设二维随机变量(X,Y)的概率密度为f(x,y)=A(x+y),0

A=1/∫(x+y)dxdy=1/3
f_X(x)=∫f(x,y)dy=2/3(x+1)
f_Y(y)=∫f(x,y)dx=1/3(y+1/2)
f_X(x)f_Y(y)=1/3(x+y)+2/3≠f(x,y)
X与Y不独立
P{X+Y<1}=∫_{0}^{1}dx∫_{0}^{1-x}dyf(x,y)=1/3∫_{0}^{1}dx(1-x^2)/2=1/9