设二维随机变是(X，Y)的概率密度为
f(x,y)=
{ye-(x+y),x﹥0,y﹥0
0，其他，
求X与Y的相关系数pXY
E(X)=∫+∞0(∫+∞0xye-(x+y)dy))dx=1 E(Y)=∫+∞0(∫+∞0y2e-(x+y)dy))dx=2 E(XY)=∫+∞0(∫+∞0xy2e-(x+y)dy))dx=2 ∴Cov(X，Y)=E(XY)-E(X)•E(Y)=0 ∴pXY=Cov(X,Y)/[√D(X)•√D(Y)]=0
设二维随机变是(X，Y)的概率密度为
f(x,y)=
{ye-(x+y),x﹥0,y﹥0
0，其他，
求X与Y的相关系数pXY
E(X)=∫+∞0(∫+∞0xye-(x+y)dy))dx=1 E(Y)=∫+∞0(∫+∞0y2e-(x+y)dy))dx=2 E(XY)=∫+∞0(∫+∞0xy2e-(x+y)dy))dx=2 ∴Cov(X，Y)=E(XY)-E(X)•E(Y)=0 ∴pXY=Cov(X,Y)/[√D(X)•√D(Y)]=0
