已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(x,y)=1,记U=X-2Y,V=2X-Y已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(X,Y)=1,记U=X-2Y,V=2X-Y,试求Cov(U,V)和ρUV.求过程,谢谢!
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![已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(x,y)=1,记U=X-2Y,V=2X-Y已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(X,Y)=1,记U=X-2Y,V=2X-Y,试求Cov(U,V)和ρUV.求过程,谢谢!](/uploads/image/z/3508923-3-3.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8FX%E5%92%8CY%E7%9A%84%E6%96%B9%E5%B7%AE%E4%B8%BAD%28X%29%3D1%2CD%28Y%29%3D4%2CCov%28x%2Cy%29%3D1%2C%E8%AE%B0U%3DX-2Y%2CV%3D2X-Y%E5%B7%B2%E7%9F%A5%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8FX%E5%92%8CY%E7%9A%84%E6%96%B9%E5%B7%AE%E4%B8%BAD%28X%29%3D1%2CD%28Y%29%3D4%2CCov%28X%2CY%29%3D1%2C%E8%AE%B0U%3DX-2Y%2CV%3D2X-Y%2C%E8%AF%95%E6%B1%82Cov%28U%2CV%29%E5%92%8C%CF%81UV.%E6%B1%82%E8%BF%87%E7%A8%8B%2C%E8%B0%A2%E8%B0%A2%21)
已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(x,y)=1,记U=X-2Y,V=2X-Y已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(X,Y)=1,记U=X-2Y,V=2X-Y,试求Cov(U,V)和ρUV.求过程,谢谢!
已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(x,y)=1,记U=X-2Y,V=2X-Y
已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(X,Y)=1,记U=X-2Y,V=2X-Y,试求Cov(U,V)和ρUV.
求过程,谢谢!
已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(x,y)=1,记U=X-2Y,V=2X-Y已知随机变量X和Y的方差为D(X)=1,D(Y)=4,Cov(X,Y)=1,记U=X-2Y,V=2X-Y,试求Cov(U,V)和ρUV.求过程,谢谢!
D(a)=2²*D(x)+D(y)+2*2*(-1)*cov(x,y)=4D(x)+D(y)-4cov(x,y)=4+4-4=4
D(b)=D(x)+(-2)²*D(y)+2*(-2)*1*cov(x,y)=D(x)+4D(y)-4cov(x,y)=1+16-4=13
cov(a,b)=E(ab)-E(a)*E(b)=E(2*x²-5xy+2y²)-E(2x-y)E(x-2y)
=2E(x²)-5E(xy)+2E(y²)-2(E(x))²+5E(x)E(y)-2(E(y))²
=2( E(x²)-(E(x))² ) + 2( E(y²)-(E(y))² ) - 5( E(xy) - E(x)E(y) )
=2D(x)+2D(y)+5cov(x,y)=2+8-5=5
∴ρ(a,b)=cov(a,b)/√(D(a)D(b))=5/(2*√13)