设二维随机变量(X,Y)的联合概率密度为f(X,Y)={Ae^-(2x+3y)x>0,y>0...答:f(x,y)=Ae^(-2x-3y),x>0,y>0 ∫∫f(x,y)dxdy=1,∫∫f(x,y)dxdy=A∫e^(-2x)dx∫e^(-3y)dy=A*[-2e^(-2x)]|(0,+无穷)*[-3e^(-3y)]|(0,+无穷)=A/6=1 ,可得A=6 f(x)=2e^(-2x),x>0 f(y)=3e^(-3y),y>0 f(x,y)=f(x)*f(y),所以X,Y相互独立...
设二维随机变量(X,Y)的联合概率密度为f(x,y)={①1/8(x+y),0<=x<=2...答:^^设随机变量(X,Y)具有概率密度f(x,y)=1/8(x+y),0<x,y<2,求E(X),cov(X,Y),ρXY f(x)=1/4*(x+1),0<x<2 f(y)=1/4*(y+1),0<y<2 EX=∫zhixf(x)dx=7/6 EY=∫yf(y)dy=7/6 EX^dao2=∫x^2f(x)dx=5/3 EY^2=∫y^2f(y)dy=5/3 DX=EX^2-(EX)^2...