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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 $y$.

A

I only.

B

II only.

C

III only.

D

I and II only.

E

I, II, and III.

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