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# 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

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

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)