Let $U$ and $V$ be discrete random variables with $U = −(V+1)/2$. What
is $Corr(U,V)$?
Do I substitute in $u$ as $(-v+1)$ and go from there?
correlationcovarianceprobabilitystatistics
Let $U$ and $V$ be discrete random variables with $U = −(V+1)/2$. What
is $Corr(U,V)$?
Do I substitute in $u$ as $(-v+1)$ and go from there?
Best Answer
Yes.
We have
$$corr(U,V) = \frac{cov(U,V)}{\sqrt{DU \cdot DV}} = \frac{cov(-\frac{V+1}2,V)}{\sqrt{D(\frac{-V-1}{2}) \cdot DV}} = \frac{cov(-\frac{V}2,V)}{\sqrt{D(\frac{-V}{2}) \cdot DV}} = \frac{-\frac12cov(V,V)}{\sqrt{\frac14 DV \cdot DV}} =$$ $$= \frac{-\frac12 DV}{\frac12 DV} = -1.$$