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十个馒头 · 2022年07月05日

Covariance -4.8是怎么得出的呢

NO.PZ2015120604000064

问题如下:

According to the above table, what is the correlation of X and Y, given the joint probability table above?

选项:

A.

-0.98.

B.

0.16.

C.

0.98.

解释:

A is correct

Corr(X,Y)=Cov(X,Y)σxσyCorr(X,Y)=\frac { Cov(X,Y) }{ { \sigma }_{ x }{ \sigma }_{ y } } ,

Cov(X,Y)=-4.8, standard deviations of X and Y are 1.90 and 2.58, as calculated before,

thus correlation of X and Y is -0.98

Covariance -4.8是怎么得出的呢

1 个答案
已采纳答案

星星_品职助教 · 2022年07月05日

同学你好,

根据公式,Cov(X,Y)​=E[((X-E(X))(Y-E(Y)))],

根据表格,X一共有三个值。其中X=-2的概率就是当X=-2时的边际概率,0.2+0+0=0.2;同理,X=1的概率为0+0.6+0=0.6,X=4的概率为0+0+0.2=0.2.

求期望就是求(加权)平均的过程,所以E(X)=0.2×(-2)+0.6×1+0.2×4=1,

同理,E(Y)=0.2×5+0.6×2+0.2×(-3)=1.6.

所以Cov(X,Y)​=0.2×(-2-1)×(5-1.6)+0.6×(1-1)×(2-1.6)+0.2×(4-1)×(-3-1.6)=-4.8

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