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Given A and B are random variables, which of the following statements is true about the random variable A+B?

A

The standard deviation of A+B is always the sum of the standard deviation of A and the standard deviation of B.

B

The variance of A+B is always the sum of the variance of A and the variance of B.

C

The standard deviation of A+B is the sum of the standard deviation of A and the standard deviation of B but only if A and B are independent.

D

The variance of A+B is the sum of the variance of A and the variance of B but only if A and B are independent.

E

The variance of A+B is the square root of the sum of the standard deviation of A and the standard deviation of B, but only if A and B are independent.

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