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If two random variables $x$ and $y$ are connected by the relation $ 2x+y=3$ then $ r_{xy} = $

$\begin {array} {1 1} (A)\;1 & \quad (B)\;-1 \\ (C)\;-2 & \quad (D)\;3 \end {array}$

 

1 Answer

$2x+y=3$
$ \Rightarrow 2\overline x+\overline y=3$
$ 2(x-\overline x)+(y-\overline y)=0$
$y-\overline y=-2(x-\overline x)$
$ \Rightarrow b_{xy} = -\large\frac{1}{2}$
$ \Rightarrow \therefore r=-\sqrt{ b_{yx} \times b_{xy}}$
$ = - \sqrt{(-2)(-\large\frac{1}{2})}$
$ = -1$
Ans : (B)
answered Feb 1, 2014 by thanvigandhi_1
 

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