设二维随机变量（X,Y）的概率密度为f（x,y）=2-x-y

网友回答

∫(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=1/3z=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