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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Statistics
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The correlation between $x$ and $a-x$ is

$\begin {array} {1 1} (A)\;-1 & \quad (B)\;1 \\ (C)\;\large\frac{1}{2} & \quad (D)\;0 \end {array}$

 

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1 Answer

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Let $ u = a-x$ and therefore
Var $(u)$ = Var $(a-x)$
$ = (-1)^2$ var $(x)$
= var $ (x) = \sigma^2$
cov $(x, a-x) = $ cov $ (x, u)$
$ = E \{ (x- \overline x )(u-\overline u) \}$
$ E (x-\overline x )^2\: \: \: [ \because u- \overline u = -(x-\overline x ) ]$
= - var $(x)$
$ = -\sigma^2$
Hence $ r(x,u) = \large\frac{cov (x,u)}{\sqrt { var(x)var(u)}}$
$ = \large\frac{-\sigma^2}{\sqrt{\sigma^2, \sigma^2}}$
$ = -1$
Hence Ans : (A)
answered Jan 27, 2014 by thanvigandhi_1
 

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