概率统计,二维连续型随机变量,已知二维随机变量（X,Y）的联合概率密度为

题不难,计算太复杂,给你个思路(1) 1=∫(0,+∞)dx∫(x,+∞)ke^(-y)dy=k(2)P(X+Y<=1)=∫(0,1/2)dx∫(x,1-x)e^(-y)dy(3)fX(x)=∫(x,+∞)e^(-y)dy=e^(-x) (x>0)(4)fY(y)=∫(0,y)e^(-y)dx=ye^(-y) (y>0)f(x|y)=f(x,y)/fY(y)=1/y (0=1/2|X>=1/2)=P(X>=1/2,Y>=1/2)/P(X>=1/2)=∫(1/2,+∞)dx∫(x,+∞)e^(-y)dy/∫(1/2,+∞)e^(-x)dx(7)f(y|x)=f(x,y)/fX(x)=e^(-y)/e^(-x)=e^[-(y-x)] (0=1/2|X=1/2)=∫(1/2,+∞)e^[-(y-1/2)]dy