Covariance between $X$ and $Y$ of a bivariate normal distribution?

Question

$X$ and $Y$ have a bivariate normal distribution with $\sigma_X$= 5 mL, $\sigma_Y$= 2 mL, $\mu_X$= 120 mL, $\mu_Y$= 100 mL, and $\rho$ = 0.6.

How do I find the covariance of $X$ and $Y$? I know the formula is $E(XY)-\mu_X\mu_Y$ but I'm not sure how to use it in this problem.

Answer 1

It looks like you are given the correlation $\rho$ of the two random variables $X$ and $Y$. There is a formula connecting the correlation to the covariance, and it is

$$\rho(X,Y) = \frac{\text{Cov}(X,Y)}{\sigma_X\sigma_Y}.$$

Do you see what to do from here?

Answer 2

I think by $p = 0.6$ you mean $\rho = 0.6,$ which is the correlation. If so, you have only to look at the relationship between covariance and correlation. If not, I wonder what $p$ might be.