# For $a$ bivariate distribution $(x,y)$ if $\Sigma x = 50 \: \Sigma y = 60 \: \Sigma xy = 350 \: \overline x = 5\: \overline y = 6 \: var \: x=4\: var \: y=9\: then \: r(x,y)=$

$\begin {array} {1 1} (A)\;\large\frac{5}{6} & \quad (B)\;\large\frac{5}{36} \\ (C)\;\large\frac{11}{3} & \quad (D)\;\large\frac{11}{18} \end {array}$

$\overline x = \large\frac{ \Sigma x}{n}\: \: \: \: \: \: \: \: \: \: 5=\large\frac{50}{n}$
$n = 10$
$cov (x,y) = \large\frac{1}{n} \Sigma xy - \overline x \overline y$
$= \large\frac{1}{1\not{0}}$ $(35\not0)-(5).(6)$
$= 35-30$
$= 5$
$r= \large\frac{cov(x,y)}{\sigma_x \sigma_y}$
$= \large\frac{5}{2 \times 3}$
$= \large\frac{5}{6}$
Ans : (A)