[理工] 台大98 工數(D) 機率的問題

看板Grad-ProbAsk作者 (Seark)時間12年前 (2012/02/12 08:15), 編輯推噓2(2011)
留言13則, 4人參與, 最新討論串1/1
A and B are playing a game as follow. First,A and B pick their own numbers uniformly from {1,2,3,4,5} and {1,3,8},resprctively. Assume that A's number (say a1)is smaller than or equal B's number(say b1),then A gets on dollar. Whoever gets one dollar(in this case,A)can pick an new number,say a2, for the next run using his uniform distribution. Whoever does not get one dollar(in this case,B)will use a new number b2 = b1-a1 for the next run. The same rule applies to B.(Note that it is possible that both get one dollar in the same run).Let A and B play this game for an infinite number of time, what is the ratio of A's money and B's money at the end of the game? a)3:5 b)3:4 c)5:3 d)5:4 e)none of above 題目有點長~ 計算到一個無止盡的深淵 希望有人能幫我解惑一下 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.194.24.76 ※ 編輯: seark1219 來自: 123.194.24.76 (02/12 08:16)

02/12 13:45, , 1F
題目只是要問取樣次數 n→∞ 的行為為何
02/12 13:45, 1F

02/12 13:46, , 2F
由題目可以發現兩人隨機選取的 total number
02/12 13:46, 2F

02/12 13:47, , 3F
其差值覺不會超過 (8-1)=7 ; 因此當 n→∞
02/12 13:47, 3F

02/12 13:48, , 4F
兩人的 total number 會"幾乎"一樣
02/12 13:48, 4F

02/12 13:51, , 5F
所以 "A平均取樣數 * A錢數 = B平均取樣數 * B錢數"
02/12 13:51, 5F

02/12 13:52, , 6F
忘記加選項上來~ 透過差值怎麼判斷到最後獲勝機率相等阿
02/12 13:52, 6F
※ 編輯: seark1219 來自: 123.194.24.76 (02/12 13:52)

02/12 13:52, , 7F
A錢數 : B錢數 = (1+3+8)/3 : (1+2+3+4+5)/5
02/12 13:52, 7F
※ 編輯: seark1219 來自: 123.194.24.76 (02/12 13:54)

02/12 13:58, , 8F
獲勝機率不會相等阿, 答案應該是 4:3, 可是沒這選項
02/12 13:58, 8F

02/12 13:59, , 9F
所以當取樣次數無限時,他們的差值就沒什麼意義了嘛
02/12 13:59, 9F

02/12 14:00, , 10F
對, 是指 總取樣數字; 答案應該是選e
02/12 14:00, 10F

02/12 14:03, , 11F
你太神了!謝謝 >.< 我在研究一下
02/12 14:03, 11F

02/12 17:56, , 12F
看到就拜了啊 ...機率也會 XD"
02/12 17:56, 12F

09/11 14:55, , 13F
題目只是要問取樣次數 https://daxiv.com
09/11 14:55, 13F
文章代碼(AID): #1FDmItFg (Grad-ProbAsk)