If X and Y are any random variables with COV(X, Y) = 0.25, $\sigma _ { x } ^ { 2 } = 0.36$ , and $\sigma _ { y } ^ { 2 } = 0.49$ , then the coefficient of correlation $\rho$ is
A)1.417
B)1.190
C)0.595
D)0.354

Question

If X and Y are any random variables with COV(X, Y) = 0.25, $\sigma _ { x } ^ { 2 } = 0.36$  , and $\sigma _ { y } ^ { 2 } = 0.49$ , then the coefficient of correlation $\rho$ is
A)1.417
B)1.190
C)0.595
D)0.354

Quizplus · Accepted Answer

The correlation coefficient $\rho$ is calculated as $\rho = \frac{COV(X, Y)}{\sigma_x \sigma_y}$. Here, $\sigma_x = \sqrt{0.36} = 0.6$ and $\sigma_y = \sqrt{0.49} = 0.7$. Thus, $\rho = \frac{0.25}{0.6 \times 0.7} = 0.595$.

If X and Y Are Any Random Variables with COV(X σx2=0.36\sigma _ { x } ^ { 2 } = 0.36σx2​=0.36

If X and Y Are Any Random Variables with COV(X $\sigma _ { x } ^ { 2 } = 0.36$