Question

If the correlation coefficient between $x$ and $y$ is $0.6$, covariance is $27$ and variance of $y$ is $25$, then what is the variance of $x$?

• A. $9/5$
• B. $81/25$
• C. $9$
• D. $81$

Answer 1

Answer: (D)

$81$

$Correlationcoefficient=\frac{cov(x,y)}{stddeviation\left(x\right)\times stddeviation\left(y\right)}$

Let std deviation of $x$ be $x$.

We have $correlationcoefficient=0.6,cov(x,y)=27,stddeviation\left(y\right)=\sqrt{25}=5$

Substituting respective values

$0.6=\frac{27}{5\times x}$

$\Rightarrow x=9$

So variance of $x$ is $9^2=81$