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石家庄二模19题 马尔可夫链

  • 2026-04-30 13:43:54
石家庄二模19题 马尔可夫链

第(1)问(ii)

若第一轮甲胜，甲直接获胜；

若第一轮甲负，则第二轮乙进攻，甲必需要胜，第三轮回到甲进攻，此时甲仍为  分，最终获胜的概率为 .

故 ，解得 

第(2)问

设  为甲为  分且乙为进攻方时，甲最终获胜的概率.

则

消去  得

即  成等差数列.

当  时，，，消去  得 ，故公差

又 ，可求得 ，故 

总结

要引入  来区分轮到谁进攻，这样才能建立起  的递推关系.

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  1. CONNECT:[ UseTime:0.000554s ] mysql:host=127.0.0.1;port=3306;dbname=nowww460;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000685s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000318s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000291s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000533s ]
  6. SELECT * FROM `set` [ RunTime:0.000201s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000581s ]
  8. SELECT * FROM `article` WHERE `id` = 502596 LIMIT 1 [ RunTime:0.018695s ]
  9. UPDATE `article` SET `lasttime` = 1777574259 WHERE `id` = 502596 [ RunTime:0.003304s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.007093s ]
  11. SELECT * FROM `article` WHERE `id` < 502596 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000643s ]
  12. SELECT * FROM `article` WHERE `id` > 502596 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000431s ]
  13. SELECT * FROM `article` WHERE `id` < 502596 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.006141s ]
  14. SELECT * FROM `article` WHERE `id` < 502596 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.014654s ]
  15. SELECT * FROM `article` WHERE `id` < 502596 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.028245s ]
0.153939s