作者buttermilk (脱脂牛奶)
看板Statistics
标题[问题] f_X,Y与F_Z的关系
时间Wed Apr 18 08:49:18 2007
f_X,Y(x,y) = 1, 0 < x < 1, 0 < y < 1
= 0, elsewhere
Let Z = X + Y.
F_Z(z) = P(Z≦z) = P(X+Y≦z).
Then F_Z(z) = 0 z < 0
z z-x
= ∫∫dydx = (z^2)/2 0≦z<1
0 0
1 1
= 1-∫∫dydx = 1-[(2-z)^2]/2 1≦z<2
z-1z-x
= 1 2≦z
请问f_X,Y(x,y)是怎麽变成F_Z(z)的？
我看不太懂F_Z(z)等式後面那些积分的上下标范围。
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