Cov (x,y) > Cov (y,x) can never be True

Hi Abbiais!

Thanks for reaching out!

The statement Cov(x, y) > Cov(y, x) suggests that the covariance between x and y is greater than the covariance between y and x. However, this statement can never be true because the covariance between two variables is symmetric: Cov(x, y)=Cov(y, x). This means that the order of the variables does not affect the covariance value.

Think of the covariance as a measure of how much two variables change together. So, whether you calculate it as Cov(x, y) or Cov(y, x), you're performing the same calculation with the same data pairs. It is commutative.

Hence, it's impossible for Cov(x, y) to be greater than Cov(y, x) because they are equal.

Best,

Ivan