设随机变量(X,Y)的概率密度为f(x,y)=xe∧-x(1+y),x>0,y>=0.0 其他,求...答:易知z<=0,时P{Z<=z}=0,当z>0时,Fz(z)=∫∫xe^(-x(1+y))dxdy (其中积分区间为xy<=z,x>0,y>0)Fz(z)=∫[0->+∞]dx∫[0->z/x] xe^(-x(1+y))dy =∫[0->+∞]xe^(-x) - xe^(-(z+x)) dx =-xe^(-x) | [0->+∞] - ∫[0->+∞]-e^(-x)dx -...
设随机变量(X,Y)的概率密度为f(x,y)={2-x-y,o<x<1,0<y<1;0,其它,求...答:f(x)=∫(2-x-y)dy=3/2-x,f(y)=∫(2-x-y)dx=3/2-y,E(X)=∫f(x)xdx=5/12 D(X)=∫f(x)x²dx=1/4 E(Y)=∫f(y)ydy=5/12 D(Y)=∫f(y)y²dy=1/4 E(XY)=∫∫f(x,y)xydxdy=1/6 cov(X,Y)=E(XY)-E(X)E(Y)=-1/144 ρ=cov(X,Y)/(√...
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: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 =0,其它 于是P{Y<=X}=∫∫{Y<=X}f(x,y)dxdy=∫(-∞,+∞)dx∫(-∞,x)f(x,y)dy =∫(-∞,0)dx∫(-∞,x)f(x,y)dy+∫[0,+∞)dx∫(-∞,x)f(x,y)dy =∫(0,+∞)dx∫(-∞,x)f(x,...