Joint PDF (20Pts)

我不確定你會否刪帖，所以我暫時在這作答。

(a)
f_X(x) = ∫[x ~ 1] f(x, y) dy = 2(1 - x) for 0 < x < 1 and zero otherwise
f_Y(y) = ∫[0 ~ y] f(x, y) dx = 2y for 0 < y < 1 and zero otherwise

(b)
No. In the joint support x < y, the range of x depends on y.

2015-04-01 22:46:23 補充：
(c)
f(x|y) = f(x,y)/f_Y(y) = 1/y for 0 < x < y

Actually, X | (Y = y) ~ U(0, y)

E(X | Y = y) = y/2

Or you can do it by integration:

∫[0 ~ y] x/y dx
= [x²/(2y)]@(x = y) - [x²/(2y)]@(x = 0)
= y²/(2y)
= y/2

2015-04-02 00:58:12 補充：
Please read:


圖片參考：https://s.yimg.com/rk/HA00430218/o/174267971.png


2015-04-02 09:41:50 補充：
可能是系統問題或者自己按錯鍵刪掉了？
不清楚。。。

請問，真的可以刪人地的帖嗎 ?

為何我要刪帖呢?之前的問題不知為何被人刪左。