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 $y$.

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