2/33, 392/363, 138/121, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0052/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 53. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,12],[2,12],[9,12],[0,1]],"values":[2,3,5,101],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(155/144, 1/18, 49/48, 155/144, 是)

Wave6第四層核對=(155/144, 1/18, 49/48, 155/144, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0053/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 54. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,13],[2,13],[10,13],[0,1]],"values":[3,4,6,102],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(172/169, 2/39, 490/507, 172/169, 是)

Wave6第四層核對=(172/169, 2/39, 490/507, 172/169, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0054/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 55. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,14],[2,14],[11,14],[0,1]],"values":[4,5,7,103],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(27/28, 1/21, 11/12, 27/28, 是)

Wave6第四層核對=(27/28, 1/21, 11/12, 27/28, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0055/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 56. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,15],[2,15],[12,15],[0,1]],"values":[5,6,8,104],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(206/225, 2/45, 196/225, 206/225, 是)

Wave6第四層核對=(206/225, 2/45, 196/225, 206/225, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0056/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 57. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,16],[2,16],[13,16],[0,1]],"values":[6,7,9,105],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(223/256, 1/24, 637/768, 223/256, 是)

Wave6第四層核對=(223/256, 1/24, 637/768, 223/256, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0057/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 58. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,17],[2,17],[14,17],[0,1]],"values":[7,8,10,106],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(240/289, 2/51, 686/867, 240/289, 是)

Wave6第四層核對=(240/289, 2/51, 686/867, 240/289, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0058/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 59. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,18],[2,18],[15,18],[0,1]],"values":[8,9,11,107],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(257/324, 1/27, 245/324, 257/324, 是)

Wave6第四層核對=(257/324, 1/27, 245/324, 257/324, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0059/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 60. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,19],[2,19],[16,19],[0,1]],"values":[9,10,12,108],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(274/361, 2/57, 784/1083, 274/361, 是)

Wave6第四層核對=(274/361, 2/57, 784/1083, 274/361, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0060/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 61. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,20],[2,20],[17,20],[0,1]],"values":[10,11,13,109],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(291/400, 1/30, 833/1200, 291/400, 是)

Wave6第四層核對=(291/400, 1/30, 833/1200, 291/400, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0061/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 62. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,21],[2,21],[18,21],[0,1]],"values":[11,12,14,110],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(44/63, 2/63, 2/3, 44/63, 是)

Wave6第四層核對=(44/63, 2/63, 2/3, 44/63, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0062/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 63. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,22],[2,22],[19,22],[0,1]],"values":[12,13,15,111],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(325/484, 1/33, 931/1452, 325/484, 是)

Wave6第四層核對=(325/484, 1/33, 931/1452, 325/484, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0063/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 64. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,23],[2,23],[20,23],[0,1]],"values":[13,14,16,112],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(342/529, 2/69, 980/1587, 342/529, 是)

Wave6第四層核對=(342/529, 2/69, 980/1587, 342/529, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0064/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 65. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,24],[2,24],[21,24],[0,1]],"values":[14,15,17,113],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(359/576, 1/36, 343/576, 359/576, 是)

Wave6第四層核對=(359/576, 1/36, 343/576, 359/576, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0065/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 66. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,25],[2,25],[22,25],[0,1]],"values":[15,16,18,114],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(376/625, 2/75, 1078/1875, 376/625, 是)

Wave6第四層核對=(376/625, 2/75, 1078/1875, 376/625, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0066/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 67. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,26],[2,26],[23,26],[0,1]],"values":[16,17,19,115],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(393/676, 1/39, 1127/2028, 393/676, 是)

Wave6第四層核對=(393/676, 1/39, 1127/2028, 393/676, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0067/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 68. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,27],[2,27],[24,27],[0,1]],"values":[17,18,20,116],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(410/729, 2/81, 392/729, 410/729, 是)

Wave6第四層核對=(410/729, 2/81, 392/729, 410/729, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0068/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 69. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,28],[2,28],[25,28],[0,1]],"values":[18,19,21,117],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(61/112, 1/42, 25/48, 61/112, 是)

Wave6第四層核對=(61/112, 1/42, 25/48, 61/112, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0069/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 70. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,29],[2,29],[26,29],[0,1]],"values":[19,20,22,118],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(444/841, 2/87, 1274/2523, 444/841, 是)

Wave6第四層核對=(444/841, 2/87, 1274/2523, 444/841, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0070/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 71. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,30],[2,30],[27,30],[0,1]],"values":[20,21,23,119],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(461/900, 1/45, 49/100, 461/900, 是)

Wave6第四層核對=(461/900, 1/45, 49/100, 461/900, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0071/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 72. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,31],[2,31],[28,31],[0,1]],"values":[21,22,24,120],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(478/961, 2/93, 1372/2883, 478/961, 是)

Wave6第四層核對=(478/961, 2/93, 1372/2883, 478/961, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0072/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 73. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,32],[2,32],[29,32],[0,1]],"values":[22,23,25,121],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(495/1024, 1/48, 1421/3072, 495/1024, 是)

Wave6第四層核對=(495/1024, 1/48, 1421/3072, 495/1024, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0073/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 74. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,33],[2,33],[30,33],[0,1]],"values":[23,24,26,122],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(512/1089, 2/99, 490/1089, 512/1089, 是)

Wave6第四層核對=(512/1089, 2/99, 490/1089, 512/1089, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0074/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 75. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={"masses":[[1,34],[2,34],[31,34],[0,1]],"values":[24,25,27,123],"partition":[[0,1],[2,3]]}。請依 [variance, within, between, sum, equal] 欄序回答。

查看答案與解釋(529/1156, 1/51, 1519/3468, 529/1156, 是)

Wave6第四層核對=(529/1156, 1/51, 1519/3468, 529/1156, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0075/)

全變異數公式 · qf-mod41-totalvar-full-identity · candidate





## 76. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,10],[2,10],[7,10],[0,1]],"values":[0,1,3,99],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 23/10, 121/100], [1, [3], 0, null, null]], 121/100, 0, 121/100, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 23/10, 121/100], [1, [3], 0, null, null]], 121/100, 0, 121/100, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0076/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 77. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,11],[2,11],[8,11],[0,1]],"values":[1,2,4,100],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 37/11, 138/121], [1, [3], 0, null, null]], 138/121, 0, 138/121, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 37/11, 138/121], [1, [3], 0, null, null]], 138/121, 0, 138/121, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0077/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 78. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,12],[2,12],[9,12],[0,1]],"values":[2,3,5,101],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 53/12, 155/144], [1, [3], 0, null, null]], 155/144, 0, 155/144, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 53/12, 155/144], [1, [3], 0, null, null]], 155/144, 0, 155/144, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0078/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 79. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,13],[2,13],[10,13],[0,1]],"values":[3,4,6,102],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 71/13, 172/169], [1, [3], 0, null, null]], 172/169, 0, 172/169, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 71/13, 172/169], [1, [3], 0, null, null]], 172/169, 0, 172/169, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0079/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 80. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,14],[2,14],[11,14],[0,1]],"values":[4,5,7,103],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 13/2, 27/28], [1, [3], 0, null, null]], 27/28, 0, 27/28, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 13/2, 27/28], [1, [3], 0, null, null]], 27/28, 0, 27/28, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0080/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 81. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,15],[2,15],[12,15],[0,1]],"values":[5,6,8,104],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 113/15, 206/225], [1, [3], 0, null, null]], 206/225, 0, 206/225, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 113/15, 206/225], [1, [3], 0, null, null]], 206/225, 0, 206/225, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0081/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 82. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,16],[2,16],[13,16],[0,1]],"values":[6,7,9,105],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 137/16, 223/256], [1, [3], 0, null, null]], 223/256, 0, 223/256, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 137/16, 223/256], [1, [3], 0, null, null]], 223/256, 0, 223/256, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0082/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 83. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,17],[2,17],[14,17],[0,1]],"values":[7,8,10,106],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 163/17, 240/289], [1, [3], 0, null, null]], 240/289, 0, 240/289, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 163/17, 240/289], [1, [3], 0, null, null]], 240/289, 0, 240/289, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0083/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 84. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,18],[2,18],[15,18],[0,1]],"values":[8,9,11,107],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 191/18, 257/324], [1, [3], 0, null, null]], 257/324, 0, 257/324, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 191/18, 257/324], [1, [3], 0, null, null]], 257/324, 0, 257/324, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0084/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 85. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,19],[2,19],[16,19],[0,1]],"values":[9,10,12,108],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 221/19, 274/361], [1, [3], 0, null, null]], 274/361, 0, 274/361, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 221/19, 274/361], [1, [3], 0, null, null]], 274/361, 0, 274/361, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0085/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 86. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,20],[2,20],[17,20],[0,1]],"values":[10,11,13,109],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 253/20, 291/400], [1, [3], 0, null, null]], 291/400, 0, 291/400, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 253/20, 291/400], [1, [3], 0, null, null]], 291/400, 0, 291/400, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0086/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 87. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,21],[2,21],[18,21],[0,1]],"values":[11,12,14,110],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 41/3, 44/63], [1, [3], 0, null, null]], 44/63, 0, 44/63, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 41/3, 44/63], [1, [3], 0, null, null]], 44/63, 0, 44/63, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0087/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 88. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,22],[2,22],[19,22],[0,1]],"values":[12,13,15,111],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 323/22, 325/484], [1, [3], 0, null, null]], 325/484, 0, 325/484, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 323/22, 325/484], [1, [3], 0, null, null]], 325/484, 0, 325/484, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0088/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 89. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,23],[2,23],[20,23],[0,1]],"values":[13,14,16,112],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 361/23, 342/529], [1, [3], 0, null, null]], 342/529, 0, 342/529, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 361/23, 342/529], [1, [3], 0, null, null]], 342/529, 0, 342/529, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0089/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 90. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,24],[2,24],[21,24],[0,1]],"values":[14,15,17,113],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 401/24, 359/576], [1, [3], 0, null, null]], 359/576, 0, 359/576, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 401/24, 359/576], [1, [3], 0, null, null]], 359/576, 0, 359/576, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0090/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 91. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,25],[2,25],[22,25],[0,1]],"values":[15,16,18,114],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 443/25, 376/625], [1, [3], 0, null, null]], 376/625, 0, 376/625, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 443/25, 376/625], [1, [3], 0, null, null]], 376/625, 0, 376/625, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0091/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 92. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,26],[2,26],[23,26],[0,1]],"values":[16,17,19,115],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 487/26, 393/676], [1, [3], 0, null, null]], 393/676, 0, 393/676, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 487/26, 393/676], [1, [3], 0, null, null]], 393/676, 0, 393/676, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0092/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 93. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,27],[2,27],[24,27],[0,1]],"values":[17,18,20,116],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 533/27, 410/729], [1, [3], 0, null, null]], 410/729, 0, 410/729, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 533/27, 410/729], [1, [3], 0, null, null]], 410/729, 0, 410/729, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0093/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 94. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,28],[2,28],[25,28],[0,1]],"values":[18,19,21,117],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 83/4, 61/112], [1, [3], 0, null, null]], 61/112, 0, 61/112, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 83/4, 61/112], [1, [3], 0, null, null]], 61/112, 0, 61/112, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0094/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 95. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,29],[2,29],[26,29],[0,1]],"values":[19,20,22,118],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 631/29, 444/841], [1, [3], 0, null, null]], 444/841, 0, 444/841, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 631/29, 444/841], [1, [3], 0, null, null]], 444/841, 0, 444/841, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0095/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 96. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,30],[2,30],[27,30],[0,1]],"values":[20,21,23,119],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 683/30, 461/900], [1, [3], 0, null, null]], 461/900, 0, 461/900, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 683/30, 461/900], [1, [3], 0, null, null]], 461/900, 0, 461/900, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0096/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 97. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,31],[2,31],[28,31],[0,1]],"values":[21,22,24,120],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 737/31, 478/961], [1, [3], 0, null, null]], 478/961, 0, 478/961, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 737/31, 478/961], [1, [3], 0, null, null]], 478/961, 0, 478/961, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0097/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 98. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,32],[2,32],[29,32],[0,1]],"values":[22,23,25,121],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 793/32, 495/1024], [1, [3], 0, null, null]], 495/1024, 0, 495/1024, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 793/32, 495/1024], [1, [3], 0, null, null]], 495/1024, 0, 495/1024, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0098/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 99. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,33],[2,33],[30,33],[0,1]],"values":[23,24,26,122],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 851/33, 512/1089], [1, [3], 0, null, null]], 512/1089, 0, 512/1089, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 851/33, 512/1089], [1, [3], 0, null, null]], 512/1089, 0, 512/1089, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0099/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate





## 100. 全變異數公式

同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={"masses":[[1,34],[2,34],[31,34],[0,1]],"values":[24,25,27,123],"partition":[[0,1,2],[3]]}。請依 [cell_rows, within, between, variance, equal, null_cell_division_claim, boundary] 欄序回答。

cell_rows依序為[index,非空cell,mass,mean或null,variance或null]；zero-mass不是empty cell，兩個外層加權項皆給零貢獻。

查看答案與解釋([[0, [0, 1, 2], 1, 911/34, 529/1156], [1, [3], 0, null, null]], 529/1156, 0, 529/1156, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)

Wave6第四層核對=([[0, [0, 1, 2], 1, 911/34, 529/1156], [1, [3], 0, null, null]], 529/1156, 0, 529/1156, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r04-law-of-total-variance-0100/)

全變異數公式 · qf-mod41-totalvar-zero-mass-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261110-r04-law-of-total-variance-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261110-r04-law-of-total-variance-foundations/validation-report.json)