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标题: Another prob question [打印本页]

作者: HF: 时间: 2008-7-19 00:47
标题: Another prob question

Toss a coin until the nth Head turns up. Let Y=number of required tosses
, calculate Prob(Y is even). Assume the probability of head of each toss is p.

作者: try-it- 时间: 2008-7-24 18:52
标题: 回复：Another prob question

let

O (n) be the total probability of nth head shows up at the odd number of toss

E (n) for even number of toss

we have

E (n) = (1-p) * O (n) + p * O (n-1)

E (n) + O (n) = 1

thus we get a recurrence relation for O (n)

O (n) = -p/(2-p) * O (n-1) + 1/(2-p)

Solving it we have

O (n) = (-p/(2-p))^(n-1) * ( O (1) - 1/2) +1/2

with O( 1 ) = 1/(2-p)

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