If X and Y are two variables with $\sigma _ { x } ^ { 2 } = 12.25$ , $\sigma _ { y } ^ { 2 } = 17.64$ , and COV(X, Y) = 11.76, then the coefficient of correlation $\rho$ = 0.8.

Question

Quizplus · Accepted Answer

The correlation coefficient $\rho$ is calculated as $\rho = \frac{\text{COV}(X, Y)}{\sigma_x \sigma_y}$. Given $\sigma_x^2 = 12.25$ and $\sigma_y^2 = 17.64$, we find $\sigma_x = 3.5$ and $\sigma_y = 4.2$. Thus, $\rho = \frac{11.76}{3.5 \times 4.2} = 0.8$.

If X and Y Are Two Variables With σx2=12.25\sigma _ { x } ^ { 2 } = 12.25σx2​=12.25

If X and Y Are Two Variables With $\sigma _ { x } ^ { 2 } = 12.25$