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?

• A. \(\frac{{{{\rm{\sigma }}_{\rm{x}}}{{\rm{\sigma }}_{\rm{y}}}}}{{{\rm{\sigma }}_{\rm{x}}^2 + {\rm{\sigma }}_{\rm{y}}^2}}\)
• B. \(\frac{{{{\rm{\sigma }}_{\rm{x}}} + {{\rm{\sigma }}_{\rm{y}}}}}{{2{{\rm{\sigma }}_{\rm{x}}}{{\rm{\sigma }}_{\rm{y}}}}}\)
• C. \(\frac{{{\rm{\sigma }}_{\rm{x}}^2 - {\rm{\sigma }}_{\rm{y}}^2}}{{{\rm{\sigma }}_{\rm{x}}^2 + {\rm{\sigma }}_{\rm{y}}^2}}\)
• D. \(\frac{{{{\rm{\sigma }}_{\rm{y}}} - {{\rm{\sigma }}_{\rm{x}}}}}{{{{\rm{\sigma }}_{\rm{x}}}{{\rm{\sigma }}_{\rm{y}}}}}\)