i*****l
发帖数: 50 | 1 【 以下文字转载自 Quant 讨论区 】
发信人: ilovekl (ibm), 信区: Quant
标 题: 请教一个概率题
发信站: BBS 未名空间站 (Thu Dec 13 23:58:15 2007), 转信
Let X have the binomial distribution bin(n, U), where U is
uniform on (0,1). Show that X is uniformly distributed on
{0,1,2,....n}
不知道发哪里好，这里牛人多，给解一解吧 | s******h
发帖数: 539 | 2 I would use P(X=k)=E{E{I{X=k}|U}}
=E{\choose(n,k)U^k(1-U)^{n-k}}
=\choose(n,k)*Beta(k+1,n-k+1)
=1/(n+1)
Notice that
Beta(\alpha,\beta0=\frac{\Gamma{\alpha}*\Gamma{\beta}}{\Gamma{\alpha+\beta}}
and
\Gamma{m}=(m-1)! |
|
