The coefficient of correlation between $x$ and $y$ is $0.5$ and their covariance is $16$ and SD of $x$ is $4$ then SD of $y$ is

Question

$\begin {array} {1 1} (A)\;4 & \quad (B)\;8 \\ (C)\;16 & \quad (D)\;64 \end {array}$

Answer 1

Given $ r = 0.5$

$cov (x,y)=16$

$ \sigma_x=4$

$ \sigma_y = \large\frac{cov (x,y)}{r\: \sigma_x}$

$ = \large\frac{16}{0.5 \times 4}$

$ = \large\frac{16}{\large\frac{1}{\not{2}} \times \not{4}2} = \large\frac{16}{2}$

$ = 8$

Ans : (B)