Two variates, x and y, are uncorrelated and have standard deviations \sigma_x and \sigma_y respectively. What is the correlation coefficient between x+y and x-y ? [NDA II 2016]

Correct Answer is : σx2−σy2σx2+σy2

{\sigma_{x}\sigma_{y}}/{\sigma_{x}^{2}+\sigma_{y}^{2}}

{\sigma_{{x}}+\sigma_{{y}}}/{2\sigma_{{x}}\sigma_{{y}}}

{\sigma_{x}^{2}-\sigma_{y}^{2}}/{\sigma_{x}^{2}+\sigma_{y}^{2}}

{\sigma_{y}-\sigma_{x}}/{\sigma_{x}\sigma_{y}}

UPSC NDA 2 2016 Mathematics Solved Paper

Question : 115 of 120

Marks: +1, -0

Two variates, x and y, are uncorrelated and have standard deviations σx and σy respectively. What is the correlation coefficient between x+y and x−y ?

[NDA II 2016]

‌‌
σxσy
σx2+σy2
‌‌
σx+σy
2σxσy
‌‌
σx2−σy2
σx2+σy2
‌‌
σy−σx
σxσy

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