作者loveliver (广伸小队正夯!!)
看板Grad-ProbAsk
标题Re: [商管] [统计] 期望值 变异数
时间Sun Jan 3 22:05:31 2010
※ 引述《pkpkpkpkpkpk (pk)》之铭言：
: 请问一下该怎麽算？？
: Problem 3 (40%) Let Z ~ U(0,1), and Y = -㏑(1-Z).
: 1. Use CDF technique to identify the distribution of Y.
1-e^(-y)
F(y)=P(Y<y)=P(-ln(1-Z)<y)=P(Z<1-e^(-y))=S 1*dz=1-e^(-y)
0
又F'(y)=f(y)=0-(-1*e^(-y))= e^(-y)
由0<Z<1 => 0<1-e^(-y)<1 => -1<-e^(-y)<0 => 1>e^(-y)>0 => 0>-y> -M
=> 0<y<M (M代表无限大)
so p.d.f of r.v.Y is f(y)= e^(-y) , 0<y<M => Y~exp(1) #
: 2. Suppose that X ~ Poisson(Y).
: (a) Find E(X｜Y=y) = ?
: (b) Find E(X) = ?
: (c) Find Var(X) = ?
: （ｂ）我的想法是用E(E(X|Y).(C)我的想法是用V(X)=V(E(X|Y))+E(V(X|Y))
: 那1跟2的(a)要如何算？
(a) E(X|Y=y)=y #
(b) E(X)=E[E(X|Y)]=E[Y]=1/1=1 #
(c) V(X)=V(E(X|Y))+E(V(X|Y))=V(Y)+E(Y)=1/(1^2) + 1/1 =2 #
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◆ From: 140.114.231.103
※ 编辑: loveliver 来自: 140.114.231.103 (01/03 22:07)
1F：推 pkpkpkpkpkpk:感谢!!!!!!!!! 01/04 00:07