If the standard deviation of X is 15,the covariance of X and Y is 94.5,and the correlation is 0.90,then the variance of Y is 7.0.

Question

Quizplus · Accepted Answer

The variance of Y can be calculated using the formula for correlation: $\rho_{X,Y} = \frac{cov(X,Y)}{\sigma_X \sigma_Y}$, where $\rho_{X,Y}$ is the correlation between X and Y, $cov(X,Y)$ is the covariance of X and Y, $\sigma_X$ is the standard deviation of X, and $\sigma_Y$ is the standard deviation of Y. Rearranging the formula to solve for $\sigma_Y^2$ (the variance of Y) gives us $\sigma_Y^2 = \frac{cov(X,Y)^2}{\rho_{X,Y}^2 \sigma_X^2}$. Plugging in the given values: $\sigma_Y^2 = \frac{94.5^2}{0.90^2 \times 15^2}$, which does not equal 7.

If the Standard Deviation of X Is 15,the Covariance of X