[商管] [統計] 期望值 變異數

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請問一下該怎麼算？？

Problem 3 (40%) Let Z ~ U(0,1), and Y = -㏑(1-Z).

1. Use CDF technique to identify the distribution of Y.

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？

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→ ha18:(a)我是直覺用雙期望值定理，一起等高手解答囉！
→ ha18:不對，應該是b，可是也看到原po說要用了XD
推 loveliver:1.f(y)=e^(-1),Y~exp(1)  2.(a) E(X｜Y=y)=y
→ loveliver:2.(b)E(X)=E(Y)=1/1=1
→ loveliver:好像是這樣XD 參考就好...
推 loveliver:2.(c)V(X)=V(E(X|Y))+E(V(X|Y))=V(Y)+V(E)=1/1^2+1/1=2
推 loveliver:寫錯 V(Y)+V(Y)=2V(Y)=2*(1/(1^2))=2 #