PTT職涯區 / CFAiafeFSA (精算師/基金經理人/銀行家)

[問題] coin tossing

看板CFAiafeFSA (精算師/基金經理人/銀行家)作者 (cjchen)時間14年前 (2011/02/01 10:59), 編輯推噓2(2推 0噓 2→)
留言4則, 2人參與, 最新討論串1/1
Assume a coin is fair and your initial position is flat. You gain $1 on a head and lose $1 on a tail. You quit the game once you position is +$1. Then what is the probability that the game terminates? I tried to draw a binomial tree and realized that the answer should be greater than 2/3, but couldn't find out an analytical solution. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 219.75.60.122
推
02/01 17:10, , 1F
with probability 1, it is a simple random walk
02/01 17:10, 1F
→
02/01 17:11, , 2F
every state space (integer) is recurrent
02/01 17:11, 2F
→
02/01 17:11, , 3F
you should study stochastic process or probability
02/01 17:11, 3F
推
02/04 11:17, , 4F
1/2+1/2*1/2+1/2*1/2*1/2....loop=1/2/(1-1/2)=1=ans.
02/04 11:17, 4F
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