Question

If $Cov(X,Y)=6$ and $U=\frac{X-1}{2},V=\frac{Y-2}{3}$ then $cov(U,V)=$

• A. $6$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

$Cov(X,Y)=6$

$X=2U+1,Y=3V+2$

Let $cov(U,V)$ $=x$

$\Rightarrow cov(2U,V)$ $=2x$

$\Rightarrow cov(2U,3V)$ $=6x$

$\Rightarrow cov(2U+1,3V+2)$ $=6x$
$\Rightarrow cov(X,Y)=6x$
$\Rightarrow 6=6x$

$\Rightarrow x=1$
$\Rightarrow cov(X,Y)=1$