Question

The coefficient of correlation between $x$ and $y$ is $0.6$, then covariance is $16$. The standard deviation of $x$ is $4$, then the standard deviation of $y$ is

• A. $5$
• B. $10$
• C. $20/3$
• D. None of these

Answer 1

The correct option is C

$20/3$

Explanation for the correct option:

Determine the standard deviation of $y$

The correlation coefficient is $\rho =0.6$.

Covariance is $\mathrm{Cov}(x,y)=16$.

The standard deviation of $x$ is ${\sigma }_x=4$.

Let, the standard deviation of $y$ is ${\sigma }_y$.

We know that the correlation coefficient is given as: $\rho =\frac{\mathrm{Cov}(\mathrm{x},\mathrm{y})}{{\sigma }_x{\sigma }_y}$.

Substitute the known values, we have:

$$\begin{gathered} \Rightarrow 0.6=\frac{16}{4{\sigma }_y} \\ \Rightarrow 0.6{\sigma }_y=4 \\ \Rightarrow {\sigma }_y=\frac{4}{0.6} \\ \Rightarrow {\sigma }_y=\frac{20}{3} \end{gathered}$$

Therefore, the correct answer is Option (C).