How do I write the square of covariance?

Question

Should it be $\mathrm{cov}^{2}(X,Y)$ or should it be $\mathrm{cov}(X,Y)^2$ or $(\mathrm{cov}(X,Y))^2$ or something completely different?

Thank you.

Answer 1

First note that $$\mathrm{cov}^2\left(X, Y\right)=\left(\mathrm{cov}\left(X, Y\right)\right)^2$$ Since the exponent is not equal to $-1$ then your okay with writing $$\mathrm{cov}^2\left(X, Y\right)$$ However, if the exponent was $-1$ then I'd recommend the following $$\left(\mathrm{cov}\left(X, Y\right)\right)^{-1}$$ This avoids any ambiguity between the inverse of $\mathrm{cov}$ and the multiplicative inverse of $\mathrm{cov}$.