[機統] 二元隨機變數

看板Math作者 (哲〃~☑)時間14年前 (2011/11/23 01:48), 編輯推噓3(3推 0噓 2→)
留言5則, 3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 02:42, , 1F
(X|Y=s)~B(n=s,p) => E(X)=E(E(X|Y))=E(Sp)=pE(S)=sp
11/23 02:42, 1F
推
11/23 02:46, , 2F
　　　　　　　　 　　=E(Yp)=pE(Y)=sp
11/23 02:46, 2F
推
11/23 08:21, , 3F
可證明得 X~P(sp)
11/23 08:21, 3F
→
11/23 08:26, , 4F
Var(x)=Var(Yp)+E(Y*p*(1-p))=sp
11/23 08:26, 4F
→
11/23 23:44, , 5F
謝謝大家:) 了解了!
11/23 23:44, 5F
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文章代碼(AID): #1Eo-1Nhi (Math)