设二维随机变量(X,Y)的概率密度为f(x,y)=2-x-y
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设二维随机变量(X,Y)的概率密度为f(x,y)=2-x-y
![设二维随机变量(X,Y)的概率密度为f(x,y)=2-x-y](/uploads/image/z/7281123-51-3.jpg?t=%E8%AE%BE%E4%BA%8C%E7%BB%B4%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%EF%BC%88X%2CY%EF%BC%89%E7%9A%84%E6%A6%82%E7%8E%87%E5%AF%86%E5%BA%A6%E4%B8%BAf%EF%BC%88x%2Cy%EF%BC%89%3D2-x-y)
∫(0~1)∫(2y~1) 2-x-y dxdy
=∫(0~1){ (2-y)x-x²/2 |(2y~1) } dy
=∫(0~1)(2-y)(1-2y)-(1-4y²)/2 dy
=∫(0~1) 2-5y+2y²-(1-4y²)/2 dy
= 2y-2.5y²+(2/3)y³-(y-4y³/3)/2 (y=1)
=2-2.5+2/3-(-1/6)
=5/6-0.5
=4/12
=1/3
z=x+y
当z=x+y1时
卷积
(z-1~1) 就是方块右上角
∫(z-1~1) f(x,z-x) dx
= (2-z)(2-z+1)
=(2-z)²
fz(z)=(2-z)z (0
=∫(0~1){ (2-y)x-x²/2 |(2y~1) } dy
=∫(0~1)(2-y)(1-2y)-(1-4y²)/2 dy
=∫(0~1) 2-5y+2y²-(1-4y²)/2 dy
= 2y-2.5y²+(2/3)y³-(y-4y³/3)/2 (y=1)
=2-2.5+2/3-(-1/6)
=5/6-0.5
=4/12
=1/3
z=x+y
当z=x+y1时
卷积
(z-1~1) 就是方块右上角
∫(z-1~1) f(x,z-x) dx
= (2-z)(2-z+1)
=(2-z)²
fz(z)=(2-z)z (0
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