[理工] [機率-期望值]
A fair coin is tossed until two tails occur successively.
Find th expected number of the tosses required.
=======================我的想法=======================
r.v.X 直到連續兩次tail出現的次數
反 反
_ _ _ _ _ _ _ _ _ _
X-1 X
x-2 2 x-2 x
f(x) = C (0.5) (0.5) = (0.5)
0
00 x
E[X] = Σ x(0.5) = 卡住了.......
x=2
答案是6 請問我哪裡出錯了?
==========================分隔線=======================
第r次成功的意思
反
_ _ _ _ _ _ _ _ _
X
另一個"反" 在x-1次中出現就好了
而連續出現規定在最後兩次一起出現 這樣應該不算負二項了吧
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◆ From: 220.129.33.146
推
08/07 19:11, , 1F
08/07 19:11, 1F
→
08/07 19:11, , 2F
08/07 19:11, 2F
→
08/07 19:21, , 3F
08/07 19:21, 3F
→
08/07 19:35, , 4F
08/07 19:35, 4F
→
08/07 22:42, , 5F
08/07 22:42, 5F
推
08/08 04:35, , 6F
08/08 04:35, 6F
→
08/08 04:35, , 7F
08/08 04:35, 7F
→
08/08 14:25, , 8F
08/08 14:25, 8F
※ 編輯: lai90043 來自: 218.175.208.231 (08/08 14:30)
推
08/08 14:54, , 9F
08/08 14:54, 9F
推
08/08 15:05, , 10F
08/08 15:05, 10F
→
08/08 15:05, , 11F
08/08 15:05, 11F
→
08/08 18:58, , 12F
08/08 18:58, 12F
推
08/08 19:09, , 13F
08/08 19:09, 13F
→
09/11 14:28, , 14F
09/11 14:28, 14F