Question

设随机变量X与Y的相关系数为0.8,若Z=10X-0.6,则,Y与Z的相关系数为?

Answer 1

D(z)=100D(x)

D(x)=D(z)/100

pxy=0.8

cov(x,y)=0.8√D(x)D(y)

cov(y,z)=10cov(y,x)=10cov(x,y)=8√D(x)D(y)=0.8√D(z)D(y)

pyz=cov(y,z)/√D(z)D(y)=0.8

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