二维随机向量(X,Y)概率密度函数为 f(x,y)=2e^[-(2x+y)],x>=0,y>=0...答:=∫(0,+∞)[∫(-∞,0)f(x,y)dy+∫[0,x)f(x,y)dy]dx =∫(0,+∞)dx∫[0,x)f(x,y)dy =∫(0,+∞)dx∫[0,x)2e^[-(2x+y)]dy =-∫(0,+∞)2e^[-(2x+y)]|[0,x)dx =∫(0,+∞)[2e^(-2x)-2e^(-3x)]dx =-e^(-2x)|(0,+∞)+(2/3)e^(-3x)|(0,...
...x>0,y>0 =0 其他 求 (1)P(X<=1,Y<=0.5) (2)p(X+Y<=1)答:(2) fz(1)=∫(-∞,∞) f(x,1-x)dx =∫(0,1) 2e^-(2x+1-x)dx =-2e^(-x-1)|(0,1)=2(e^(-1)-e^(-2))(3) x>0 fx(x)=∫(-∞,∞) f(x,y)dy =∫(0,∞) 2e^-(2x+y)dy =-2e^-(2x+y)|(0,∞)=2e^(-2x)其他 fx(x)=0 同理fy(y)=e^-y y>0...