If two random variables $x$ and $y$ are independent, which of the following statements are true?
I. The correlation between $x$ and $y$ is $0$.
II. The mean of $x + y = $ the mean of $x + $ the mean of $ y$
III. The variance of the distribution of the difference between $x$ and $y$ equals the sum of the individual variances of $x$ and $y$.