雙期望值 - 考試
By Todd Johnson
at 2013-01-27T00:08
at 2013-01-27T00:08
Table of Contents
有一小題 雙期望值 我覺得解答寫得很怪 想請教板上各位大大...
假設
1.x服從E(X)=b的指數分配，即x~exp(1/b)
2.y也服從E(X)=b的指數分配，即x~exp(1/b)
求E(X│X+Y)=?
ANS:E(E(X│X+Y))=(X+Y)/2
由於動差母函數的相加性，X+Y服從GAMMA(2,1/b)
基於雙期望值定理
E(E(X│X+Y))=(X+Y)/2
解答直接跳到這裡
我的理解是：E(E(X│X+Y))=E(2b(x))=2b*E(X)=2b*b=2*b^2
這根解答差很多，這題過程有點無法理解
想要請教 拜託了
--
假設
1.x服從E(X)=b的指數分配，即x~exp(1/b)
2.y也服從E(X)=b的指數分配，即x~exp(1/b)
求E(X│X+Y)=?
ANS:E(E(X│X+Y))=(X+Y)/2
由於動差母函數的相加性，X+Y服從GAMMA(2,1/b)
基於雙期望值定理
E(E(X│X+Y))=(X+Y)/2
解答直接跳到這裡
我的理解是：E(E(X│X+Y))=E(2b(x))=2b*E(X)=2b*b=2*b^2
這根解答差很多，這題過程有點無法理解
想要請教 拜託了
--
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考試
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