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,+∞)dx∫(-∞,x)f(x,y)dy =∫(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^(...
设随机变量(X,Y)的联合概率密度分别如下,f(x,y)=ke^-(3x+4y),x,y>0...答:解答如图:∫∫ f(x,y)dxdy=1 所以∫(0,∞)∫(0,∞) k*e^-(3x+4y) dxdy =k*∫(0,∞) dx ∫(0,∞)e^-(3x+4y)dy =k*∫(0,∞) dx (-1/4)*e^(-3x-4y) (0,∞)=k/4*∫(0,∞) e^(-3x) dx =k/4*(-1/3)*e^(-3x) (0,∞)=k/12 所以k=12。E(XY)...
已知随机向量(X,Y)的联合密度函数f(x,y)= ,则E(X)=?答:设D: 0<=x<=2, 0<=y<=1.E(X) = ∫∫( xf(x,y) dxdy (在D上)=∫ dx ∫ x(3xy^2/2) dy =(3/2)∫ dx ∫ (x^2)(y^2) dy 对x的积分限为 (0,2),对y的积分限为 (0,1),=(3/2) ∫x^2 dx ∫ (y^2) dy 对x的积分限为 (0,2),对y的积...