Chebyshev不等式基礎 · 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-20261108-r04-chebyshev-inequality-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
1. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,6],[2,6],[3,6]],"values":[0,1,4]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/6, 1/3, 1/2], [0, 1, 4], 7/3, 26/9, 是, finite_mean_and_variance)
Wave6第二層核對=([1/6, 1/3, 1/2], [0, 1, 4], 7/3, 26/9, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
2. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,7],[2,7],[4,7]],"values":[0,2,5]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/7, 2/7, 4/7], [0, 2, 5], 24/7, 180/49, 是, finite_mean_and_variance)
Wave6第二層核對=([1/7, 2/7, 4/7], [0, 2, 5], 24/7, 180/49, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
3. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,8],[2,8],[5,8]],"values":[0,3,6]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/8, 1/4, 5/8], [0, 3, 6], 9/2, 9/2, 是, finite_mean_and_variance)
Wave6第二層核對=([1/8, 1/4, 5/8], [0, 3, 6], 9/2, 9/2, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
4. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,9],[2,9],[6,9]],"values":[0,4,7]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/9, 2/9, 2/3], [0, 4, 7], 50/9, 434/81, 是, finite_mean_and_variance)
Wave6第二層核對=([1/9, 2/9, 2/3], [0, 4, 7], 50/9, 434/81, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
5. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,10],[2,10],[7,10]],"values":[0,5,8]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/10, 1/5, 7/10], [0, 5, 8], 33/5, 156/25, 是, finite_mean_and_variance)
Wave6第二層核對=([1/10, 1/5, 7/10], [0, 5, 8], 33/5, 156/25, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
6. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,11],[2,11],[8,11]],"values":[0,6,9]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/11, 2/11, 8/11], [0, 6, 9], 84/11, 864/121, 是, finite_mean_and_variance)
Wave6第二層核對=([1/11, 2/11, 8/11], [0, 6, 9], 84/11, 864/121, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
7. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,12],[2,12],[9,12]],"values":[0,7,10]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/12, 1/6, 3/4], [0, 7, 10], 26/3, 145/18, 是, finite_mean_and_variance)
Wave6第二層核對=([1/12, 1/6, 3/4], [0, 7, 10], 26/3, 145/18, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
8. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,13],[2,13],[10,13]],"values":[0,8,11]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/13, 2/13, 10/13], [0, 8, 11], 126/13, 1518/169, 是, finite_mean_and_variance)
Wave6第二層核對=([1/13, 2/13, 10/13], [0, 8, 11], 126/13, 1518/169, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
9. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,14],[2,14],[11,14]],"values":[0,9,12]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/14, 1/7, 11/14], [0, 9, 12], 75/7, 486/49, 是, finite_mean_and_variance)
Wave6第二層核對=([1/14, 1/7, 11/14], [0, 9, 12], 75/7, 486/49, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
10. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,15],[2,15],[12,15]],"values":[0,10,13]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/15, 2/15, 4/5], [0, 10, 13], 176/15, 2444/225, 是, finite_mean_and_variance)
Wave6第二層核對=([1/15, 2/15, 4/5], [0, 10, 13], 176/15, 2444/225, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
11. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,16],[2,16],[13,16]],"values":[0,11,14]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/16, 1/8, 13/16], [0, 11, 14], 51/4, 189/16, 是, finite_mean_and_variance)
Wave6第二層核對=([1/16, 1/8, 13/16], [0, 11, 14], 51/4, 189/16, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
12. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,17],[2,17],[14,17]],"values":[0,12,15]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/17, 2/17, 14/17], [0, 12, 15], 234/17, 3690/289, 是, finite_mean_and_variance)
Wave6第二層核對=([1/17, 2/17, 14/17], [0, 12, 15], 234/17, 3690/289, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
13. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,18],[2,18],[15,18]],"values":[0,13,16]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/18, 1/9, 5/6], [0, 13, 16], 133/9, 1112/81, 是, finite_mean_and_variance)
Wave6第二層核對=([1/18, 1/9, 5/6], [0, 13, 16], 133/9, 1112/81, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
14. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,19],[2,19],[16,19]],"values":[0,14,17]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/19, 2/19, 16/19], [0, 14, 17], 300/19, 5304/361, 是, finite_mean_and_variance)
Wave6第二層核對=([1/19, 2/19, 16/19], [0, 14, 17], 300/19, 5304/361, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
15. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,20],[2,20],[17,20]],"values":[0,15,18]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/20, 1/10, 17/20], [0, 15, 18], 84/5, 783/50, 是, finite_mean_and_variance)
Wave6第二層核對=([1/20, 1/10, 17/20], [0, 15, 18], 84/5, 783/50, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
16. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,21],[2,21],[18,21]],"values":[0,16,19]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/21, 2/21, 6/7], [0, 16, 19], 374/21, 7334/441, 是, finite_mean_and_variance)
Wave6第二層核對=([1/21, 2/21, 6/7], [0, 16, 19], 374/21, 7334/441, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
17. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,22],[2,22],[19,22]],"values":[0,17,20]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/22, 1/11, 19/22], [0, 17, 20], 207/11, 2130/121, 是, finite_mean_and_variance)
Wave6第二層核對=([1/22, 1/11, 19/22], [0, 17, 20], 207/11, 2130/121, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
18. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,23],[2,23],[20,23]],"values":[0,18,21]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/23, 2/23, 20/23], [0, 18, 21], 456/23, 9828/529, 是, finite_mean_and_variance)
Wave6第二層核對=([1/23, 2/23, 20/23], [0, 18, 21], 456/23, 9828/529, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
19. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,24],[2,24],[21,24]],"values":[0,19,22]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/24, 1/12, 7/8], [0, 19, 22], 125/6, 176/9, 是, finite_mean_and_variance)
Wave6第二層核對=([1/24, 1/12, 7/8], [0, 19, 22], 125/6, 176/9, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
20. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,25],[2,25],[22,25]],"values":[0,20,23]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/25, 2/25, 22/25], [0, 20, 23], 546/25, 12834/625, 是, finite_mean_and_variance)
Wave6第二層核對=([1/25, 2/25, 22/25], [0, 20, 23], 546/25, 12834/625, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
21. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,26],[2,26],[23,26]],"values":[0,21,24]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/26, 1/13, 23/26], [0, 21, 24], 297/13, 3636/169, 是, finite_mean_and_variance)
Wave6第二層核對=([1/26, 1/13, 23/26], [0, 21, 24], 297/13, 3636/169, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
22. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,27],[2,27],[24,27]],"values":[0,22,25]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/27, 2/27, 8/9], [0, 22, 25], 644/27, 16400/729, 是, finite_mean_and_variance)
Wave6第二層核對=([1/27, 2/27, 8/9], [0, 22, 25], 644/27, 16400/729, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
23. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,28],[2,28],[25,28]],"values":[0,23,26]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/28, 1/14, 25/28], [0, 23, 26], 174/7, 2301/98, 是, finite_mean_and_variance)
Wave6第二層核對=([1/28, 1/14, 25/28], [0, 23, 26], 174/7, 2301/98, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
24. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,29],[2,29],[26,29]],"values":[0,24,27]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/29, 2/29, 26/29], [0, 24, 27], 750/29, 20574/841, 是, finite_mean_and_variance)
Wave6第二層核對=([1/29, 2/29, 26/29], [0, 24, 27], 750/29, 20574/841, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
25. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={"masses":[[1,30],[2,30],[27,30]],"values":[0,25,28]}。請依 [masses, values, mean, variance, finite_moment_certificate, certificate] 欄序回答。
查看答案與解釋
([1/30, 1/15, 9/10], [0, 25, 28], 403/15, 5726/225, 是, finite_mean_and_variance)
Wave6第二層核對=([1/30, 1/15, 9/10], [0, 25, 28], 403/15, 5726/225, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-qualification · candidate
26. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,6],[2,6],[3,6]],"values":[0,1,4],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(7/3, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(7/3, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
27. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,7],[2,7],[4,7]],"values":[0,2,5],"epsilon":[2,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(24/7, 2, 1/7, exact_absolute_deviation_tail)
Wave6第二層核對=(24/7, 2, 1/7, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
28. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,8],[2,8],[5,8]],"values":[0,3,6],"epsilon":[3,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(9/2, 3, 1/8, exact_absolute_deviation_tail)
Wave6第二層核對=(9/2, 3, 1/8, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
29. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,9],[2,9],[6,9]],"values":[0,4,7],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(50/9, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(50/9, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
30. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,10],[2,10],[7,10]],"values":[0,5,8],"epsilon":[2,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(33/5, 2, 1/10, exact_absolute_deviation_tail)
Wave6第二層核對=(33/5, 2, 1/10, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
31. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,11],[2,11],[8,11]],"values":[0,6,9],"epsilon":[3,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(84/11, 3, 1/11, exact_absolute_deviation_tail)
Wave6第二層核對=(84/11, 3, 1/11, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
32. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,12],[2,12],[9,12]],"values":[0,7,10],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(26/3, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(26/3, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
33. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,13],[2,13],[10,13]],"values":[0,8,11],"epsilon":[2,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(126/13, 2, 1/13, exact_absolute_deviation_tail)
Wave6第二層核對=(126/13, 2, 1/13, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
34. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,14],[2,14],[11,14]],"values":[0,9,12],"epsilon":[3,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(75/7, 3, 1/14, exact_absolute_deviation_tail)
Wave6第二層核對=(75/7, 3, 1/14, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
35. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,15],[2,15],[12,15]],"values":[0,10,13],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(176/15, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(176/15, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
36. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,16],[2,16],[13,16]],"values":[0,11,14],"epsilon":[2,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(51/4, 2, 1/16, exact_absolute_deviation_tail)
Wave6第二層核對=(51/4, 2, 1/16, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
37. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,17],[2,17],[14,17]],"values":[0,12,15],"epsilon":[3,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(234/17, 3, 1/17, exact_absolute_deviation_tail)
Wave6第二層核對=(234/17, 3, 1/17, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
38. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,18],[2,18],[15,18]],"values":[0,13,16],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(133/9, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(133/9, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
39. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,19],[2,19],[16,19]],"values":[0,14,17],"epsilon":[2,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(300/19, 2, 1/19, exact_absolute_deviation_tail)
Wave6第二層核對=(300/19, 2, 1/19, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
40. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,20],[2,20],[17,20]],"values":[0,15,18],"epsilon":[3,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(84/5, 3, 1/20, exact_absolute_deviation_tail)
Wave6第二層核對=(84/5, 3, 1/20, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
41. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,21],[2,21],[18,21]],"values":[0,16,19],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(374/21, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(374/21, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
42. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,22],[2,22],[19,22]],"values":[0,17,20],"epsilon":[2,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(207/11, 2, 1/22, exact_absolute_deviation_tail)
Wave6第二層核對=(207/11, 2, 1/22, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
43. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,23],[2,23],[20,23]],"values":[0,18,21],"epsilon":[3,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(456/23, 3, 1/23, exact_absolute_deviation_tail)
Wave6第二層核對=(456/23, 3, 1/23, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
44. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,24],[2,24],[21,24]],"values":[0,19,22],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(125/6, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(125/6, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
45. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,25],[2,25],[22,25]],"values":[0,20,23],"epsilon":[2,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(546/25, 2, 1/25, exact_absolute_deviation_tail)
Wave6第二層核對=(546/25, 2, 1/25, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
46. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,26],[2,26],[23,26]],"values":[0,21,24],"epsilon":[3,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(297/13, 3, 1/26, exact_absolute_deviation_tail)
Wave6第二層核對=(297/13, 3, 1/26, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
47. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,27],[2,27],[24,27]],"values":[0,22,25],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(644/27, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(644/27, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
48. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,28],[2,28],[25,28]],"values":[0,23,26],"epsilon":[2,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(174/7, 2, 1/28, exact_absolute_deviation_tail)
Wave6第二層核對=(174/7, 2, 1/28, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
49. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,29],[2,29],[26,29]],"values":[0,24,27],"epsilon":[3,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(750/29, 3, 1/29, exact_absolute_deviation_tail)
Wave6第二層核對=(750/29, 3, 1/29, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
50. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={"masses":[[1,30],[2,30],[27,30]],"values":[0,25,28],"epsilon":[1,1]}。請依 [mean, epsilon, tail_probability, certificate] 欄序回答。
查看答案與解釋
(403/15, 1, 1, exact_absolute_deviation_tail)
Wave6第二層核對=(403/15, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-tail-probability · candidate
51. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,6],[2,6],[3,6]],"values":[0,1,4],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 26/9, 26/9, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 26/9, 26/9, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
52. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,7],[2,7],[4,7]],"values":[0,2,5],"epsilon":[2,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/7, 180/49, 45/49, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/7, 180/49, 45/49, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
53. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,8],[2,8],[5,8]],"values":[0,3,6],"epsilon":[3,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/8, 9/2, 1/2, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/8, 9/2, 1/2, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
54. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,9],[2,9],[6,9]],"values":[0,4,7],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 434/81, 434/81, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 434/81, 434/81, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
55. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,10],[2,10],[7,10]],"values":[0,5,8],"epsilon":[2,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/10, 156/25, 39/25, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/10, 156/25, 39/25, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
56. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,11],[2,11],[8,11]],"values":[0,6,9],"epsilon":[3,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/11, 864/121, 96/121, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/11, 864/121, 96/121, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
57. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,12],[2,12],[9,12]],"values":[0,7,10],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 145/18, 145/18, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 145/18, 145/18, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
58. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,13],[2,13],[10,13]],"values":[0,8,11],"epsilon":[2,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/13, 1518/169, 759/338, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/13, 1518/169, 759/338, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
59. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,14],[2,14],[11,14]],"values":[0,9,12],"epsilon":[3,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/14, 486/49, 54/49, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/14, 486/49, 54/49, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
60. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,15],[2,15],[12,15]],"values":[0,10,13],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 2444/225, 2444/225, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 2444/225, 2444/225, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
61. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,16],[2,16],[13,16]],"values":[0,11,14],"epsilon":[2,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/16, 189/16, 189/64, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/16, 189/16, 189/64, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
62. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,17],[2,17],[14,17]],"values":[0,12,15],"epsilon":[3,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/17, 3690/289, 410/289, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/17, 3690/289, 410/289, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
63. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,18],[2,18],[15,18]],"values":[0,13,16],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 1112/81, 1112/81, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 1112/81, 1112/81, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
64. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,19],[2,19],[16,19]],"values":[0,14,17],"epsilon":[2,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/19, 5304/361, 1326/361, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/19, 5304/361, 1326/361, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
65. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,20],[2,20],[17,20]],"values":[0,15,18],"epsilon":[3,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/20, 783/50, 87/50, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/20, 783/50, 87/50, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
66. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,21],[2,21],[18,21]],"values":[0,16,19],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 7334/441, 7334/441, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 7334/441, 7334/441, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
67. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,22],[2,22],[19,22]],"values":[0,17,20],"epsilon":[2,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/22, 2130/121, 1065/242, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/22, 2130/121, 1065/242, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
68. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,23],[2,23],[20,23]],"values":[0,18,21],"epsilon":[3,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/23, 9828/529, 1092/529, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/23, 9828/529, 1092/529, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
69. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,24],[2,24],[21,24]],"values":[0,19,22],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 176/9, 176/9, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 176/9, 176/9, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
70. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,25],[2,25],[22,25]],"values":[0,20,23],"epsilon":[2,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/25, 12834/625, 6417/1250, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/25, 12834/625, 6417/1250, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
71. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,26],[2,26],[23,26]],"values":[0,21,24],"epsilon":[3,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/26, 3636/169, 404/169, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/26, 3636/169, 404/169, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
72. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,27],[2,27],[24,27]],"values":[0,22,25],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 16400/729, 16400/729, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 16400/729, 16400/729, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
73. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,28],[2,28],[25,28]],"values":[0,23,26],"epsilon":[2,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/28, 2301/98, 2301/392, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/28, 2301/98, 2301/392, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
74. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,29],[2,29],[26,29]],"values":[0,24,27],"epsilon":[3,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1/29, 20574/841, 2286/841, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1/29, 20574/841, 2286/841, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
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Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
75. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={"masses":[[1,30],[2,30],[27,30]],"values":[0,25,28],"epsilon":[1,1]}。請依 [tail_probability, variance, raw_upper_bound, bound_holds, certificate] 欄序回答。
raw_upper_bound可大於1且不等於實際尾機率；Chebyshev不需要independence，零變異只約束同一law下幾乎必然的值。
查看答案與解釋
(1, 5726/225, 5726/225, 是, upper_bound_not_tail_equality_and_no_independence_needed)
Wave6第二層核對=(1, 5726/225, 5726/225, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-bound-comparison · candidate
76. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,6],[2,6],[3,6]],"values":[0,1,4],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([49/9, 16/9, 25/9], 1, 1, 1, 是, 26/9, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([49/9, 16/9, 25/9], 1, 1, 1, 是, 26/9, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
77. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,7],[2,7],[4,7]],"values":[0,2,5],"epsilon":[2,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([576/49, 100/49, 121/49], 4, 1/7, 1/7, 是, 45/49, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([576/49, 100/49, 121/49], 4, 1/7, 1/7, 是, 45/49, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
78. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,8],[2,8],[5,8]],"values":[0,3,6],"epsilon":[3,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([81/4, 9/4, 9/4], 9, 1/8, 1/8, 是, 1/2, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([81/4, 9/4, 9/4], 9, 1/8, 1/8, 是, 1/2, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
79. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,9],[2,9],[6,9]],"values":[0,4,7],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([2500/81, 196/81, 169/81], 1, 1, 1, 是, 434/81, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([2500/81, 196/81, 169/81], 1, 1, 1, 是, 434/81, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
80. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,10],[2,10],[7,10]],"values":[0,5,8],"epsilon":[2,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([1089/25, 64/25, 49/25], 4, 1/10, 1/10, 是, 39/25, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([1089/25, 64/25, 49/25], 4, 1/10, 1/10, 是, 39/25, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
81. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,11],[2,11],[8,11]],"values":[0,6,9],"epsilon":[3,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([7056/121, 324/121, 225/121], 9, 1/11, 1/11, 是, 96/121, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([7056/121, 324/121, 225/121], 9, 1/11, 1/11, 是, 96/121, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
82. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,12],[2,12],[9,12]],"values":[0,7,10],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([676/9, 25/9, 16/9], 1, 1, 1, 是, 145/18, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([676/9, 25/9, 16/9], 1, 1, 1, 是, 145/18, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
83. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,13],[2,13],[10,13]],"values":[0,8,11],"epsilon":[2,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([15876/169, 484/169, 289/169], 4, 1/13, 1/13, 是, 759/338, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([15876/169, 484/169, 289/169], 4, 1/13, 1/13, 是, 759/338, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
84. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,14],[2,14],[11,14]],"values":[0,9,12],"epsilon":[3,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([5625/49, 144/49, 81/49], 9, 1/14, 1/14, 是, 54/49, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([5625/49, 144/49, 81/49], 9, 1/14, 1/14, 是, 54/49, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
85. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,15],[2,15],[12,15]],"values":[0,10,13],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([30976/225, 676/225, 361/225], 1, 1, 1, 是, 2444/225, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([30976/225, 676/225, 361/225], 1, 1, 1, 是, 2444/225, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
86. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,16],[2,16],[13,16]],"values":[0,11,14],"epsilon":[2,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([2601/16, 49/16, 25/16], 4, 1/16, 1/16, 是, 189/64, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([2601/16, 49/16, 25/16], 4, 1/16, 1/16, 是, 189/64, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
87. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,17],[2,17],[14,17]],"values":[0,12,15],"epsilon":[3,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([54756/289, 900/289, 441/289], 9, 1/17, 1/17, 是, 410/289, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([54756/289, 900/289, 441/289], 9, 1/17, 1/17, 是, 410/289, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
88. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,18],[2,18],[15,18]],"values":[0,13,16],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([17689/81, 256/81, 121/81], 1, 1, 1, 是, 1112/81, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([17689/81, 256/81, 121/81], 1, 1, 1, 是, 1112/81, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
89. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,19],[2,19],[16,19]],"values":[0,14,17],"epsilon":[2,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([90000/361, 1156/361, 529/361], 4, 1/19, 1/19, 是, 1326/361, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([90000/361, 1156/361, 529/361], 4, 1/19, 1/19, 是, 1326/361, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
90. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,20],[2,20],[17,20]],"values":[0,15,18],"epsilon":[3,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([7056/25, 81/25, 36/25], 9, 1/20, 1/20, 是, 87/50, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([7056/25, 81/25, 36/25], 9, 1/20, 1/20, 是, 87/50, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
91. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,21],[2,21],[18,21]],"values":[0,16,19],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([139876/441, 1444/441, 625/441], 1, 1, 1, 是, 7334/441, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([139876/441, 1444/441, 625/441], 1, 1, 1, 是, 7334/441, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
92. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,22],[2,22],[19,22]],"values":[0,17,20],"epsilon":[2,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([42849/121, 400/121, 169/121], 4, 1/22, 1/22, 是, 1065/242, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([42849/121, 400/121, 169/121], 4, 1/22, 1/22, 是, 1065/242, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
93. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,23],[2,23],[20,23]],"values":[0,18,21],"epsilon":[3,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([207936/529, 1764/529, 729/529], 9, 1/23, 1/23, 是, 1092/529, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([207936/529, 1764/529, 729/529], 9, 1/23, 1/23, 是, 1092/529, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
94. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,24],[2,24],[21,24]],"values":[0,19,22],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([15625/36, 121/36, 49/36], 1, 1, 1, 是, 176/9, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([15625/36, 121/36, 49/36], 1, 1, 1, 是, 176/9, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
95. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,25],[2,25],[22,25]],"values":[0,20,23],"epsilon":[2,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([298116/625, 2116/625, 841/625], 4, 1/25, 1/25, 是, 6417/1250, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([298116/625, 2116/625, 841/625], 4, 1/25, 1/25, 是, 6417/1250, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
96. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,26],[2,26],[23,26]],"values":[0,21,24],"epsilon":[3,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([88209/169, 576/169, 225/169], 9, 1/26, 1/26, 是, 404/169, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([88209/169, 576/169, 225/169], 9, 1/26, 1/26, 是, 404/169, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
97. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,27],[2,27],[24,27]],"values":[0,22,25],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([414736/729, 2500/729, 961/729], 1, 1, 1, 是, 16400/729, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([414736/729, 2500/729, 961/729], 1, 1, 1, 是, 16400/729, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
98. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,28],[2,28],[25,28]],"values":[0,23,26],"epsilon":[2,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([30276/49, 169/49, 64/49], 4, 1/28, 1/28, 是, 2301/392, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([30276/49, 169/49, 64/49], 4, 1/28, 1/28, 是, 2301/392, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
99. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,29],[2,29],[26,29]],"values":[0,24,27],"epsilon":[3,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([562500/841, 2916/841, 1089/841], 9, 1/29, 1/29, 是, 2286/841, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([562500/841, 2916/841, 1089/841], 9, 1/29, 1/29, 是, 2286/841, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
100. Chebyshev不等式
完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={"masses":[[1,30],[2,30],[27,30]],"values":[0,25,28],"epsilon":[1,1]}。請依 [squared_deviations, epsilon_squared, squared_tail, absolute_tail, same_event, raw_upper_bound, certificate] 欄序回答。
查看答案與解釋
([162409/225, 784/225, 289/225], 1, 1, 1, 是, 5726/225, Markov_applied_to_nonnegative_squared_deviation)
Wave6第二層核對=([162409/225, 784/225, 289/225], 1, 1, 1, 是, 5726/225, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。
本題逐步詳解（AI 二次覆核）
Chebyshev不等式 · qf-mod39-cheb-markov-square-derivation · candidate
原始題目 JSONL · 驗收報告