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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Statistics
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If $ \sigma_x= \sigma_y$ and $x,y$ are related by $u=x+y\: v=x-y$ then $cov (u,v)$ is

$\begin {array} {1 1} (A)\;-1 & \quad (B)\;0 \\ (C)\;1 & \quad (D)\;cov\: (x,y) \end {array}$


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$ u = x+y$
$ v = x-y$
$ \Rightarrow \overline u = \overline x+\overline y$
$ \overline v=\overline x-\overline y$
$ u - \overline u=(x-\overline x)+(y-\overline y)$
$ v-\overline v=(x-\overline x)-(y-\overline y)$
$ (u-\overline u)(v-\overline v)=(x-\overline x)^2-(y-\overline y)^2$
$ \Rightarrow \large\frac{1}{n} \Sigma ( u-\overline u)(v-\overline v) = \large\frac{1}{n} \Sigma (x-\overline x)^2-\large\frac{1}{x} \Sigma (y-\overline y)^2$
$ = \sigma_x^2-\sigma_y^2=0$
$ \Rightarrow cov (u,v)=0$
Ans : (B)
answered Jan 31, 2014 by thanvigandhi_1

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