Correct Answer - Option 1 :
\(\rm \frac{1}{{4}}\)
Concept:
Correlation coefficeient of x and y is given by, \(\rm r = \frac{cov(x, y)}{\sqrt{V(x)\times V(y)}}\)
Where cov(x, y) = covariance between x and y, V(x) = variance of x and V(y) = variance of y
Calculation:
Here, covariance(x, y) = 12, V(x) = 64, V(y) = 36
Correlation coefficeient, \(\rm r = \frac{cov(x, y)}{\sqrt{V(x)\times V(y)}}\)
\(=\rm \frac{12}{\sqrt{64\times36}}\)
\(=\rm \frac{12}{{8\times6}}\)
\(=\rm \frac{1}{{4}}\)
Hence, option (1) is correct.