Statistics — properties of the bivariate normal distribution

Let $(X,Y)\sim\mathrm{BVN}(\mu_1,\mu_2,\sigma_1^2,\sigma_2^2,\rho)$. If $\sigma_1^2=2$, $\sigma_2^2=3$ and $\rho=0$, then consider the following:

I. $E(X)=E(Y)$

II. $E(XY)=2$

III. $X$ and $Y$ are independent

Which of the above is/are correct?