作者cllcsonia (哲〃~☑)
看板Statistics
標題[問題] 二元隨機變數
時間Wed Nov 23 01:50:30 2011
台大統計學作業.......
Each customer who enters Larry's clothing store will
purchase a suit with probability p.
Assume that the number of customers entering the store in one day
is Poisson distributed with mean s.
Let X denote the number of suits Larry sold out
and Y denote the number of customers entered Larry's store.
Find E(X) and Var(X)
(USE E(X)=E(E(X|Y)) and Var(X)=Var(E(X|Y))+E(Var(X|Y))
完全沒有什麼概念...
只知道f(Y)=poisson分配 E(Y)=s
請板友們解答疑惑謝謝:))
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1F：推 srarod:給定Y,X會是B(Y,p) 這就是X|Y的分佈.用提示的話都能算了吧 11/23 02:37
2F：推 goshfju:E(Y)=s , E(X|y)=yp -> EE(X|Y)=E(Yp)=pE(Y)=ps 11/23 12:06
3F：→ goshfju: E(X)= 11/23 12:06
4F：→ goshfju:..推文亂了 反正就這樣算 提示已經提示完了 11/23 12:07
5F：→ panda0822:企鵝蛋 11/23 20:29
6F：推 panda0822:Y~Poi(s) X|Y=y~B(n=y P=p) E(X)=E[E(X|Y)]=E(py)=pE(y) 11/23 20:46
7F：→ panda0822:=ps 11/23 20:46
8F：→ panda0822:Var(X)=Var[E(X|Y)]+E[Var(X|Y)]=Var(ypq)+E(yp) 11/23 20:48
9F：→ panda0822:p(1-p)s+p^2s=ps 11/23 20:49
10F：→ cllcsonia:謝謝大家! 看懂了:) 11/23 23:43