已知二维随机变量(X,Y)的联合分布律如图片所示,则X与Y的协方差COV(X,Y)= 设二维随机变量(X，Y)的协方差Cov(X，Y)=1/6 且...
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\u5219 E(X)=-1\u00d70.3+0\u00d70.4+1\u00d70.3=0\uff1bE\uff08Y\uff09=1\u00d70.4+2\u00d70.2+3\u00d70.4=2;
E\uff08XY\uff09=E(X)E(Y)=0;
D(X)=E(X²)-[E(X)]²=[(-1-0)²\u00d70.3+(0-0)²\u00d70.4+(1-0)²\u00d70.3]-0=0.6;
D(Y)=E(Y²)-[E(Y)]²=[(1-2)²\u00d70.4+(2-2)²\u00d70.2+(3-2)²\u00d70.4]-2=-1.2;
E[(X+1)(Y-1)]=E(X+1)\u00d7E(Y-1)=[(-1+1)\u00d70.3+(0+1)\u00d70.4+(1+1)\u00d70.3]\u00d7[(1-1)\u00d70.4+(2-1)\u00d70.2+(3-1)\u00d70.4]=1;
cov(X,Y)=E\uff08XY\uff09- E(X)E\uff08Y\uff09=0; \u03c1xy=cov(X,Y)/[(\u221aD(X))(\u221aD(Y))]=0.
\u03a1xy=cov(x,y)/\u6839\uff08DXDY\uff09=1/6/(3*3/2)=1/6*2/9=2/54=1/27
解：E（Y）=0×（0.3+0.1）+1×（0.2+0.4）=0.6E（X）=2×（0.3+0.2）+3×（0.1+0.4）=2.5
E（XY）=2*0*0.3 + 3*0*0.1 + 2*1*0.2+3*1*0.4=1.6
则cov（X,Y)=E（XY）-E（x）E（Y）=1.6-2.5*0.6=0.1
解：E（Y）=0×（0.3+0.1）+1×（0.2+0.4）=0.6
E（X）=2×（0.3+0.2）+3×（0.1+0.4）=2.5
E（XY）=2*0*0.3 + 3*0*0.1 + 2*1*0.2+3*1*0.4=1.6
则cov（X,Y)=E（XY）-E（x）E（Y）=1.6-2.5*0.6=0.1
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