n个均匀分布随机量之和的分布函数


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送交者: testtest 于 2008-12-18, 00:40:28:

回答: 008你是怎么算的?能不能用解析法证明N=3的时候答案就是1/6? 由 Amsel 于 2008-12-17, 12:36:44:

http://www.xys.org/forum/db/4/95/13.html

according to the link you provided, when 0<=x<=n,

f(x) = sum_{i=0}^{[x]} (-1)^i C(n,i) (x-i)^(n-1) / (n-1)!

This has the similar idea to a Pascal Triangle.
Integrating f(x) from (0.5n+0.5) to n will give the answer. When n is big enough, f(x) is close to be symmetric, and the probability will be close to 0.5.




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