设二维随机变量(X,Y)的概率密度为f(x,y)=kx(x-y),0

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设二维随机变量(X,Y)的概率密度为f(x,y)=kx(x-y),0
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设二维随机变量(X,Y)的概率密度为f(x,y)=kx(x-y),0
设二维随机变量(X,Y)的概率密度为f(x,y)=kx(x-y),0

设二维随机变量(X,Y)的概率密度为f(x,y)=kx(x-y),0
1=∫(0~2)∫(-x~x) kx(x-y)dydx
1=∫(0~2) kx(xy-y^2/2)|(-x~x) dx
1=∫(0~2)2kx^3dx
1=2kx^4/4(0~2)
1=8k
k=1/8
画图可知范围
fy(y)=∫(|y|~2) kx(x-y)dx
=kx^3/3-kyx^2/2 | |y|~2
=1/8(8/3-2-(y^2|y|/3-y^3/2))
=1/12-y^2|y|/24+y^3/16
(-2