[問題] 二元隨機變數

看板Statistics作者 (哲〃~☑)時間14年前 (2011/11/23 01:50), 編輯推噓3(3推 0噓 7→)
留言10則, 4人參與, 最新討論串1/1
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:)) -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.193.23.246
推
11/23 02:37, , 1F
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, 1F
推
11/23 12:06, , 2F
E(Y)=s , E(X|y)=yp -> EE(X|Y)=E(Yp)=pE(Y)=ps
11/23 12:06, 2F
→
11/23 12:06, , 3F
E(X)=
11/23 12:06, 3F
→
11/23 12:07, , 4F
..推文亂了 反正就這樣算 提示已經提示完了
11/23 12:07, 4F
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11/23 20:29, , 5F
企鵝蛋
11/23 20:29, 5F
推
11/23 20:46, , 6F
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, 6F
→
11/23 20:46, , 7F
=ps
11/23 20:46, 7F
→
11/23 20:48, , 8F
Var(X)=Var[E(X|Y)]+E[Var(X|Y)]=Var(ypq)+E(yp)
11/23 20:48, 8F
→
11/23 20:49, , 9F
p(1-p)s+p^2s=ps
11/23 20:49, 9F
→
11/23 23:43, , 10F
謝謝大家! 看懂了:)
11/23 23:43, 10F
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文章代碼(AID): #1Eo-3fAl (Statistics)