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-20261013-advance-20261025-r06-finite-markov-chain-foundations · 2026-10-13 · 100 題
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 1, [[1/5, 4/5], [1/4, 3/4]], [19/80, 61/80])
收束波核對=([1/4, 3/4], 1, [[1/5, 4/5], [1/4, 3/4]], [19/80, 61/80])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[2,5],[3,5]],[[1,4],[3,4]]],"steps":2}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 2, [[31/100, 69/100], [23/80, 57/80]], [469/1600, 1131/1600])
收束波核對=([1/4, 3/4], 2, [[31/100, 69/100], [23/80, 57/80]], [469/1600, 1131/1600])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[3,5],[2,5]],[[1,4],[3,4]]],"steps":3}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 3, [[411/1000, 589/1000], [589/1600, 1011/1600]], [12123/32000, 19877/32000])
收束波核對=([1/4, 3/4], 3, [[411/1000, 589/1000], [589/1600, 1011/1600]], [12123/32000, 19877/32000])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[4,5],[1,5]],[[1,4],[3,4]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 1, [[4/5, 1/5], [1/4, 3/4]], [31/80, 49/80])
收束波核對=([1/4, 3/4], 1, [[4/5, 1/5], [1/4, 3/4]], [31/80, 49/80])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[1,5],[4,5]],[[1,2],[1,2]]],"steps":2}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 2, [[11/25, 14/25], [7/20, 13/20]], [149/400, 251/400])
收束波核對=([1/4, 3/4], 2, [[11/25, 14/25], [7/20, 13/20]], [149/400, 251/400])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[2,5],[3,5]],[[1,2],[1,2]]],"steps":3}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 3, [[227/500, 273/500], [91/200, 109/200]], [1819/4000, 2181/4000])
收束波核對=([1/4, 3/4], 3, [[227/500, 273/500], [91/200, 109/200]], [1819/4000, 2181/4000])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[3,5],[2,5]],[[1,2],[1,2]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 1, [[3/5, 2/5], [1/2, 1/2]], [21/40, 19/40])
收束波核對=([1/4, 3/4], 1, [[3/5, 2/5], [1/2, 1/2]], [21/40, 19/40])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[4,5],[1,5]],[[1,2],[1,2]]],"steps":2}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 2, [[37/50, 13/50], [13/20, 7/20]], [269/400, 131/400])
收束波核對=([1/4, 3/4], 2, [[37/50, 13/50], [13/20, 7/20]], [269/400, 131/400])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[1,5],[4,5]],[[3,4],[1,4]]],"steps":3}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 3, [[199/500, 301/500], [903/1600, 697/1600]], [16729/32000, 15271/32000])
收束波核對=([1/4, 3/4], 3, [[199/500, 301/500], [903/1600, 697/1600]], [16729/32000, 15271/32000])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[2,5],[3,5]],[[3,4],[1,4]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 1, [[2/5, 3/5], [3/4, 1/4]], [53/80, 27/80])
收束波核對=([1/4, 3/4], 1, [[2/5, 3/5], [3/4, 1/4]], [53/80, 27/80])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[3,5],[2,5]],[[3,4],[1,4]]],"steps":2}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 2, [[33/50, 17/50], [51/80, 29/80]], [1029/1600, 571/1600])
收束波核對=([1/4, 3/4], 2, [[33/50, 17/50], [51/80, 29/80]], [1029/1600, 571/1600])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,4],[3,4]],"transition":[[[4,5],[1,5]],[[3,4],[1,4]]],"steps":3}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/4, 3/4], 3, [[1579/2000, 421/2000], [1263/1600, 337/1600]], [25261/32000, 6739/32000])
收束波核對=([1/4, 3/4], 3, [[1579/2000, 421/2000], [1263/1600, 337/1600]], [25261/32000, 6739/32000])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 1, [[1/5, 4/5], [1/4, 3/4]], [9/40, 31/40])
收束波核對=([1/2, 1/2], 1, [[1/5, 4/5], [1/4, 3/4]], [9/40, 31/40])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[2,5],[3,5]],[[1,4],[3,4]]],"steps":2}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 2, [[31/100, 69/100], [23/80, 57/80]], [239/800, 561/800])
收束波核對=([1/2, 1/2], 2, [[31/100, 69/100], [23/80, 57/80]], [239/800, 561/800])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[3,5],[2,5]],[[1,4],[3,4]]],"steps":3}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 3, [[411/1000, 589/1000], [589/1600, 1011/1600]], [6233/16000, 9767/16000])
收束波核對=([1/2, 1/2], 3, [[411/1000, 589/1000], [589/1600, 1011/1600]], [6233/16000, 9767/16000])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[4,5],[1,5]],[[1,4],[3,4]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 1, [[4/5, 1/5], [1/4, 3/4]], [21/40, 19/40])
收束波核對=([1/2, 1/2], 1, [[4/5, 1/5], [1/4, 3/4]], [21/40, 19/40])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[1,5],[4,5]],[[1,2],[1,2]]],"steps":2}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 2, [[11/25, 14/25], [7/20, 13/20]], [79/200, 121/200])
收束波核對=([1/2, 1/2], 2, [[11/25, 14/25], [7/20, 13/20]], [79/200, 121/200])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[2,5],[3,5]],[[1,2],[1,2]]],"steps":3}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 3, [[227/500, 273/500], [91/200, 109/200]], [909/2000, 1091/2000])
收束波核對=([1/2, 1/2], 3, [[227/500, 273/500], [91/200, 109/200]], [909/2000, 1091/2000])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[3,5],[2,5]],[[1,2],[1,2]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 1, [[3/5, 2/5], [1/2, 1/2]], [11/20, 9/20])
收束波核對=([1/2, 1/2], 1, [[3/5, 2/5], [1/2, 1/2]], [11/20, 9/20])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[4,5],[1,5]],[[1,2],[1,2]]],"steps":2}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 2, [[37/50, 13/50], [13/20, 7/20]], [139/200, 61/200])
收束波核對=([1/2, 1/2], 2, [[37/50, 13/50], [13/20, 7/20]], [139/200, 61/200])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[1,5],[4,5]],[[3,4],[1,4]]],"steps":3}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 3, [[199/500, 301/500], [903/1600, 697/1600]], [7699/16000, 8301/16000])
收束波核對=([1/2, 1/2], 3, [[199/500, 301/500], [903/1600, 697/1600]], [7699/16000, 8301/16000])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[2,5],[3,5]],[[3,4],[1,4]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 1, [[2/5, 3/5], [3/4, 1/4]], [23/40, 17/40])
收束波核對=([1/2, 1/2], 1, [[2/5, 3/5], [3/4, 1/4]], [23/40, 17/40])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[3,5],[2,5]],[[3,4],[1,4]]],"steps":2}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 2, [[33/50, 17/50], [51/80, 29/80]], [519/800, 281/800])
收束波核對=([1/2, 1/2], 2, [[33/50, 17/50], [51/80, 29/80]], [519/800, 281/800])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[1,2],[1,2]],"transition":[[[4,5],[1,5]],[[3,4],[1,4]]],"steps":3}。請依 [initial,steps,power_matrix,law] 欄序回答。
([1/2, 1/2], 3, [[1579/2000, 421/2000], [1263/1600, 337/1600]], [12631/16000, 3369/16000])
收束波核對=([1/2, 1/2], 3, [[1579/2000, 421/2000], [1263/1600, 337/1600]], [12631/16000, 3369/16000])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-law；資料={"initial":[[3,4],[1,4]],"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"steps":1}。請依 [initial,steps,power_matrix,law] 欄序回答。
([3/4, 1/4], 1, [[1/5, 4/5], [1/4, 3/4]], [17/80, 63/80])
收束波核對=([3/4, 1/4], 1, [[1/5, 4/5], [1/4, 3/4]], [17/80, 63/80])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-law · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 1, [[1/5, 4/5], [1/4, 3/4]], 4/5)
收束波核對=(0, 1, 1, [[1/5, 4/5], [1/4, 3/4]], 4/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[2,5],[3,5]],[[1,4],[3,4]]],"from":1,"to":0,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 1, [[2/5, 3/5], [1/4, 3/4]], 1/4)
收束波核對=(1, 0, 1, [[2/5, 3/5], [1/4, 3/4]], 1/4)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[3,5],[2,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 1, [[3/5, 2/5], [1/4, 3/4]], 2/5)
收束波核對=(0, 1, 1, [[3/5, 2/5], [1/4, 3/4]], 2/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[4,5],[1,5]],[[1,4],[3,4]]],"from":1,"to":0,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 1, [[4/5, 1/5], [1/4, 3/4]], 1/4)
收束波核對=(1, 0, 1, [[4/5, 1/5], [1/4, 3/4]], 1/4)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[1,5],[4,5]],[[1,2],[1,2]]],"from":0,"to":1,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 1, [[1/5, 4/5], [1/2, 1/2]], 4/5)
收束波核對=(0, 1, 1, [[1/5, 4/5], [1/2, 1/2]], 4/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[2,5],[3,5]],[[1,2],[1,2]]],"from":1,"to":0,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 1, [[2/5, 3/5], [1/2, 1/2]], 1/2)
收束波核對=(1, 0, 1, [[2/5, 3/5], [1/2, 1/2]], 1/2)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[3,5],[2,5]],[[1,2],[1,2]]],"from":0,"to":1,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 1, [[3/5, 2/5], [1/2, 1/2]], 2/5)
收束波核對=(0, 1, 1, [[3/5, 2/5], [1/2, 1/2]], 2/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[4,5],[1,5]],[[1,2],[1,2]]],"from":1,"to":0,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 1, [[4/5, 1/5], [1/2, 1/2]], 1/2)
收束波核對=(1, 0, 1, [[4/5, 1/5], [1/2, 1/2]], 1/2)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[1,5],[4,5]],[[3,4],[1,4]]],"from":0,"to":1,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 1, [[1/5, 4/5], [3/4, 1/4]], 4/5)
收束波核對=(0, 1, 1, [[1/5, 4/5], [3/4, 1/4]], 4/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[2,5],[3,5]],[[3,4],[1,4]]],"from":1,"to":0,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 1, [[2/5, 3/5], [3/4, 1/4]], 3/4)
收束波核對=(1, 0, 1, [[2/5, 3/5], [3/4, 1/4]], 3/4)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[3,5],[2,5]],[[3,4],[1,4]]],"from":0,"to":1,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 1, [[3/5, 2/5], [3/4, 1/4]], 2/5)
收束波核對=(0, 1, 1, [[3/5, 2/5], [3/4, 1/4]], 2/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[4,5],[1,5]],[[3,4],[1,4]]],"from":1,"to":0,"steps":1}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 1, [[4/5, 1/5], [3/4, 1/4]], 3/4)
收束波核對=(1, 0, 1, [[4/5, 1/5], [3/4, 1/4]], 3/4)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 2, [[6/25, 19/25], [19/80, 61/80]], 19/25)
收束波核對=(0, 1, 2, [[6/25, 19/25], [19/80, 61/80]], 19/25)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[2,5],[3,5]],[[1,4],[3,4]]],"from":1,"to":0,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 2, [[31/100, 69/100], [23/80, 57/80]], 23/80)
收束波核對=(1, 0, 2, [[31/100, 69/100], [23/80, 57/80]], 23/80)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[3,5],[2,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 2, [[23/50, 27/50], [27/80, 53/80]], 27/50)
收束波核對=(0, 1, 2, [[23/50, 27/50], [27/80, 53/80]], 27/50)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[4,5],[1,5]],[[1,4],[3,4]]],"from":1,"to":0,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 2, [[69/100, 31/100], [31/80, 49/80]], 31/80)
收束波核對=(1, 0, 2, [[69/100, 31/100], [31/80, 49/80]], 31/80)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[1,5],[4,5]],[[1,2],[1,2]]],"from":0,"to":1,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 2, [[11/25, 14/25], [7/20, 13/20]], 14/25)
收束波核對=(0, 1, 2, [[11/25, 14/25], [7/20, 13/20]], 14/25)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[2,5],[3,5]],[[1,2],[1,2]]],"from":1,"to":0,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 2, [[23/50, 27/50], [9/20, 11/20]], 9/20)
收束波核對=(1, 0, 2, [[23/50, 27/50], [9/20, 11/20]], 9/20)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[3,5],[2,5]],[[1,2],[1,2]]],"from":0,"to":1,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 2, [[14/25, 11/25], [11/20, 9/20]], 11/25)
收束波核對=(0, 1, 2, [[14/25, 11/25], [11/20, 9/20]], 11/25)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[4,5],[1,5]],[[1,2],[1,2]]],"from":1,"to":0,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 2, [[37/50, 13/50], [13/20, 7/20]], 13/20)
收束波核對=(1, 0, 2, [[37/50, 13/50], [13/20, 7/20]], 13/20)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[1,5],[4,5]],[[3,4],[1,4]]],"from":0,"to":1,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 2, [[16/25, 9/25], [27/80, 53/80]], 9/25)
收束波核對=(0, 1, 2, [[16/25, 9/25], [27/80, 53/80]], 9/25)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[2,5],[3,5]],[[3,4],[1,4]]],"from":1,"to":0,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 2, [[61/100, 39/100], [39/80, 41/80]], 39/80)
收束波核對=(1, 0, 2, [[61/100, 39/100], [39/80, 41/80]], 39/80)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[3,5],[2,5]],[[3,4],[1,4]]],"from":0,"to":1,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 2, [[33/50, 17/50], [51/80, 29/80]], 17/50)
收束波核對=(0, 1, 2, [[33/50, 17/50], [51/80, 29/80]], 17/50)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[4,5],[1,5]],[[3,4],[1,4]]],"from":1,"to":0,"steps":2}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(1, 0, 2, [[79/100, 21/100], [63/80, 17/80]], 63/80)
收束波核對=(1, 0, 2, [[79/100, 21/100], [63/80, 17/80]], 63/80)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-n-step-entry；資料={"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":3}。請依 [from,to,steps,power_matrix,entry] 欄序回答。
(0, 1, 3, [[119/500, 381/500], [381/1600, 1219/1600]], 381/500)
收束波核對=(0, 1, 3, [[119/500, 381/500], [381/1600, 1219/1600]], 381/500)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-n-step-entry · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 0, 1, 1, 1/4, 4/5, 1/5)
收束波核對=([1/4, 3/4], 0, 1, 1, 1/4, 4/5, 1/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[2,5],[3,5]],[[1,4],[3,4]]],"from":1,"to":0,"steps":2}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 1, 0, 2, 3/4, 23/80, 69/320)
收束波核對=([1/4, 3/4], 1, 0, 2, 3/4, 23/80, 69/320)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[3,5],[2,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":3}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 0, 1, 3, 1/4, 589/1000, 589/4000)
收束波核對=([1/4, 3/4], 0, 1, 3, 1/4, 589/1000, 589/4000)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[4,5],[1,5]],[[1,4],[3,4]]],"from":1,"to":0,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 1, 0, 1, 3/4, 1/4, 3/16)
收束波核對=([1/4, 3/4], 1, 0, 1, 3/4, 1/4, 3/16)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[1,5],[4,5]],[[1,2],[1,2]]],"from":0,"to":1,"steps":2}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 0, 1, 2, 1/4, 14/25, 7/50)
收束波核對=([1/4, 3/4], 0, 1, 2, 1/4, 14/25, 7/50)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[2,5],[3,5]],[[1,2],[1,2]]],"from":1,"to":0,"steps":3}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 1, 0, 3, 3/4, 91/200, 273/800)
收束波核對=([1/4, 3/4], 1, 0, 3, 3/4, 91/200, 273/800)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[3,5],[2,5]],[[1,2],[1,2]]],"from":0,"to":1,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 0, 1, 1, 1/4, 2/5, 1/10)
收束波核對=([1/4, 3/4], 0, 1, 1, 1/4, 2/5, 1/10)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[4,5],[1,5]],[[1,2],[1,2]]],"from":1,"to":0,"steps":2}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 1, 0, 2, 3/4, 13/20, 39/80)
收束波核對=([1/4, 3/4], 1, 0, 2, 3/4, 13/20, 39/80)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[1,5],[4,5]],[[3,4],[1,4]]],"from":0,"to":1,"steps":3}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 0, 1, 3, 1/4, 301/500, 301/2000)
收束波核對=([1/4, 3/4], 0, 1, 3, 1/4, 301/500, 301/2000)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[2,5],[3,5]],[[3,4],[1,4]]],"from":1,"to":0,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 1, 0, 1, 3/4, 3/4, 9/16)
收束波核對=([1/4, 3/4], 1, 0, 1, 3/4, 3/4, 9/16)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[3,5],[2,5]],[[3,4],[1,4]]],"from":0,"to":1,"steps":2}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 0, 1, 2, 1/4, 17/50, 17/200)
收束波核對=([1/4, 3/4], 0, 1, 2, 1/4, 17/50, 17/200)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,4],[3,4]],"transition":[[[4,5],[1,5]],[[3,4],[1,4]]],"from":1,"to":0,"steps":3}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/4, 3/4], 1, 0, 3, 3/4, 1263/1600, 3789/6400)
收束波核對=([1/4, 3/4], 1, 0, 3, 3/4, 1263/1600, 3789/6400)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 0, 1, 1, 1/2, 4/5, 2/5)
收束波核對=([1/2, 1/2], 0, 1, 1, 1/2, 4/5, 2/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[2,5],[3,5]],[[1,4],[3,4]]],"from":1,"to":0,"steps":2}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 1, 0, 2, 1/2, 23/80, 23/160)
收束波核對=([1/2, 1/2], 1, 0, 2, 1/2, 23/80, 23/160)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[3,5],[2,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":3}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 0, 1, 3, 1/2, 589/1000, 589/2000)
收束波核對=([1/2, 1/2], 0, 1, 3, 1/2, 589/1000, 589/2000)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[4,5],[1,5]],[[1,4],[3,4]]],"from":1,"to":0,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 1, 0, 1, 1/2, 1/4, 1/8)
收束波核對=([1/2, 1/2], 1, 0, 1, 1/2, 1/4, 1/8)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[1,5],[4,5]],[[1,2],[1,2]]],"from":0,"to":1,"steps":2}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 0, 1, 2, 1/2, 14/25, 7/25)
收束波核對=([1/2, 1/2], 0, 1, 2, 1/2, 14/25, 7/25)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[2,5],[3,5]],[[1,2],[1,2]]],"from":1,"to":0,"steps":3}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 1, 0, 3, 1/2, 91/200, 91/400)
收束波核對=([1/2, 1/2], 1, 0, 3, 1/2, 91/200, 91/400)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[3,5],[2,5]],[[1,2],[1,2]]],"from":0,"to":1,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 0, 1, 1, 1/2, 2/5, 1/5)
收束波核對=([1/2, 1/2], 0, 1, 1, 1/2, 2/5, 1/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[4,5],[1,5]],[[1,2],[1,2]]],"from":1,"to":0,"steps":2}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 1, 0, 2, 1/2, 13/20, 13/40)
收束波核對=([1/2, 1/2], 1, 0, 2, 1/2, 13/20, 13/40)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[1,5],[4,5]],[[3,4],[1,4]]],"from":0,"to":1,"steps":3}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 0, 1, 3, 1/2, 301/500, 301/1000)
收束波核對=([1/2, 1/2], 0, 1, 3, 1/2, 301/500, 301/1000)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[2,5],[3,5]],[[3,4],[1,4]]],"from":1,"to":0,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 1, 0, 1, 1/2, 3/4, 3/8)
收束波核對=([1/2, 1/2], 1, 0, 1, 1/2, 3/4, 3/8)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[3,5],[2,5]],[[3,4],[1,4]]],"from":0,"to":1,"steps":2}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 0, 1, 2, 1/2, 17/50, 17/100)
收束波核對=([1/2, 1/2], 0, 1, 2, 1/2, 17/50, 17/100)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[1,2],[1,2]],"transition":[[[4,5],[1,5]],[[3,4],[1,4]]],"from":1,"to":0,"steps":3}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([1/2, 1/2], 1, 0, 3, 1/2, 1263/1600, 1263/3200)
收束波核對=([1/2, 1/2], 1, 0, 3, 1/2, 1263/1600, 1263/3200)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-endpoint-joint-probability；資料={"initial":[[3,4],[1,4]],"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"from":0,"to":1,"steps":1}。請依 [initial,from,to,steps,initial_mass,n_step_entry,joint_probability] 欄序回答。
([3/4, 1/4], 0, 1, 1, 3/4, 4/5, 3/5)
收束波核對=([3/4, 1/4], 0, 1, 1, 3/4, 4/5, 3/5)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-endpoint-joint-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"path":[0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0], [4/5, 1/4], 1/5, conditional_on_initial_state)
收束波核對=([0, 1, 0], [4/5, 1/4], 1/5, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[2,5],[3,5]],[[1,4],[3,4]]],"path":[1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1], [1/4, 3/5], 3/20, conditional_on_initial_state)
收束波核對=([1, 0, 1], [1/4, 3/5], 3/20, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[3,5],[2,5]],[[1,4],[3,4]]],"path":[0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0], [2/5, 1/4], 1/10, conditional_on_initial_state)
收束波核對=([0, 1, 0], [2/5, 1/4], 1/10, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[4,5],[1,5]],[[1,4],[3,4]]],"path":[1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1], [1/4, 1/5], 1/20, conditional_on_initial_state)
收束波核對=([1, 0, 1], [1/4, 1/5], 1/20, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[1,5],[4,5]],[[1,2],[1,2]]],"path":[0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0], [4/5, 1/2], 2/5, conditional_on_initial_state)
收束波核對=([0, 1, 0], [4/5, 1/2], 2/5, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[2,5],[3,5]],[[1,2],[1,2]]],"path":[1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1], [1/2, 3/5], 3/10, conditional_on_initial_state)
收束波核對=([1, 0, 1], [1/2, 3/5], 3/10, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[3,5],[2,5]],[[1,2],[1,2]]],"path":[0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0], [2/5, 1/2], 1/5, conditional_on_initial_state)
收束波核對=([0, 1, 0], [2/5, 1/2], 1/5, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[4,5],[1,5]],[[1,2],[1,2]]],"path":[1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1], [1/2, 1/5], 1/10, conditional_on_initial_state)
收束波核對=([1, 0, 1], [1/2, 1/5], 1/10, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[1,5],[4,5]],[[3,4],[1,4]]],"path":[0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0], [4/5, 3/4], 3/5, conditional_on_initial_state)
收束波核對=([0, 1, 0], [4/5, 3/4], 3/5, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[2,5],[3,5]],[[3,4],[1,4]]],"path":[1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1], [3/4, 3/5], 9/20, conditional_on_initial_state)
收束波核對=([1, 0, 1], [3/4, 3/5], 9/20, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[3,5],[2,5]],[[3,4],[1,4]]],"path":[0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0], [2/5, 3/4], 3/10, conditional_on_initial_state)
收束波核對=([0, 1, 0], [2/5, 3/4], 3/10, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[4,5],[1,5]],[[3,4],[1,4]]],"path":[1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1], [3/4, 1/5], 3/20, conditional_on_initial_state)
收束波核對=([1, 0, 1], [3/4, 1/5], 3/20, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"path":[0,1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0, 1], [4/5, 1/4, 4/5], 4/25, conditional_on_initial_state)
收束波核對=([0, 1, 0, 1], [4/5, 1/4, 4/5], 4/25, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[2,5],[3,5]],[[1,4],[3,4]]],"path":[1,0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1, 0], [1/4, 3/5, 1/4], 3/80, conditional_on_initial_state)
收束波核對=([1, 0, 1, 0], [1/4, 3/5, 1/4], 3/80, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[3,5],[2,5]],[[1,4],[3,4]]],"path":[0,1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0, 1], [2/5, 1/4, 2/5], 1/25, conditional_on_initial_state)
收束波核對=([0, 1, 0, 1], [2/5, 1/4, 2/5], 1/25, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[4,5],[1,5]],[[1,4],[3,4]]],"path":[1,0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1, 0], [1/4, 1/5, 1/4], 1/80, conditional_on_initial_state)
收束波核對=([1, 0, 1, 0], [1/4, 1/5, 1/4], 1/80, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[1,5],[4,5]],[[1,2],[1,2]]],"path":[0,1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0, 1], [4/5, 1/2, 4/5], 8/25, conditional_on_initial_state)
收束波核對=([0, 1, 0, 1], [4/5, 1/2, 4/5], 8/25, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[2,5],[3,5]],[[1,2],[1,2]]],"path":[1,0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1, 0], [1/2, 3/5, 1/2], 3/20, conditional_on_initial_state)
收束波核對=([1, 0, 1, 0], [1/2, 3/5, 1/2], 3/20, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[3,5],[2,5]],[[1,2],[1,2]]],"path":[0,1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0, 1], [2/5, 1/2, 2/5], 2/25, conditional_on_initial_state)
收束波核對=([0, 1, 0, 1], [2/5, 1/2, 2/5], 2/25, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[4,5],[1,5]],[[1,2],[1,2]]],"path":[1,0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1, 0], [1/2, 1/5, 1/2], 1/20, conditional_on_initial_state)
收束波核對=([1, 0, 1, 0], [1/2, 1/5, 1/2], 1/20, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[1,5],[4,5]],[[3,4],[1,4]]],"path":[0,1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0, 1], [4/5, 3/4, 4/5], 12/25, conditional_on_initial_state)
收束波核對=([0, 1, 0, 1], [4/5, 3/4, 4/5], 12/25, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[2,5],[3,5]],[[3,4],[1,4]]],"path":[1,0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1, 0], [3/4, 3/5, 3/4], 27/80, conditional_on_initial_state)
收束波核對=([1, 0, 1, 0], [3/4, 3/5, 3/4], 27/80, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[3,5],[2,5]],[[3,4],[1,4]]],"path":[0,1,0,1]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0, 1], [2/5, 3/4, 2/5], 3/25, conditional_on_initial_state)
收束波核對=([0, 1, 0, 1], [2/5, 3/4, 2/5], 3/25, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[4,5],[1,5]],[[3,4],[1,4]]],"path":[1,0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([1, 0, 1, 0], [3/4, 1/5, 3/4], 9/80, conditional_on_initial_state)
收束波核對=([1, 0, 1, 0], [3/4, 1/5, 3/4], 9/80, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate
精確有限時間齊次row-stochastic kernel。操作=markovdeep-conditional-path-probability；資料={"transition":[[[1,5],[4,5]],[[1,4],[3,4]]],"path":[0,1,0,1,0]}。請依 [path,transition_factors,conditional_probability,scope] 欄序回答。
([0, 1, 0, 1, 0], [4/5, 1/4, 4/5, 1/4], 1/25, conditional_on_initial_state)
收束波核對=([0, 1, 0, 1, 0], [4/5, 1/4, 4/5, 1/4], 1/25, conditional_on_initial_state)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只計有限步律或條件路徑；不推出平穩不可約遍歷或極限。
有限狀態 Markov 鏈 · qf-mod25-markovdeep-conditional-path-probability · candidate