Question

If the covariance of two variables is equal to the product of the standard deviations of the variables, then the correlation coefficient will be?

Answer 1

"The covariance is equal to the product of the correlation coefficient and standard deviation of each of the two variables. The covariance can be measures as how two random variables vary together.

The covariance is related to the correlation coefficient as follows:

Cov(X1,X2) = std(X1)std(X2) cor(X1,X2)

where, cor(X1,X2) is the correlation between the X1 and X2.

The standard deviation will always positive, the covariance will have the same sign as the correlation coefficient.

If the random variables are positevily correlated , will have positive covariance. Similarly the covariance will be negative if the random variables are negatively correlated."